# Outdoor Position Recovery from Heterogeneous Telco Cellular Data

Yige Zhang, Weixiong Rao, Kun Zhang and Lei Chen  Yige Zhang and Weixiong Rao
are with School of Software Engineering, Tongji University, Shanghai, China.
E-mail: {wxrao<EMAIL_ADDRESS>Kun Zhang is with Department of
Philosophy Carnegie Mellon University, Pittsburgh, United States. E-mail:
<EMAIL_ADDRESS>Lei Chen is withDepartment of Computer Science and Engineering,
Hong Kong University of Science and Technology, Kowloon, Hong Kong, China.
E-mail<EMAIL_ADDRESS>
###### Abstract

Recent years have witnessed unprecedented amounts of data generated by
telecommunication (Telco) cellular networks. For example, measurement records
(MRs) are generated to report the connection states between mobile devices and
Telco networks, e.g., received signal strength. MR data have been widely used
to localize outdoor mobile devices for human mobility analysis, urban
planning, and traffic forecasting. Existing works using first-order sequence
models such as the Hidden Markov Model (HMM) attempt to capture spatio-
temporal locality in underlying mobility patterns for lower localization
errors. The HMM approaches typically assume stable mobility patterns of the
underlying mobile devices. Yet real MR datasets exhibit heterogeneous mobility
patterns due to mixed transportation modes of the underlying mobile devices
and uneven distribution of the positions associated with MR samples. Thus, the
existing solutions cannot handle these heterogeneous mobility patterns. we
propose a multi-task learning-based deep neural network (DNN) framework,
namely PRNet+, to incorporate outdoor position recovery