[]AdyashaMohanty and Grace Gao*

]Aeronautics and Astronautics, Stanford University, 496 Lomita Mall, Palo
Alto, 94305, CA, USA

# A Survey of Machine Learning Techniques for Improving Global Navigation
Satellite Systems

<EMAIL_ADDRESS>[

###### Abstract

Global Navigation Satellite Systems (GNSS)-based positioning plays a crucial
role in various applications, including navigation, transportation, logistics,
mapping, and emergency services. Traditional GNSS positioning methods are
model-based and they utilize satellite geometry and the known properties of
satellite signals. However, model-based methods have limitations in
challenging environments and often lack adaptability to uncertain noise
models. This paper highlights recent advances in Machine Learning (ML) and its
potential to address these limitations. It covers a broad range of ML methods,
including supervised learning, unsupervised learning, deep learning, and
hybrid approaches. The survey provides insights into positioning applications
related to GNSS such as signal analysis, anomaly detection, multi-sensor
integration, prediction, and accuracy enhancement using ML. It discusses the
strengths, limitations, and challenges of current ML-based approaches for GNSS
positioning, providing a comprehensive overview of the field.

###### keywords:

GNSS, GPS, Machine Learning, Deep Learning, Survey

##  1 Introduction

Global Navigation Satellite Systems (GNSS)-based positioning underpins
numerous essential applications, enabling efficiency, safety, and reliability
across various industries. It serves a wide range of applications, including
navigation, transportation, logistics, mapping, surveying, and precision
agriculture, among others. Additionally, emergency services rely on GNSS for
search and rescue operations. Maritime navigation, and aviation also heavily
rely on GNSS for positioning information that enhances situational awareness
and reduces response times. Furthermore, GNSS plays a crucial role in
synchronizing critical infrastructure systems such as power grids,
telecommunication networks, and financial transactions [1, 2].

However, GNSS measurements are subject to various sources of error that can
affect positioning accuracy [3, 4, 5]. One source of error is signal
interference that is caused by natural or man-made obstructions, such as tall
buildings or dense foliage, leading to signal blockage, Non-Line-of-Sight
(NLOS) errors, and multipath (MP) effects in urban environments. Another
factor is atmospheric delays caused by the ionosphere and troposphere, which
can influence the speed of the signals and introduce errors in distance
measurements. Additionally, clock inaccuracies in both the satellites and
receivers can contribute to errors in timing and positioning calculations.
Other sources of error include satellite orbit inaccuracies and receiver
noise. Mitigating these error sources is crucial in improving GNSS positioning
performance for various applications.

Traditionally, model-based methods are used for GNSS positioning and error
mitigation/detection because of the following advantages. Model-based methods
incorporate knowledge about signal propagation characteristics in urban
environments via statistical models that capture the characteristics of GNSS
signals in urban environments. These models are based on well-understood
physical principles, which have been refined and validated over decades,
making their behavior predictable in different environments. Model-based
algorithms are also less computationally intensive and do not necessarily need
vast amounts of labeled data for training.

Model-based methods for GNSS positioning include Newton-Raphson [6], Weighted
Least Squares (WLS) [1], and Kalman Filters [7]. While the Newton-Raphson
method enables iterative refinement of the receiver’s position estimate [6,
8], WLS statistically optimizes the solution by assigning weights to each
observation based on the measurement quality [9]. Kalman Filters estimate the
state recursively by combining measurements with known system dynamics [7].
Other techniques include differential positioning which uses measurements from
both the receiver as well as a reference station to correct for common errors
affecting both the reference and receiver, such as atmospheric delays, clock
errors, and orbit inaccuracies [10, 1]. Real-time kinematic (RTK) is a
commonly used differential positioning technique in applications such as
surveying and precision agriculture [11, 12]. It involves the use of a base
station with known coordinates and a rover receiver. The base station provides
correction data to the rover in real-time, allowing for centimeter-level
positioning accuracy. Similarly, another technique, notably, Precise Point
Positioning (PPP) can achieve centimeter-level accuracy without external
reference stations [13]. It utilizes precise satellite orbit and clock
information, along with correction models for atmospheric delays. Differential
positioning techniques, such as RTK and PPP, often rely on the availability of
reference stations or precise orbit and clock data. This dependency can limit
their practicality and flexibility in remote or challenging environments [14].
Some methods like PPP involve computationally intensive operations and require
longer observation times for accurate results. Real-time processing of high-
precision positioning can be challenging, particularly in time-critical
applications.

Traditionally, errors such as NLOS errors are identified and mitigated using
the signal-to-noise ratio (SNR), weighting models, statistical approaches,
and, consistency checking [4, 15]. MP errors are handled by using elevation-
enhanced maps, successive-time double differences [16], and analysis of the
SNR fluctuation [17], among others. Receiver clock errors are typically
mitigated using a clock-steering mechanism [18], differencing between
satellites and estimating the error as an additional unknown parameter in the
position estimation process [19]. Signal propagation errors, such as
ionospheric and tropospheric errors are removed using dual-frequency receivers
[20] and with models such as the Klobuchar [21] and Saastamoinen models [22].
Satellite orbital errors are mitigated using a global or local network of
corrections for the satellite positions or in a post-processed manner [23,
24].

While model-based methods are extensively used for positioning, error
detection, and mitigation, they have certain limitations. Model-based
techniques face challenges due to their strict initial assumptions concerning
sensor noise and model parameters. The conventional model-based methods often
assume noise to be Gaussian (or normally distributed), which simplifies the
mathematics involved in filtering and estimation processes, such as in the
application of Kalman filters for real-time positioning. In real-world
scenarios, the noise affecting GNSS signals can deviate significantly from
Gaussian behavior. Sources such as MP effects, where signals bounce off
surfaces before reaching the receiver, create a complex error structure that
is not well-modeled by a normal distribution. Similarly, atmospheric
disturbances, signal reflection, and interference can introduce noise with
heavy tails or skewed distributions that Gaussian models fail to capture
accurately. Noise characteristics can vary with location, time, and
environmental conditions, introducing further complexity. For instance, urban
environments might experience more significant MP effects due to tall
buildings, while rural areas might have different noise profiles. Temporal
changes, such as atmospheric conditions can also affect noise characteristics
over time. Such assumptions limit the adaptability of model-based techniques,
especially in challenging environments where the noise characteristics, model
parameters, and error models may not adhere to the predefined assumptions [25,
26, 27, 28]. In contrast, ML techniques have emerged as novel approaches in
GNSS-based positioning, addressing the limitations of model-based methods.
These techniques are more suitable for handling nonlinear relationships
between variables, can learn from large amounts of data, and adapt to new and
changing environments. ML algorithms can learn hidden and nonlinear
relationships from data directly without relying on noise assumptions. These
algorithms are also robust to missing data and handle outliers more
effectively than model-based methods [29, 30, 31, 32].

Given the significance of ML techniques in enhancing GNSS positioning and
performance, there is a need to design a comprehensive survey paper to
consolidate and disseminate knowledge in this field. In this regard, Jagiwala
et al. [33] provide an insightful review, emphasizing the role of support
vector machines (SVMs) and convolutional neural networks (CNNs) in enhancing
position accuracy. While a systematic review of machine learning techniques
for GNSS use cases is covered in [34], our survey paper distinguishes itself
by making the following contributions.

  * •

It provides a comprehensive review of a wide range of ML methods applied to
GNSS positioning, including supervised learning, unsupervised learning, deep
learning, and hybrid approaches. This provides a broader perspective on the
subject by showcasing the diverse applications of ML in the field.

  * •

It includes the latest research developments and advancements post-2021 in ML
techniques for GNSS positioning. This equips readers with a current
understanding of recent trends, innovations, and the state-of-the-art in the
domain.

  * •

Beyond the performance evaluation of machine learning techniques, the paper
describes various ML use cases in GNSS. Key topics include using machine
learning for signal analysis, anomaly detection, multi-sensor integration,
prediction, forecasting, and more.

  * •

By evaluating the strengths, challenges, and potential limitations of existing
ML techniques, the paper provides readers with an improved understanding of
the potential and constraints of ML in enhancing GNSS positioning accuracy.

The paper is organized as follows. Section 2 provides a brief background on
the relevance of ML methods to GNSS positioning. Section 3 discusses various
ML methods for the analysis and classification of GNSS signals, including
supervised machine learning techniques such as SVM and decision trees,
unsupervised ML methods, deep learning techniques, and hybrid approaches.
Section 4 focuses on ML techniques for environmental context and scenario
recognition using GNSS measurements, while Section 5 explores ML techniques
for anomaly detection and quality assessment. Section 6 covers ML methods for
GNSS-based multi-sensor integration, and Section 7 discusses prediction and
forecasting techniques leveraging GNSS measurements and AI. In Section 8,
techniques for enhancing positioning accuracy and position error modeling are
discussed. Section 9 highlights other notable applications of using ML for
improving GNSS. Section 10 addresses the limitations and challenges associated
with the discussed ML methods. Finally, Section 11 identifies potential areas
for future research and development in the field of AI-based GNSS positioning.

##  2 Background of ML Methods

###  2.1 Regression methods

Regression methods predict continuous numerical values by mapping input
features to a target variable using a mathematical model with adjustable
parameters. The model is trained by minimizing the difference between
predicted and actual values. We discuss commonly used regression techniques
below.

  * •

Quantile Regression, an extension of traditional regression analysis [35],
estimates different quantiles of the target variable’s conditional
distribution. Unlike ordinary least squares regression, which focuses on the
conditional mean, Quantile Regression provides a comprehensive understanding
of the conditional distribution by considering multiple quantiles. It achieves
this by minimizing a loss function that measures the discrepancy between
predicted and actual quantiles. This optimization process determines the
optimal parameters governing the relationship between input features and the
target variable’s quantiles.

  * •

SVMs are used for both classification and regression tasks [36]. They identify
optimal hyperplanes to separate classes and handle nonlinear data through the
kernel trick. Support Vector Regression (SVR), a variation of SVM, fits data
by allowing a margin for error and utilizes kernel functions to capture linear
and nonlinear relationships [37]. An example SVM is shown in Figure 1. Support
vectors, identified during training, play a vital role in generalization and
prediction. SVR estimates numerical values for new data points by applying
learned parameters and support vectors.

Figure 1: Illustration of SVM from [38]. SVM is a supervised learning
algorithm that finds the hyperplane that best separates different classes with
the maximum margin. It uses support vectors and kernels to optimize the
separation boundary in both linear and non-linear classification tasks.

###  2.2 Unsupervised learning methods

Unsupervised learning involves training models on unlabeled data without
explicit guidance or predefined labels. Instead of predicting specific
outcomes, unsupervised learning algorithms focus on discovering hidden
patterns, structures, or relationships within the data. The primary categories
of unsupervised learning methods include the following.

  * •

K-means algorithm is a widely used method for clustering, which partitions a
dataset into k distinct, non-overlapping subsets or clusters [39]. The
algorithm assigns each data point to the cluster with the nearest mean,
serving as a prototype of the cluster. This process iteratively adjusts the
positions of the centroids (the means of the clusters) and reassigns the data
points to their closest centroids until the positions of the centroids
stabilize, indicating that the clusters are as compact and distinct from each
other as possible.

  * •

Autoencoders are neural networks that are commonly used for dimensionality
reduction [40]. As illustrated in Figure 2, they consist of an encoder network
that maps the input data to a lower-dimensional representation, and a decoder
network that reconstructs the original input from this representation.
Autoencoders learn a compressed and efficient representation of the input
data, capturing essential features.

Figure 2: Illustration of an autoencoder from [41]. Autoencoder compresses the
inputs into a latent-space representation and then reconstructs the output
from this representation, aiming to match the original input.

  * •

Variational autoencoders (VAE) learn a lower-dimensional latent space
representation of input data, capturing its underlying structure and
distribution [42]. VAEs consist of an encoder network and a decoder network.
The encoder maps input data to a latent space, typically represented by the
mean and the variance of a Gaussian distribution. The decoder reconstructs
input data from latent space samples. Training VAEs involves optimizing two
objectives: reconstruction loss and the Kullback-Leibler (KL) divergence
regularization term. The reconstructed output resembles the original input,
while the regularization term encourages a structured latent space. VAEs can
generate new samples resembling training data and compress data by encoding
and decoding it from the latent space.

###  2.3 Classification methods

AI algorithms for classification utilize machine learning techniques to
automatically assign data instances into predefined categories or classes
based on their features or attributes. These algorithms learn from labeled
training data to build models that can accurately classify new, unseen data.
Two common classification approaches are Decision Trees and Naive Bayes.

  * •

Decision Trees: As illustrated in Figure 3, decision tree is a flowchart-like
structure where each internal node represents a decision based on a feature,
each branch represents an outcome or decision rule, and each leaf node
represents a class label or a final decision [43]. The tree is constructed by
recursively splitting the data based on the values of input features until a
stopping criterion is met, such as maximum depth.

Figure 3: An example illustrating how decision trees are used in
classification tasks [44]. Decision Trees make decisions by recursively
partitioning the data set into smaller subsets based on the most
discriminative features. The goal is to create branches that lead to
homogenous leaves, where each leaf node corresponds to the most probable
target outcome.

  * •

Naive Bayes is a classification algorithm based on Bayes’ theorem, assuming
conditional independence of features given the class label [45]. It estimates
the likelihood of each feature value for each class in the training dataset.
For categorical features, it calculates the probability of occurrence in each
class, while for numerical features, it assumes a probability distribution and
estimates parameters for each class. By considering prior probabilities and
using Bayes’ theorem, it calculates posterior probabilities for unlabeled
instances. The class label with the highest posterior probability is assigned
as the predicted class.

  * •

The k-nearest neighbors (KNN) algorithm is a non-parametric classification
algorithm based on the principle that similar data points are close to each
other in the feature space [46]. As illustrated in Figure 4, when a new,
unseen instance needs to be classified, the KNN algorithm evaluates the
distances between this instance and all other instances in the dataset,
identifying the $k$ nearest neighbors. The algorithm then assigns the most
frequent label of these nearest neighbors to the new instance.

Figure 4: An example illustrating how KNNs are used in classification tasks
[47]. KNN is a non-parametric learning algorithm that classifies new cases
based on the majority vote of the $k$ most similar instances from the training
data, often using distance metrics like Euclidean distance to determine
similarity.

###  2.4 Reinforcement Learning

Reinforcement Learning (RL) enables an agent to learn and make decisions in an
environment through interactions and feedback [48]. The agent takes action,
receives rewards or punishments, and updates its decision-making strategy
accordingly, as shown in Figure 5. The RL algorithm’s objective is to develop
an optimal policy that maximizes cumulative rewards over time. Key components
of RL include the agent, environment, state, action, and reward. The agent
interacts with the environment by selecting actions based on its current
state. The environment provides feedback through rewards or penalties. The
agent’s decision-making strategy is determined by its policy. The feedback
received after taking an action is known as the reward. RL algorithms can be
categorized as model-free or model-based. Model-free algorithms directly learn
the optimal policy without explicitly modeling the environment, while model-
based algorithms learn environment dynamics to plan and make decisions.
Notable RL algorithms include Q-Learning, Deep Q-Networks (DQN), Proximal
Policy Optimization (PPO), and Advantage Actor-Critic (A2C) [49, 50].

Figure 5:  Reinforcement Learning (RL) involves agents learning to make
decisions by taking actions in an environment to maximize cumulative reward.
Through trial and error, the agent refines its policy to achieve optimal
outcomes. Figure adapted from [51].

###  2.5 Deep Neural networks

Deep Neural Networks (DNNs) refer to neural networks with multiple hidden
layers between the input and output layers. These hidden layers enable the
network to learn hierarchical representations of the input data, allowing for
more complex and abstract feature extraction. Various categories of DNNs
include the following:

Figure 6: Illustration of the Transformer architecture from [52]. While this
architecture has revolutionized language models, it has been used recently to
capture temporal and spatial dependencies in GNSS measurements and improve
positioning accuracy.

  * •

Convolution Neural Networks (CNNs) are widely used in computer vision tasks.
They are designed to automatically learn and extract meaningful features from
images or other grid-like data through the use of convolutional layers.
Convolutional layers apply filters to input data, enabling the network to
capture local patterns and spatial dependencies. The pooling layers then
downsample the feature maps, reducing their spatial dimensions while retaining
important information. Finally, fully connected layers at the end of the
network perform classification or regression based on the learned features.
CNNs have demonstrated remarkable success in tasks such as image
classification, object detection, and image segmentation due to their ability
to capture and exploit local patterns and hierarchical representations in
visual data.

Figure 7: An example RNN architecture from [53]. RNN is a class of neural
networks where connections between nodes form a directed graph along a
temporal sequence, allowing it to use its internal state or memory to process
a sequence of inputs. RNNs process sequential data by maintaining a hidden
state that captures information from previous inputs in the sequence. This
state is updated at each time step as the network processes the next input,
making RNNs ideal for time-series prediction

  * •

Recurrent Neural Networks (RNNs) [54] are designed to process sequential or
time-dependent data. RNNs have feedback connections, allowing information to
be fed back into the network at each time step as illustrated in Figure 7.
This recurrent nature enables RNNs to maintain an internal state and capture
temporal dependencies. Long Short-Term Memory (LSTM) [55] is an RNN
architecture specifically designed to model sequential data. Unlike standard
feedforward neural networks, which process inputs independently, LSTMs have
memory cells that can retain information over time. This memory mechanism
makes LSTMs effective in capturing temporal dependencies and long-term
patterns in sequential data.

  * •

Multilayer Perceptron (MLP) [56] consists of an input layer, one or more
hidden layers, and an output layer. Each neuron in the MLP is connected to
neurons in adjacent layers, and these connections have associated weights.
MLPs use activation functions to introduce non-linearity into the model,
enabling the network to learn complex relationships between the input features
and the target variable.

  * •

Radial Basis Function Neural Network (RBFNN) [57] is a type of neural network
that uses radial basis functions as activation functions in its hidden layers.
The radial basis functions compute the similarity between the input data and a
set of learned prototypes or centers.

  * •

Transformer-based deep learning models, as introduced by Vaswani et al. [52]
and shown in Figure 6 use self-attention to capture dependencies among all
elements in a sequence concurrently. Through the attention mechanism, these
models calculate the significance weights for each element, allowing for
effective modeling of relationships between words or tokens. Transformers
comprise an encoder and decoder, both consisting of self-attention layers and
feed-forward neural networks. The self-attention mechanism employs query, key,
and value vectors to compute attention weights and produces outputs that
prioritize crucial elements in the sequence.

  * •

Graph Neural Networks (GNNs) are a class of deep learning models specifically
designed for processing data represented as graphs or networks [58, 59]. They
have gained significant attention in recent years for their effectiveness in
various applications, including social network analysis, recommendation
systems, and biological network analysis. GNNs handle irregular, graph-
structured data by aggregating information from neighboring nodes, enabling
them to capture complex relationships and dependencies within the data. An
example GNN is illustrated in Figure 8.

Figure 8: Graph Neural Networks (GNNs) process data on graphs by aggregating
information from neighboring nodes. Through iterative updates, they capture
complex patterns and relationships inherent in graph structures. An example
graph structure (GraphSAGE) is shown here [60].

###  2.6 Ensemble methods

Ensemble methods combine the predictions of multiple individual models to
improve overall predictive accuracy and robustness. By aggregating the
predictions of diverse models, ensemble models can capture different aspects
of the data and reduce individual model biases. The key categories of ensemble
models include the following.

  * •

Random Forest combines multiple decision trees to make predictions [61] as
shown in Figure 9. Each decision tree in the forest is trained on a different
subset of the data, and the final prediction is obtained by aggregating the
predictions of all trees.

Figure 9:  Random Forest is an ensemble learning method that constructs
multiple decision trees during training and outputs the mode of the classes
for classification tasks or mean prediction for regression tasks. It
introduces randomness by selecting different subsets of features for each
tree, improving the model’s accuracy and reducing overfitting. Figure adapted
from [62].

  * •

Gradient Boosting Decision Tree (GBDT) builds trees in a sequential manner,
where each new tree is trained to correct the mistakes made by the previous
trees [63].

  * •

LightGBM uses a tree-based learning algorithm similar to GBDT but incorporates
several optimizations to speed up training and improve memory efficiency [64].
LightGBM supports both classification and regression tasks and has gained
popularity for its fast training speed and high performance.

  * •

Extreme Gradient Boosting (XGBoost) is another gradient-boosting framework
that incorporates additional enhancements, such as regularization techniques,
to improve model performance [65]. XGBoost is known for its flexibility,
speed, and its ability to handle various data types.

##  3 GNSS Signal Analysis and Classification

In urban environments, GNSS positioning is primarily challenged by MP errors
from signal reflections, NLOS errors, and signal blockage due to tall
structures. These error sources are depicted in Figure 10. Previous ML
techniques have attempted to detect NLOS signals and MP errors as well as
classify signals into direct, NLOS, blocked, and MP. Several comparative
studies have analyzed the efficacy of different ML techniques for these tasks
and these studies are explained below.

Figure 10: The main error sources in GNSS positioning in urban environments
include Non-line-of-sight (NLOS) errors, blocked signals, and MP from
reflected signals. By using ML techniques that can classify the signals into
these categories, we can improve the accuracy and reliability of positioning.
Figure adapted from [66].

NLOS Detection: In [67], various ML algorithms, including Logistic Regression,
SVM, Naïve Bayes, and Decision Tree, were used to detect NLOS signals.
Decision Tree and logistic regression models outperformed the other models,
achieving an average NLOS prediction correctness rate of 90 %. [68]
demonstrated integrated GNSS shadow matching combined with an intelligent
LOS/NLOS classifier based on ML algorithms. Various ML methods were evaluated,
achieving classification accuracies between 69.50 % and 86.47 % for different
urban scenarios. Integrating shadow matching with the ML classifier improved
positioning accuracy when compared to traditional weighted least squares
methods. For GNSS signal classification and weighting scheme design in built-
up areas, [69] proposed an ML-based strategy. The study identified Random
forest as the highest-performing classifier for LOS/NLOS classification,
achieving a classification accuracy of 93.4 %.

Time Series Modeling and Prediction: In [70], ML models, namely GBDT, LSTM,
and SVM, were used for the modeling and prediction of GNSS time series. These
ML techniques significantly outperformed traditional methods, enhancing the
fitting precision by over 30 %.

MP Detection: [71] introduced an ML approach in the context of GPS MP
detection leveraging dual antennas. The model, developed using GPS
measurements and various algorithms like GBDT, random forest, decision tree,
and KNN, achieved classification accuracies between 82 % to 96 % for test data
from identical training locations. However, the accuracy decreased to 44 %-77
% when testing on different locations, with the random forest showing the best
classification performance.

Monitoring GNSS Satellite Signals for Anomalies: In [72], anomalies were
detected in GPS satellite signals using data from globally distributed
stations to differentiate between intended and unintended anomalies.
Validations involved datasets with known anomalies, testing both supervised
and unsupervised algorithms.

We now discuss works that apply either a single technique or combine several
ML techniques for enhancing GNSS-based positioning performance.

###  3.1 Supervised ML

####  3.1.1 SVM

Table 1 lists the studies that use SVMs for classification tasks.

Table 1: GNSS Signal Classification Methods Using SVMs Paper | Task | Accuracy
---|---|---
Hsu et al. [73] | Categorizing pseudorange measurements | 75%
Ozeki et al. [74] | NLOS signal detection |  $>$80%
Lee et al. [75] | MP prediction model | 58.4% horizontal
Suzuki et al. [76] | NLOS MP detection | 97.7%
Xu et al. [77] | GNSS shadow matching in urban environments | 91.5%

Classifier Design: In the paper by Hsu et al. [73], a classifier is proposed,
trained with SVMs, to categorize GNSS pseudorange measurements into clean, MP,
and NLOS categories. Using features extracted from GNSS raw data, the
classifier achieves an approximate classification accuracy of 75%. In [78],
SVMs are proposed for correlator-level GPS LOS/MP/NLOS signal reception
classification, aiming to enhance positioning performance in urban
environments. Traditional LOS/MP/NLOS classifiers rely on attributes extracted
from basic measurements such as received signal strength and satellite
elevation angle. However, their accuracy is limited in urban settings due to
complex signal propagation. By extracting LOS/MP/NLOS features at the baseband
signal processing stage, the proposed approach achieves improved
classification rates, providing valuable insights for enhancing GPS
positioning in challenging urban scenarios.

MP Prediction: In Lee et al. [75], a MP prediction model based on SVR is
designed to improve GNSS performance in deep urban zones. The model factors in
the elevation and azimuth angle of each satellite to generate a nonlinear MP
map, marking significant improvements of 58.4% horizontally and 77.7%
vertically in positioning accuracy within a deep urban region in Seoul, Korea.

NLOS Detection: Suzuki et al. [76] introduced a method to detect NLOS MP by
using two supervised learning techniques, SVM and NN. The evaluation shows
that NN surpasses SVM and achieves a discrimination accuracy of 97.7% for NLOS
signals. [79] designed an incremental learning method using an adaptive RBF
SVM to detect NLOS signals. The proposed method considers the diversity and
complexity of practical factors and shows enhanced performance in harsh canyon
cities. Xu et al. [77] performed a study on improving the accuracy of GNSS
shadow matching in urban environments. They combined a robust estimator with
an SVM-based LOS/NLOS classifier. The SVM classifier achieves a classification
rate of 91.5% in urban scenarios. Ozeki et al. [74] proposed a method for NLOS
signal detection using an SVM classifier trained with unique features derived
from receiver-independent exchange format-based information and GNSS
pseudorange residual check. By combining the SVM classifier and pseudorange
residual check, they achieved more than an 80% improvement in positioning
errors within 10 meters in static tests conducted in dense urban areas.

Assessing the Effectiveness of GNSS Features for Signal Classification: The
research in [80] is centered around evaluating the efficacy of different GNSS
observation features for signal classification using SVMs. The primary metric
for evaluation is classification accuracy, and the study is based on an open-
source dataset gathered from Hong Kong’s urban road segments. Similarly, [81]
performed another study on the efficacy of various features. The authors
empirically show the importance of different features in LOS/NLOS signal
classification tasks, especially in urban canyon environments.

The literature highlights the success of SVMs in categorizing GNSS pseudorange
measurements into clean, MP, and NLOS categories, showcasing their accuracy in
signal classification. SVMs have proven to enhance GPS signal reception and
processing, particularly in software-defined receivers, outperforming
traditional classifiers. They have been successfully utilized for NLOS signal
detection and improving positioning accuracy in dense urban areas. By
combining SVM classifiers with other techniques, such as pseudorange residual
checks and shadow-matching algorithms, significant improvements in positioning
accuracy have been demonstrated.

####  3.1.2 Decision Trees

Table 2 lists studies that have utilized decision trees for the classification
of GNSS signals.

Table 2: GNSS Signal Classification Methods Using Decision Trees and GBDT Paper | Task | Accuracy
---|---|---
Guermah et al. [82] | Fusion of left and right antennas | 99%
Sun et al. [83] | GPS signal reception classification | 100% LOS, 82% MP, 86% NLOS
Ye et al. [84] | RTK positioning | 95.64% NLOS detection
Pan et al. [85] | MP mitigation | 24.9 %- 36.2 % residual reduction

Classifier Design: In the study conducted by Guermah et al. [82], a signal
classifier system is proposed to fuse information from the left and right-
polarized antennas using Decision Trees. The classifier achieves an accuracy
of 99 % by utilizing satellite elevation and C/N0 ratio as features,
outperforming techniques such as KNN and SVM. Another variant of decision
trees, namely the GBDT, is used in Sun et al.’s research [83] for GPS signal
reception classification in urban areas, using features such as carrier-to-
noise ratio (C/N0), pseudorange residuals, and satellite elevation angle. The
GBDT algorithm achieves classification accuracies of 100 % for LOS signals, 82
% for MP signals, and 86 % for NLOS signals, surpassing other algorithms such
as decision trees, KNNs, and adaptive network-based fuzzy inference systems.

RTK Positioning: Furthermore, Ye et al. [84] designed a robust real-time
kinematic (RTK) positioning method that incorporates a decision tree for NLOS
signal detection and real-time estimation of double-differenced MP errors.
Their method shows remarkable results, achieving an NLOS detection rate of
95.64 % and enhancing the ambiguity fixing rate by 43 % in the instantaneous
mode. This leads to an approximately 81.77 % improvement in 3D position
accuracy compared to standard RTK methods.

MP Mitigation: In [85], the authors proposed a machine learning-based method
for mitigating MP in high-precision GNSS data processing. They used XGBoost
and formulated MP modeling as a regression task. The XGB-based MP model
outperformed conventional methods, achieving substantial residual reduction
rates ranging from 24.9 % to 36.2 % for various GPS observations. After
implementing the XGB-based MP corrections, significant improvements in
kinematic positioning precision were observed.

Existing literature shows that decision tree-based classifiers can achieve
high accuracy rates and provide robust NLOS signal detection, leading to
improved positioning performance. However, these classifiers have limitations
that should be considered. They are sensitive to feature selection and
engineering, requiring careful consideration for optimal performance.
Overfitting is a concern, necessitating regularization techniques and model
validation. Additionally, decision trees may exhibit instability and lack
robustness in the presence of data variations, requiring further exploration
of ensemble methods and hybrid approaches.

###  3.2 Unsupervised ML

The literature on utilizing unsupervised learning techniques to enhance GNSS-
based positioning is sparse and limited, however, we discuss a few notable
works.

Classifier Design:[86] used an unsupervised ML approach for the classification
of NavIC signals affected by MP interference. By leveraging unsupervised
learning algorithms, the proposed method classified signals based on unlabeled
data, addressing the limitations of supervised learning algorithms that
require labeled data. The approach demonstrated promise in detecting and
removing MP-affected signals, thereby contributing to more robust positioning
applications.

MP Detection: In the study by [87], a MP detection method based on K-means
clustering was proposed. The authors applied the K-means algorithm to identify
MP signals and evaluated the algorithm’s performance in a MP-prone
environment. The results indicated that the proposed method exhibited
potential for MP detection in GNSS receivers. Similarly, in [88], an
unsupervised machine-learning approach for GNSS MP detection was introduced.
The method utilizes a CNN within an autoencoder framework combined with
k-means clustering. Compared to baseline approaches, the proposed method
improved MP detection accuracy and achieved a prediction accuracy of up to 99
% using unsupervised domain adaptation.

While supervised learning algorithms, such as SVMs and Decision Trees, have
been extensively explored and proven effective in GPS signal classification
and positioning accuracy improvement, the application of unsupervised learning
methods in this domain remains relatively unexplored. Unsupervised learning
algorithms, such as clustering or dimensionality reduction techniques, have
the potential to discover hidden patterns and structures in GNSS data without
the need for labeled training data. By leveraging unsupervised learning, it
may be possible to uncover valuable insights and improve positioning
performance in novel ways.

###  3.3 Deep Learning

Deep learning approaches are popular for GNSS signal analysis and
classification since they can learn directly from raw GNSS signal data,
eliminating the need for handcrafted feature engineering. This capability is
advantageous in GNSS signal analysis, where the underlying patterns and
characteristics may be challenging to define explicitly. Table 3 provides an
overview of commonly used deep learning approaches for GNSS signal analysis
and classification.

Table 3: Deep Learning Approaches for GNSS MP Mitigation Study |  Method/Approach |  Application/Result
---|---|---
Suzuki et al. [76] |  SVM and NN-based method for detecting NLOS MP in GNSS. |  NN achieved 97.7 % discrimination accuracy for NLOS signals, outperforming SVM.
Maaref et al. [89] |  DNN-based framework for MP mitigation in GNSS pure L5 receivers. |  Significant improvement in positioning accuracy and reduction of pseudorange error standard deviation in heavy MP signal environments.
Orabi et al. [90] |  NN-based DLL for GPS code phase estimation in high MP environments. |  Outperformed conventional techniques in terms of code phase root mean squared error.
Kim et al. [91] |  Wavelet transform and NN-based method for GNSS signal quality monitoring and MP detection. |  High accuracy in signal quality monitoring and MP detection using real GNSS data.
Li et al. [92] |  DNN-based correlation schemes for mitigating MP propagation in GNSS. |  Enhanced performance compared to standard correlation schemes in LOS scenarios.
Klimenko et al. [93] |  Neural network-based MP estimation algorithm for GNSS receivers. |  Promising results in compensating for MP errors in GNSS receivers, demonstrating advantages over existing parametric algorithms.

MP Detection: In [76], the authors proposed a method for detecting NLOS MP
using two supervised learning methods, SVM and DNN. The evaluation shows that
the NN outperforms SVM, achieving a 97.7 % discrimination accuracy for NLOS
signals. In [89], an ML-based framework is developed for mitigating MP in a
GNSS pure L5 receiver. They quantified the performance of a pure L5 receiver
in static and dynamic heavy MP signal environments and proposed a DNN-based
methodology to leverage ML for MP mitigation. The proposed framework
significantly improves positioning accuracy and reduces the standard deviation
of the pseudorange error. [90] developed a neural network (NN)-based delay-
locked loop (DLL) for GPS code phase estimation in MP environments. The
proposed NN-based DLL outperforms conventional techniques, including early-
minus-late DLL, narrow correlator, and high-resolution correlator, in terms of
code phase root mean squared error in high MP environments. In the paper by
[91], a combination of wavelet transform and neural network is proposed for
GNSS signal quality monitoring and MP detection. Signal features, including
signal strength and spectral characteristics, are extracted using wavelet
transform, while a trained neural network performs classification and MP
detection. The proposed method is evaluated using real GNSS data and achieves
high accuracy in both signal quality monitoring and MP detection tasks. In a
study by [92], DNN-based correlation schemes are investigated to mitigate the
effects of MP propagation in GNSS. These DNN-based schemes exhibit superior
performance compared to standard correlation schemes, particularly in line-of-
sight (LOS) scenarios. In [69], the authors also demonstrate that DNN-based
correlation schemes outperform standard correlation schemes in line-of-sight
scenarios by filtering out more noise and effectively distinguishing MP
signals from line-of-sight signals. The proposed DNN-trained models exhibit
enhanced performance in time-delay tracking across various realistic
scenarios. Another research by [93] presents a neural network-based MP
estimation algorithm for GNSS receivers. The algorithm leverages a 5-point
complex correlator implemented in a high-precision GNSS ASIC to mitigate MP
errors. Evaluation against existing parametric algorithms demonstrates the
algorithm’s advantages in accurate MP estimation.

The studies demonstrate that DNN-based methods outperform traditional
approaches, such as SVM and conventional correlators, in discriminating NLOS
signals and mitigating MP effects. Additionally, the integration of wavelet
transform with neural networks shows promise for signal quality monitoring and
MP detection.

####  3.3.1 CNN

Several studies have explored the application of CNNs, as illustrated in
Figure 11, for addressing MP and NLOS reception issues and improving
positioning accuracy in urban environments. Table 4 provides an overview of
these studies.

Figure 11:  Convolutional Neural Networks (CNNs) use layered filters to
automatically and adaptively learn spatial hierarchies of features from input
images. Through pooling and convolution operations, they efficiently recognize
and classify visual patterns. Figure adapted from [94].

MP Detection: [95] proposed a CNN for mitigating MP in an L5 receiver in urban
environments. Experimental results show that the proposed framework
significantly improves horizontal positioning accuracy and reduces pseudorange
errors. Correlator level measurements are used in [96] along with CNNs for MP
detection in GNSS receivers. The correlator output signal is mapped as a 2D
input image, and a CNN is trained to automatically extract relevant features
and achieve MP detection. In [97], the correlation outputs of GNSS signals are
mapped into 2D grayscale images, which are fed into a CNN for automatic
feature extraction and MP pattern detection. The proposed CNN-based algorithm
demonstrates superior performance over the benchmark SVM technique, achieving
prediction accuracy of over 93 % even under poor receiving conditions. The
proposed CNN-based algorithm demonstrates superior performance over the
benchmark SVM technique, achieving prediction accuracy of over 93 % even under
poor receiving conditions. CNNs are used for MP detection in both static and
kinematic settings in [98]. The proposed method leverages the ability of CNNs
to learn and identify the features of MP characteristics from MP-contaminated
GPS data. The results demonstrate that the CNN-based method can detect
approximately 80 % of MP errors, leading to improved positioning accuracy when
down-weighting the detected MP measurements. [99] developed a CNN-based
approach to detect GNSS MP using only correlator outputs. The CNN was trained
on images representing correlator output values as a function of delay and
time. The proposed model achieved F scores of 94.7 % for Galileo E1-B and 91.6
% for GPS L1 C/A, demonstrating its effectiveness in MP detection. In [100], a
CNN-based approach for GNSS positioning is proposed to mitigate MP NLOS
reception issues. It introduces a new input feature called single-differenced
residual map, which effectively mitigates MP/NLOS. The network extracts
features from residual maps and generates heat maps to indicate the user’s
location. PositionNet significantly improves positioning accuracy in dense
urban areas, achieving 5-meter-level accuracy for 84 % of the epochs. In [101]
a novel NLOS MP detection technique is presented using CNNs to improve
positioning accuracy in urban environments. The CNN-based NLOS discriminator
achieved approximately 98 % correct discrimination of NLOS MP signals,
outperforming a simple neural network. By applying the NLOS probability output
of the CNN to positioning calculations, the proposed method improved
positioning accuracy from 34.1 to 1.6 meters.

Signal Classification: [102] proposed a robust deep-learning-based technique
for detecting and classifying disruptive GNSS signals, including jammers,
spoofing, and MP signals. The approach utilized transfer learning with pre-
trained CNNs such as AlexNet, GoogleNet, ResNet-18, VGG-16, and MobileNet-V2.
The MobileNet-V2 model achieved an accuracy of 99.8 % in classifying different
types of disruptive signals. In [103], a CNN is proposed that utilizes
correlator-level measurements. They employ vector tracking to generate
correlator-level measurements and the CNN automatically extracts features and
identifies the signal reception type. The proposed CNN outperforms other
methods such as KNN and SVMs in terms of classification accuracy. In [76], the
authors use GNSS signal correlation output as input for supervised learning
methods, specifically SVMs and DNNs, to classify NLOS signals. The evaluation
shows that the DNN outperforms SVM, achieving 97.7 % correct discrimination of
NLOS signals. For smartphone-based positioning, [104] designed a method to
detect and correct NLOS signals utilizing a CNN that achieves enhanced
positioning accuracy in urban environments.

Table 4: CNN Methods for GNSS MP Mitigation and Signal Analysis Study |  Approach |  Result
---|---|---
Munin et al. [95] |  CNN-based framework for mitigating MP in a pure L5 GNSS receiver |  Significant improvement in horizontal positioning accuracy
Elango et al. [102] |  Transfer learning with pre-trained CNN models for detecting and classifying disruptive GNSS signals. |  99.8 % accuracy in classifying disruptive signals
Jiang et al. [103] |  CNN-based method for signal classification using correlator-level measurements. |  CNN outperformed KNN and SVM in terms of classification accuracy.
Liu et al. [104] |  CNN-based method for NLOS signal detection and correction in smartphone-based positioning. |  Enhanced positioning accuracy and stability in urban environments.
Li et al. [69] |  DNN-based correlation for mitigating MP propagation. |  Improved performance in time-delay tracking and MP signal classification
Blais et al. [97] |  CNN-based method for MP prediction using correlation outputs of GNSS signals. |  Superior performance over SVM in MP prediction even under poor receiving conditions.
Guillard et al. [99] |  CNN-based approach using correlator outputs for GNSS MP detection. |  High accuracy in classifying signals as line-of-sight (LOS) or MP, outperforming traditional ML classification models.
Quan et al. [98] |  CNN-based method for MP detection in static and kinematic GNSS settings. |  80 % detection of MP errors
Suzuki et al. [76] |  NN-based method for detecting NLOS MP in GNSS signals. |  NN achieved 97.7 % correct discrimination of NLOS signals, outperforming SVM.
Liu et al. [104] |  CNN-based approach using single-differenced residual map |  5 m accuracy for 84 % epochs.

Based on the discussed papers, several key insights emerge regarding the
effectiveness of CNNs in GNSS signal analysis and classification. Firstly,
CNNs show promise in mitigating MP effects, resulting in notable enhancements
in horizontal positioning accuracy and reduced pseudorange errors. Secondly,
CNNs exhibit strong capabilities in detecting and classifying MP signals,
achieving high accuracy rates. Thirdly, CNN-based regression models outperform
traditional methods in GNSS MP estimation, enabling uncertainty modeling and
maintaining estimation performance even with lower input image resolution.
Fourthly, CNNs excel in signal classification tasks utilizing correlator-level
measurements, surpassing alternative approaches. Lastly, CNNs contribute
significantly to NLOS signal detection and correction, leading to improved
positioning accuracy and stability in urban environments.

####  3.3.2 RNN

We summarize key papers in Table 5 that utilize RNNs for GNSS signal analysis
and classification.

Table 5: GNSS NLOS/LOS Classification Methods Using RNN Paper | Classification Task | Accuracy
---|---|---
Su et al.[105] | NLOS/LOS classification | 91%
Cho et al.[106] | NLOS/LOS classification in urban environments | 90%
Lyu et al.[107] | LOS/NLOS signal classification | 95.97%
Liu et al.[108] | Context classification | 99.41%

NLOS classifier: In [105], the authors proposed an NLOS/LOS classification
model based on RNNs to classify satellite signals received in urban canyon
environments. The model achieves an accuracy of 91 % in classification and
demonstrates improved three-dimensional positioning accuracy and stability in
the BDS/GPS fusion system. The proposed method outperforms traditional ML
classification models like SVMs. [106] proposed an RNN-based NLOS classifier
that discriminates between LOS and NLOS satellites in urban environments. The
classifier achieved about 90 % accuracy in NLOS classification and showed a 20
% improvement in discrimination performance compared to the conventional SVM-
based NLOS classifier. The proposed technique was also applied to pedestrian
road crossing detection and demonstrated a positioning accuracy of about 45 %
better than that of conventional techniques. [107] proposed a hybrid RNN and
fully connected network approach to distinguish between LOS and NLOS signals
in GNSS positioning. The method considered inter-epoch information and time
series data features to enhance classification accuracy. The proposed
classifier achieved an overall testing accuracy improvement from 93.00 % to
95.97 % for Rinex-level observations.

Context Recognition: A Gated Recurrent Unit (GRU) for real-time processing is
proposed in [108] to categorize fine-grained contexts based on the
characteristics of different environments and their corresponding integrated
navigation method. The proposed method enhances context recognition using a
new feature called the C/N0-weighted azimuth distribution factor and achieves
a recognition accuracy of 99.41 % on a real-world urban driving dataset. Xia
et al. [109] proposed a scenario recognition method based on RNN and LSTM
models, utilizing smartphone GNSS measurements. Their analysis focuses on the
impact of multi-constellation satellite signals on scenario recognition
performance. The results indicate that the accuracy of scenario recognition
improves with an increased number of constellations received by smartphones.
The proposed algorithm achieves an impressive recognition accuracy of 98.65 %
and effectively handles scenario transitions with a maximum delay of only 3
seconds.

The papers discussed highlight the effectiveness of RNNs for NLOS/LOS
classification and GNSS positioning in urban environments. These RNN-based
models achieve high classification accuracy, leading to improved positioning
accuracy compared to models like SVMs which do not consider inter-epoch
information and time series data features.

###  3.4 Hybrid Approach

In [77], robust estimation and ML techniques are combined for LOS/NLOS
classification and improving shadow matching in urban GNSS positioning. The
proposed approach utilizes a robust estimator for initial positioning and an
SVM for satellite visibility classification. The classification rate of the
SVM reaches 91.5 % in urban scenarios, contributing to improved shadow-
matching accuracy.

Hybrid methods have also been recently proposed in other domains, for example,
in the context of Kalman filtering and particle filtering which could be
directly applied to improving GNSS positioning accuracy. KalmanNet [110]
introduces a novel approach to real-time state estimation for dynamical
systems with non-linear dynamics or partial information, merging the classic
Kalman filter’s structure with a recurrent neural network to learn from data.
This hybrid model enhances the traditional filter’s capabilities, allowing it
to adapt to complex dynamics and outperform conventional filtering methods,
regardless of the accuracy of the domain knowledge. In [111], the authors
introduce an unsupervised learning adaptation for KalmanNet, a deep neural
network system inspired by the Kalman filter, eliminating the need for ground-
truth states by using its hybrid architecture to predict observations and
compute loss. It demonstrates that unsupervised KalmanNet can match the
performance of its supervised counterpart and adapt to changing state space
models without new data, showcasing flexibility and efficiency in dynamic
environments. Similarly, in [112], a novel approach called DANSE is introduced
for non-linear state estimation, offering a model-free method to compute the
posterior state in a Bayesian framework with linear measurements. By employing
recurrent neural networks to capture non-linear dynamics and utilizing a
combination of maximum likelihood and gradient descent for unsupervised
training, DANSE operates effectively without process model knowledge. Its
performance is demonstrated to be competitive with both classic model-based
estimators.

The authors in [113] introduced a particle filter RNN (PF-RNN) architecture
that combines an advanced RNN architecture with uncertainty modeling by
maintaining a distribution of latent states represented as particles. This
approach contrasts with traditional RNNs’ single deterministic latent vector.
PF-RNNs leverage a differentiable particle filter mechanism for updating the
latent state distribution in line with Bayes’ rule, enhancing the model’s
adaptability to variable and multi-modal data. In [114], a particle filter
network is designed that integrates a system model and particle filter
algorithm into a unified, fully differentiable neural network. Although it has
been only applied to visual localization tasks, it has demonstrated superior
performance and generalization over traditional and alternative learning-based
approaches, adapting effectively to various and unseen sensor inputs. Hybrid
particle filters were also explored in [115] wherein neural networks were
integrated with particle filters for scalable real-world applications,
focusing on the challenge of optimizing dynamic and measurement models without
access to expensive or unavailable true states. By utilizing a differentiable
implementation of particle filters and an end-to-end learning objective based
on maximizing a pseudo-likelihood function, the approach improves state
estimation accuracy even when true states are largely unknown. The
effectiveness of this method is evaluated through state estimation tasks in
robotics, using both simulated and real-world datasets.

SVMDecision TreesUnsupervised LearningDeep
LearningCNNRNNHybrid$0$$2$$4$$6$$8$$10$$12$Number of Papers Figure 12:
Distribution of Papers on ML Methods for GNSS Signal Analysis and
Classification

###  3.5 Other approaches

In [116], a novel approach is proposed for predicting and eliminating MP
errors, particularly in urban areas with complex signal reflections. The
proposed method utilizes a graph transformer neural network (GTNN) to
effectively learn environment representations from irregular GNSS
measurements. Experimental results on real-world GNSS data show that the GTNN
achieves over 96 % accuracy in satellite visibility prediction and outperforms
existing MP prediction methods in terms of generalization performance. In
[117], a novel method using Neural City Maps, built on Neural Radiance Fields,
is proposed to represent urban geometry more accurately. The study evaluates
different prediction methods for NLOS effects using Neural City Maps and
demonstrates their effectiveness in improving localization accuracy in
challenging urban environments.

##  4 Environmental Context and Scenario Recognition

We discuss ML approaches that are used for scenario recognition and
environmental context detection.

Supervised machine learning is used in the study by Baldini et al. [118] to
train a classifier for propagation scenario identification. The researchers
extracted various features from GNSS pseudorange measurements and demonstrated
the classifier’s accurate identification of propagation scenarios affected by
MP. The adoption of an overlapping window approach further enhances
identification accuracy. In the work by İşik et al. [119], a machine learning-
based performance prediction algorithm for GNSS in urban air mobility
applications is presented. The algorithm considers environmental parameters
and evaluates the prediction performance of three algorithms: KNN, SVR, and
Random Forest. The researchers analyze the performance prediction results and
the importance of parameters across different urban environments using
synthetic data generated by a GNSS simulator.

[120] explores the utilization of GNSS signals alongside ML algorithms to
characterize the operational environment for Unmanned Aerial Vehicles and
Unmanned Ground Vehicles by extracting features relevant to situational
awareness in urban and harsh conditions. It presents case studies
demonstrating how digital signal processing techniques combined with
unsupervised and supervised ML algorithms (like K-means and SVMs) can analyze
GNSS observables to identify propagation scenarios affected by MP,
interference, and atmospheric conditions. The study in [121] focuses on
enhancing GNSS accuracy for train localization by identifying environmental
characteristics across scenarios like tunnels, open areas, and urban canyons.
Utilizing NMEA-0183 protocol data from GNSS receivers, such as PRN codes,
azimuth, elevation, and SNR, the research creates heatmap states of these
scenarios through satellite observations, interpolation, and position
transformation. By training a Vision Transformer model on these heatmap
datasets, the study successfully recognizes varying environmental scenarios,
achieving an overall model accuracy of 88.7 % on the validation set.

In [122], the authors propose to improve high-precision GNSS positioning for
intelligent transportation systems through a context-aware model, addressing
the challenges posed by complex environmental contexts and feature
variability. The study evaluates eight models, including various neural
networks and SVM, for their ability to recognize context. The LSTM model
outperforms others, achieving high accuracy and mean average precision in
distinct and continuous context areas. The study in [123] introduces a novel
signal-based environment recognition algorithm designed for vehicular
positioning in urban settings, capable of distinguishing between six distinct
environmental conditions. By constructing a signal feature vector that
encapsulates signal attenuation, blockage, and MP effects, the algorithm
leverages the SVM for scene classification. To improve accuracy, a temporal
filtering technique is integrated, allowing the model to adapt and function in
real-time for the receiver. Demonstrating the algorithm’s broad applicability,
datasets for both training and testing were gathered from various cities,
achieving an overall recognition accuracy of 89.3 % across diverse
environments. In [124], the authors improve scenario recognition for mobile
applications by classifying environments into four categories and using a
Hidden Markov Model and an RNN. The RNN method effectively handles scenario
transitions and environmental changes, achieving an overall accuracy of 98.65
% and a transition recognition accuracy of 90.94 %, with minimal transition
delay. [125] introduces a deep-learning method for scenario recognition using
smartphone GNSS measurements, categorizing environments into four types: deep
indoors, shallow indoors, semi-outdoors, and open outdoors. Leveraging Voronoi
tessellations for spatial structuring and employing CNNs and ConvLSTM networks
for feature extraction and sequence processing, the technique achieves
accuracies of 98.82 % with CNNs and 99.92 % with ConvLSTMs. This approach,
relying solely on GNSS measurements without additional sensors, demonstrates
both efficiency and suitability for real-time applications, with minimal
computational latency.

##  5 Anomaly Detection and Quality Assessment

The characterization and assessment of signal quality in multi-GNSS systems
are crucial for enhancing the performance of GNSS-based positioning. In [126],
the focus is on evaluating measurement signal quality and developing an ML-
based MP detection model for multiple GNSS systems, including GPS, GLONASS,
Galileo, BDS, and QZSS. The proposed model achieves high accuracy rates using
simulated and real GNSS data. Additionally, [127] combined clustering-based
anomaly detection with supervised classification to improve positioning
accuracy significantly in different directions. These studies highlight the
use of ML-based approaches for evaluating signal quality, detecting anomalies,
and enhancing GNSS positioning performance.

M. Kiani introduces a machine learning algorithm tailored for GNSS position
time series prediction, demonstrating superior accuracy in outlier and anomaly
detection as well as earthquake prediction capabilities by analyzing over
three thousand GNSS station time series globally [128]. This method
outperforms seventeen other algorithms and offers practical applications in
detecting time series outliers and earthquake forecasting, exemplified by the
Tohoku 2011 case study. In [129], the authors explore enhancing GNSS signal
anomaly detection for navigation systems using time-delayed neural networks
(TDNN), proposing a TDNN-based integrity monitoring system that significantly
outperforms standard receiver autonomous integrity monitoring (RAIM) methods
in speed and reliability. An innovative approach for automatic anomaly
detection is proposed in [130] for monitoring GNSS reference stations. The
authors use predictive modeling and statistical rules to identify anomalous
signals, demonstrating the method’s effectiveness on historical data. ML
algorithms such as random forest [131] and SVMs [132] are used to detect GPS
and Galileo satellite oscillator anomalies, respectively, with high accuracy,
outperforming other algorithms and demonstrating global applicability for
satellite anomaly monitoring.

Unsupervised ML methods are used for autonomous GNSS data anomaly detection in
[133], focusing on volcanic activity monitoring. Unsupervised methods are also
used for spatial outlier detection in GNSS velocity fields using a robust
Mahalanobis-distance-based classification method [134]. Their approach,
validated on synthetic and real datasets, yields high classification accuracy,
enhancing GNSS data reliability without requiring pre-defined labels.

##  6 GNSS Integration with Other Sensors

The integration of ML methods in GNSS-based positioning systems, particularly
in combination with other sensors like inertial measurement units (IMUs), has
opened up new possibilities for improving accuracy and addressing challenges
in various environmental contexts. We discuss some notable works below.

NLOS Detection:  In their paper, Wang et al. [135] introduced a method that
utilizes the K-means clustering algorithm to detect MP and NLOS signals in
urban areas for GNSS/INS integrated positioning. The method incorporates
various feature parameters derived from GNSS raw observations and demonstrates
significant improvements in positioning accuracy. The offline dataset exhibits
a remarkable improvement of 16 % and 85 % in the horizontal and vertical
directions, respectively, while the online dataset showcases improvements of
21 % and 41 % in these two directions. Smolyakov et al.

MP Prediction: [136] proposed a two-part architecture for GNSS MP prediction
and detection in IMU/GNSS integration for urban navigation. It employs signal
quality monitoring techniques to identify and exclude MP-contaminated GNSS
signals. The architecture dynamically adjusts the integration Kalman filter
based on a crowdsourced GNSS MP environment map, which is extended to
unsurveyed areas using a random forest ML model. Evaluation in an automotive
scenario shows a significant accuracy improvement compared to a conventional
Kalman filter (13-17 %).

Positioning Improvement: Han [137] proposed a reinforcement learning-based
approach to optimize the process noise covariance matrix of a GNSS/IMU
integration Kalman filter. Experimental results show improved navigation
performance by effectively utilizing the learned process noise covariance
matrix. Additionally, Shin et al. [138] designed an Actor-Critic (A2C)
Reinforcement Learning algorithm that achieves higher scores compared to the
baseline. Gao et al. [139] presented the RL-AKF (adaptive Kalman filter)
navigation algorithm, which adaptively estimates the process noise covariance
matrix using a reinforcement learning approach. The RL-AKF demonstrates an
average positioning error of 0.6517 m within a 10 s GNSS outage for the
GNSS/INS integrated navigation system. For the GNSS/INS/Odometer (ODO) and
GNSS/INS/Non-Holonomic Constraint (NHC) integrated navigation systems, the RL-
AKF achieves positioning errors of 14.9426 m and 15.3380 m, respectively,
within a 300 s GNSS outage. In their study, Li et al. [140] enhanced the
GNSS/INS integration methodology for vehicle navigation by using the LightGBM
regression model. This model predicts vehicle position changes during GNSS
outages based on INS data. The proposed methodology demonstrates reduced
errors in predicting vehicle positions during GNSS outages compared to the
existing methodology based on Random Forest. The integration of artificial
intelligence improves the accuracy of GNSS/INS integrated navigation systems
in situations where GNSS signals are unavailable or during GNSS outages. Chiou
et al. [141] developed an ML model to enhance the utilization of GNSS
positions in a loosely coupled GNSS/IMU system. The proposed model combines
rule-based methods with machine learning techniques to classify the quality of
GNSS position outputs. The results show that the model achieves a true
positive rate of 90 % in identifying bad GNSS position outputs. In [142], the
authors integrated GNSS and INS sensors using deep learning techniques. They
combine DNN, LSTM, and CNN to optimize Kalman filter gain and improve
navigation accuracy for land vehicles.

The papers in this section present valuable contributions to the field of GNSS
integration with other sensors for navigation in urban environments. These
contributions include the application of ML techniques, such as clustering
algorithms and reinforcement learning, to enhance positioning accuracy. The
development of dynamic sensor integration models based on environmental maps
and MP detection techniques offers improved performance.

##  7 Prediction and Forecasting

In the domains of geodesy and GNSS analysis, ML methods have proven to be
instrumental in prediction and forecasting tasks.

Time Series Prediction: In their study, Shahvandi et al. [143] used deep
transformers to predict time series in the field of geodesy. They make
modifications to the original network architecture and optimization procedure,
resulting in a remarkable improvement of 21.5 % in prediction accuracy
compared to traditional statistical methods. Furthermore, their approach
outperforms other machine learning algorithms by at least 2.7 %. The method
exhibits the potential to achieve millimeter accuracy in time series
prediction. Loli Piccolomini [144] introduced a network architecture based on
LSTMs for denoising and prediction tasks in GNSS time series analysis. Despite
being a shallow network, it reduces scattering from real GNSS time series,
removing nearly 50 % of the noise. Additionally, the architecture achieves
coordinate prediction with a mean squared error of 1.1 millimeters. The
approach is evaluated using both synthetic and real GNSS time series data. In
their research, Ji et al. [145] presented a weighted wavelet analysis-based
signal extraction method for GNSS position time series. This method
successfully extracts signals from daily position time series data by
considering noise characteristics and variations in signal strength. The
application of weighted wavelet analysis enhances the accuracy of signal
extraction, particularly in the presence of noise and disturbances.

Satellite Visibility Prediction: Zhang et al. [146] proposed a deep learning
network architecture that combines fully connected neural networks (FCNNs) and
LSTM networks to predict GNSS satellite visibility and pseudorange error based
on GNSS measurement-level data. The proposed networks achieve an accuracy of
80.1 % in satellite visibility prediction and an average difference of 4.9
meters in pseudorange error prediction. The LSTM layer effectively captures
representations of the environment, leading to improved prediction
performance.

##  8 Position Error Modeling/Accuracy Enhancement

A significant body of work focuses on utilizing ML techniques to model GNSS
errors in the position domain and enhance positioning accuracy directly. These
works form the majority of research efforts in this field and are summarized
in Table 6 and Table 7. Figure 13 shows the distribution of different ML
methods that have been used to improve GNSS positioning accuracy. These
various approaches highlight the effectiveness of ML techniques in enhancing
GNSS positioning accuracy and addressing specific challenges in different
domains and environments.

SVMDecision TreesRNN or LSTMOther Deep LearningOther
MLHybrid$0$$2$$4$$6$Number of Papers Figure 13: Distribution of Papers that
use ML methods for Position Error Modeling and Accuracy Enhancement

Improving PPP and RTK: Qafisheh et al. [147] utilized SVMs to reduce latency
in real-time Precise Point Positioning (PPP), leading to improved clock
corrections. Menzori and Teunissen [148] adopt Decision Trees for classifying
PPP/GNSS coordinates based on precision. Additionally, Yun et al. [149]
proposed leveraging dual-frequency GNSS measurements, and Mendonca et al.
[150] introduced a Genetic Algorithm (GA)-based machine learning classifier to
improve RTK positioning. Lacambre et al. [151] designed machine learning and
outlier detection methods to optimize RTK positioning, achieving a substantial
boost in real-world positioning performance.

Improving Accuracy in MP Environments: Ziedan et al. [152] proposed two novel
ML-based algorithms that make use of maps and neural networks to accurately
estimate positions in MP environments. The paper by [153] introduced a Random
Forest-based technique to rectify errors in differential corrections for
Cooperative Differential GNSS in urban landscapes. This approach aims to
predict and amend biases stemming from positioning errors of cooperative
vehicles, enhancing overall accuracy. Urban road tests demonstrate a reduction
in RMSE from 1.557 to 1.279 m using reference stations. Sun et al. [154]
addressed the challenges of achieving accurate positioning in urban terrains.
They introduced a GBDT-based method that predicts pseudorange errors and
corrects positioning inaccuracies caused by MP and NLOS signals, achieving a
marked 70 % improvement in 3D positioning accuracy compared to traditional
methodologies.

Table 6: ML Methods for Improving GNSS Positioning Accuracy Study |  Method/Approach |  Application/Result
---|---|---
Qafisheh et al. [147] |  SVM-based solution for latency reduction in PPP |  Reduced standard deviation and range of clock corrections by approximately 30 % and 20 %, respectively
Ziedan et al. [152] |  ML-based algorithms improve position estimation accuracy in MP environments. |  Accuracy enhancements of up to 96 % compared to traditional methods
Mendonca et al. [155] |  ML algorithms (decision tree, neural network, etc.) to enhance integrity measurements in GNSS positioning. |  Neural network model increased information metric by 20-fold compared to EKF.
Menzori and Teunissen [148] |  Decision Tree classification of the accuracy of PPP/GNSS coordinates |  Prediction of accuracy from the precision with a large dataset of known coordinates.
Kim et al. [156] |  Multilayer RNN with LSTM algorithm |  Improved position accuracy by 40 % compared to GNSS-only navigation.
Yang et al. [157] |  Real-time LSTM RNN for predicting GPS positioning errors |  Prediction accuracy within 1-3 % of ground truth values.
Gupta et al. [158] |  Hybrid learning-based approach combining traditional positioning models with DNNs |  Low positioning errors with reduced memory requirements.
Kanhere et al. [159] |  DNN-based corrections using set transformer |  Improved accuracy over WLS
Dai et al. [160] |  Global optimization method incorporating various constraints for smartphone positioning |  Second place in Google Smartphone Decimeter Challenge 2022.
Liu et al. [161] |  LSTM-based prediction method |  Improved prediction accuracy by 16 % .
Thomas et al. [162] |  ML-based post-processing techniques for low-cost GPS receivers |  Improved position accuracy
Zhou et al. [163] |  LSSVM-KF algorithm for by estimating dynamic modeling bias. |  Reliable and accurate GNSS navigation solutions
Gao et al. [164] |  Decision tree model for estimating vehicle positioning accuracy |  Achieved probability of accurate positioning estimation of more than 95 %
Wei et al. [165] |  GRNN-based satellite selection algorithm for optimizing visible satellites |  Improved robustness, accuracy, and real-time performance

Improving Accuracy for Smartphone Positioning: Google has also shown active
involvement in refining urban GNSS accuracy, focusing on mitigating
inaccuracies experienced by Android devices in dense urban settings, a vital
endeavor for widely-used location apps [166]. Hybrid methods that combine
traditional models with deep neural networks are introduced by Gupta et al.
[158] and Kanhere et al. [159] with the aim to enhance data efficiency and
positional accuracy for smartphones. Additionally, Dai et al. [160] presented
a global optimization strategy for smartphone GNSS positioning. Lastly, in
[167], [168], and [169], the authors proposed advanced GNSS solutions using
Graph Convolution Neural Networks and a combination of RL and GNN,
demonstrating significant improvements in smartphone positioning accuracy in
various environments.

Table 7: ML Methods for Improving GNSS Positioning Accuracy (Continued) Study |  Method/Approach |  Application/Result
---|---|---
Ragheb et al. [170] |  SlipNet LSTM neural network model for cycle slip detection. |  High-performance results with 99.7 % detection and localization accuracy
Neri et al. [171] |  ML architecture for local hazard detection and RAIM in the rail domain. |  Optimizing ML architecture for enhancing the accuracy and reliability of train positioning systems.
He et al. [172] |  LSTM neural network model for BDS-3 satellite clock bias prediction. |  Outperformed traditional models for long-term satellite clock bias prediction.
Yun et al. [149] |  Practical approach using dual-frequency GNSS measurements to improve smartphone position accuracy. |  Overcoming limitations of smartphones and leveraging dual-frequency measurements for quality monitoring.
Mendonca et al. [150] |  Genetic Algorithm-based machine learning classifier for validating ambiguity terms in RTK positioning. |  Improved classification performance compared to traditional ratio test.
Lacambre et al. [151] |  Methodology incorporating ML methods for optimizing and qualifying new RTK GNSS algorithms. |  Improved real-world positioning performance through outlier detection and reference comparison.
Sun et al. [154] |  GBDT-based approach for correcting GPS positioning errors caused by MP and NLOS signals. |  Significant improvement in 3D positioning accuracy compared to conventional methods.
Mohanty et al. [167, 168] |  Graph Convolution Network and Kalman Filter. |  Improved accuracy compared to model-based and learning-based methods.
Zhao et al. [169] |  Graph Neural Network combined with Reinforcement Learning. |  26 % improvement in urban datasets; 10 % improvement in semi-urban.

Recurrent Neural Networks: Kim et al. [156] used LSTM-based recurrent neural
networks to enhance accuracy and stability in autonomous vehicle navigation.
Yang et al. [157] furthered this effort by developing an LSTM RNN model
tailored for real-time prediction of GPS positioning errors. Other works, such
as those by Thomas et al. [162] and Zhou et al. [163], explored ML-based post-
processing techniques for improving position accuracy in autonomous vehicle
applications and GNSS navigation integrated with Kalman filtering,
respectively. Liu et al. [161] used LSTM-based prediction to enhance the
accuracy of GPS in vehicular navigation.

Other Methods and Applications: The research by Neri et al. [171] is tailored
specifically for the rail domain. They aim to enhance the accuracy and
reliability of train positioning systems by combining classical observables
with advanced RAIM techniques. A unique approach is introduced in [173] to
enhance high-precision GNSS positioning in dynamic urban terrains using a deep
reinforcement learning framework. Random Forest was explored in [174] along
with conformal prediction to learn positioning errors and integrity intervals
with $99.999\%$ confidence.

##  9 Other Use Cases

In various GNSS applications, different ML methods have been employed to go
beyond improving the receiver’s positioning performance. While these
applications are not the main focus of our survey paper, we provide a concise
overview of some existing works.

GNSS Augmentation Systems and Carrier Phase Measurements: The authors in [175]
presented an anomaly detection algorithm tailored for carrier phase
measurements in GNSS augmentation systems. Targeting safety-critical
applications like autonomous vehicles, their machine learning-based approach
estimates standard deviations of residual errors. This enables continuous
fault monitoring even with single-frequency measurements, and the real-world
tests validate the method’s efficiency.

Direction-of-Arrival (DOA) Estimation: In [176], a novel method for DOA
estimation is introduced. Unlike conventional neural network-based approaches,
this method addresses real-world array imperfections. A Transformer-based
calibration network (TCN) models these imperfections at the antenna level,
utilizing global and long-term properties of array errors. Experiments
indicate superiority over traditional techniques, especially under amplitude
and phase deviations and antenna position perturbations.

Velocity and Acceleration Measurements: The study in [177] analyzed the
performance of a stand-alone GNSS receiver after incorporating sparse kernel
learning. This AI-based solution improves accuracy in measuring velocity and
acceleration, paving the way for applications in vehicle dynamics analysis and
geodetic monitoring.

Ionospheric Prediction and Total Electron Content (TEC) Variations: The work
in [178] presented a real-time ionosphere prediction model using LSTM,
utilizing International GNSS Service products to estimate and correct
ionospheric delays. In [179], LSTM and Transformer networks are used to
predict TEC variations, showing performance enhancements over traditional
methods. Additionally, a spatiotemporal Graph Neural Network, coupled with
transformers, is utilized in [180] for predicting VTEC maps. Graph nodes in
this approach symbolize pixels holding VTEC values, while edges are determined
by inter-node distances. Another deep learning-based system in [181] is used
to forecast TEC maps for South America’s ionosphere. Finally, the global TEC
map prediction framework in [182] compared LSTM and Transformer networks,
illustrating the superiority of the suggested networks over IGS rapid
products.

Earthquake Detection and Environmental Characterization: The research in [183]
used supervised machine learning for analyzing GNSS velocities tied to
earthquake-strong motion signals. The models, trained on datasets of strong
motion events, offer increased accuracy in seismic activity detection. On a
related note, [184] used ML to exploit GNSS signals for environmental
characterization. Through this approach, they extract significant
environmental data, facilitating applications in climate studies, precision
agriculture, and environmental monitoring.

GNSS Functional Safety and Satellite Orbit Predictions: Ensuring GNSS
functional safety is at the forefront of [185]. By leveraging machine
learning, this research addressed potential safety hazards in GNSS systems.
Orbit prediction for Low Earth Orbit satellites, as explored in [186] combined
analytical models with ML techniques to predict orbits, respectively. Another
model, presented in [187], employed a transformer deep learning framework for
satellite orbit correction prediction, outclassing existing prediction
methods.

Satellite Selection, Interference Detection, and Data Fusion: The deep
learning network in [188] performed optimal satellite selection in GNSS
positioning. By intelligently accounting for factors like signal quality,
satellite geometry, and user demands, this model promises enhanced positioning
accuracy. Works like [189] and [190] used ML for GNSS interference detection
and classification. Finally, [191] and [192] used ML techniques for innovative
GNSS science applications, unlocking potential in atmospheric sensing and
climate studies.

Spoofing Detection and Signal Security: Several contributions target GNSS
spoofing detection. Research like [193], [194], [195], and [196] employed
diverse machine learning techniques ranging from tree-based models to deep
learning for effective spoofing detection. While [197] and [198] focused on
jamming detection and measurement association in spoofing environments, [199]
used supervised ML for detecting GNSS signal spoofing, further showcasing the
significance of MLin ensuring GNSS signal integrity and security.

##  10 Limitations of Discussed Methods and Potential Solutions

Although the methods discussed for enhancing GNSS positioning through ML
demonstrate promising results, it is essential to consider their limitations.
Additionally, we provide potential solutions to directly address these
limitations which include the following:

  1. 1.

Data Dependency: Many of the ML-based methods rely heavily on the availability
of large and diverse datasets for training. While data-driven approaches have
demonstrated success in improving GNSS positioning, gathering and maintaining
such datasets can be challenging. Insufficient or biased training data may
limit the generalizability and effectiveness of the ML models. Furthermore,
collecting data for specific environments or rare scenarios may be time-
consuming and resource-intensive. Adequate data collection efforts and quality
control measures are necessary to ensure the reliability of ML models.

  2. 2.

Computational Requirements: ML models, especially deep learning models, often
require significant computational resources for training. Training deep
learning models on large datasets can be computationally intensive and time-
consuming. Deploying these models in resource-constrained environments, such
as embedded systems or low-power devices, may pose challenges. Developing
lightweight ML models or exploring alternative architectures that strike a
balance between computational efficiency and accuracy is essential for
practical deployment.

  3. 3.

Generalizability to Unseen Scenarios: While ML models trained on extensive
datasets can exhibit impressive performance in controlled test environments,
their generalizability to unseen or evolving scenarios remains a concern.
Changes in satellite constellations, emerging technologies, or novel
interference sources may require model retraining or adaptation. Ensuring the
long-term effectiveness and adaptability of these models in dynamic GNSS
environments requires continuous monitoring, updating, and reevaluation of the
models.

  4. 4.

Dependency on GNSS Signal Availability: ML models designed to improve GNSS
positioning heavily rely on the availability of GNSS signals. However, there
are instances when GNSS signals may be temporarily unavailable or degraded due
to signal blockage, jamming, or interference. In such cases, the performance
of ML models that rely solely on GNSS inputs may be limited. Developing hybrid
positioning approaches that combine GNSS with other sensors, such as inertial
sensors or environmental context data, can help mitigate this limitation and
provide robust positioning solutions.

  5. 5.

Lack of Standardization: The field of ML for improving GNSS positioning is
still evolving, and there is a lack of standardized methodologies, evaluation
metrics, and benchmark datasets. The absence of standards makes it challenging
to compare and replicate results across different studies. Developing
standardized evaluation frameworks, sharing benchmark datasets, and promoting
reproducibility are essential for advancing the field and enabling meaningful
comparisons between different AI-based methods.

  6. 6.

Integration Complexity: Integrating ML-based algorithms into existing GNSS
positioning systems can be complex and may require modifications to the system
architecture or hardware. Compatibility issues, system interoperability, and
deployment challenges need to be addressed to ensure seamless integration and
practical implementation of ML techniques. Collaborative efforts among ML
researchers, GNSS experts, and industry stakeholders are necessary to overcome
integration barriers and facilitate the adoption of ML in real-world GNSS
positioning applications.

  7. 7.

Cost and Scalability: The implementation of ML-based methods for improving
GNSS positioning may involve initial investment costs, including
infrastructure, computational resources, and expertise. The scalability of ML
models to handle large-scale positioning systems and accommodate increasing
data volumes may also pose challenges. Ensuring cost-effective solutions and
scalability is crucial for the practical adoption of ML techniques in GNSS
positioning. Exploring cloud-based solutions, distributed computing, or edge
computing approaches can help address scalability concerns and optimize
resource utilization.

##  11 Promising Opportunities

Several promising opportunities arise for the application of ML techniques to
enhance GNSS positioning systems. We discuss some key opportunities below.

  1. 1.

Integration with Other Sensor Modalities: ML techniques offer opportunities
for seamless integration of GNSS data with other sensor modalities, such as
IMUs, odometers, or digital maps. By leveraging the complementary information
from different sensor modalities, ML-based integration methods can overcome
limitations associated with individual sensors and provide more reliable and
accurate positioning solutions. GNNs can also be employed to integrate GNSS
measurements with data from other sensors, such as LiDAR or camera sensors. By
representing the sensor data as a graph structure and leveraging GNNs, the
models can capture the complex relationships and dependencies between
different sensor modalities. This integration allows for more comprehensive
and accurate positioning solutions, especially in scenarios where GNSS signals
may be affected by obstructions or limitations.

  2. 2.

Adaptive Algorithms for Dynamic Environments: ML algorithms can adapt and
learn from dynamic environments, allowing for real-time adjustments in GNSS
positioning. These algorithms can continuously analyze and update models based
on changing environmental conditions, satellite availability, or user
dynamics. By considering factors such as satellite constellation health,
signal quality, and user motion patterns, ML-based algorithms can dynamically
optimize positioning solutions to provide accurate and reliable results.

  3. 3.

Crowd-Sourced Positioning: ML techniques can harness the power of crowd-
sourced data to enhance GNSS positioning accuracy. By collecting positioning
data from a large number of users and applying machine learning algorithms,
patterns, and trends can be extracted to improve the overall accuracy of
positioning solutions. This approach can be especially beneficial in areas
with limited GNSS coverage or challenging signal conditions, as it relies on
collective data contributions to overcome individual limitations.

  4. 4.

Transfer Learning for Cross-Domain Positioning: Transfer learning techniques
can be applied to leverage knowledge gained from one GNSS domain to another
with limited data. Such an approach can save data collection efforts and
enhance the performance of GNSS systems in underrepresented domains.

  5. 5.

Meta-Learning for Adaptive GNSS Algorithms: Meta-learning algorithms can be
used to learn the optimal algorithmic configurations for GNSS positioning
based on historical performance data. By training a meta-learning model on a
variety of datasets, it can learn which algorithms work best under different
conditions and adaptively select or combine them to achieve optimal
positioning accuracy. This adaptive approach allows GNSS systems to
continuously improve their performance and adapt to changing environments.

  6. 6.

Generative Adversarial Networks (GANs) for Data Augmentation: GANs can be used
to generate synthetic GNSS data that closely resemble real-world measurements.
By training a GAN on a large dataset of GNSS observations, it can learn the
underlying distribution of the data and generate additional samples. These
synthetic samples can be used to augment the training data for GNSS
positioning algorithms, thereby improving their performance, especially in
scenarios with limited training data.

  7. 7.

Uncertainty Estimation using Bayesian Neural Networks: Utilize Bayesian neural
networks to estimate uncertainty in GNSS positioning solutions, providing
confidence intervals and probabilistic measures of accuracy for better
decision-making in critical applications.

  8. 8.

Federated Learning: Employ federated learning approaches to train positioning
models collaboratively across multiple devices or users, ensuring privacy
while improving the accuracy and robustness of GNSS positioning.

  9. 9.

Edge Computing for Real-time GNSS Processing: Utilize edge computing
architectures to perform real-time GNSS data processing and positioning
calculations at the network edge, reducing latency and enabling faster and
more responsive positioning solutions.

##  12 Conclusion

In conclusion, this survey paper has explored the application of ML methods
for GNSS-based positioning. The paper has provided a comprehensive overview of
various ML techniques and their relevance to different aspects of GNSS
positioning. It has covered topics such as signal analysis and classification,
environmental context recognition, anomaly detection, multi-sensor
integration, prediction and forecasting, accuracy enhancement, and position
error modeling. Additionally, the paper has discussed other notable
applications of ML in GNSS and has identified the limitations and challenges
associated with these methods. The survey concludes by highlighting potential
areas for future research and development in the field of ML-based GNSS
positioning. Overall, this survey contributes to a deeper understanding of the
role of ML in improving GNSS positioning and provides valuable insights for
researchers and practitioners in the field.

List of Abbreviations

  * •

GNSS \- Global Navigation Satellite Systems

  * •

ML \- Machine Learning

  * •

GPS \- Global Positioning System

  * •

NLOS \- Non-Line-of-Sight

  * •

MP \- MP

  * •

WLS \- Weighted Least Squares

  * •

RTK \- Real-time kinematic

  * •

PPP \- Precise Point Positioning

  * •

SNR \- Signal-to-noise ratio

  * •

SVMs \- Support Vector Machines

  * •

CNNs \- Convolutional Neural Networks

  * •

SVR \- Support Vector Regression

  * •

DNN \- Deep Neural Network

  * •

RNN \- Recurrent Neural Network

  * •

KNN \- K-Nearest Neighbors

  * •

LSTM \- Long Short-Term Memory

  * •

MLP \- Multilayer Perceptron

  * •

RBFNN \- Radial Basis Function Neural Network

  * •

GNN \- Graph Neural Network

  * •

GraphSAGE \- Graph Sample and Aggregation

  * •

GBDT \- Gradient Boosting Decision Tree

  * •

XGBoost \- Extreme Gradient Boosting

  * •

RL \- Reinforcement Learning

  * •

DQN \- Deep Q-Networks

  * •

PPO \- Proximal Policy Optimization

  * •

A2C \- Advantage Actor-Critic

  * •

VAE \- Variational Autoencoders

  * •

KL \- Kullback-Leibler

  * •

LOS \- Line-of-sight

  * •

SVM \- Support Vector Machine

  * •

NN \- Neural Network

  * •

RBF SVM \- Radial Basis Function Support Vector Machines

  * •

ML \- Machine Learning

  * •

C/N0 \- Carrier-to-Noise Ratio

  * •

NavIC \- Navigation with Indian Constellation

  * •

L5 \- Likely referring to a specific GNSS signal frequency band

  * •

DLL \- Delay-Locked Loop

  * •

ASIC \- Application-Specific Integrated Circuit

  * •

BDS \- BeiDou Navigation Satellite System

  * •

GRU \- Gated Recurrent Unit

  * •

GTNN \- Graph Transformer Neural Network

  * •

IMU \- Inertial Measurement Unit

  * •

RAIM \- Receiver Autonomous Integrity Monitoring

  * •

TDNN \- Time-delayed Neural Network

  * •

PFRNN \- Particle Filter Recurrent Neural Network Neural Network

Acknowledgments We would like to acknowledge Derek Knowles and Asta Wu for
providing feedback on the paper.

## Declarations

  * •

Funding: Not applicable

  * •

Conflict of interest/Competing interests: The authors declare that they have
no competing interests.

  * •

Ethics approval: Not applicable

  * •

Consent to participate: Not applicable

  * •

Consent for publication: Yes

  * •

Availability of data and materials: Data sharing is not applicable to this
article as no datasets were generated or analyzed during the current study.

  * •

Code availability: Not applicable

  * •

Authors’ contributions: AM wrote the first draft of the manuscript and
conducted the survey. AM and GG finalized the manuscript write-up, proofread,
and checked the technical correctness of the manuscript. All authors read and
approved the final manuscript.

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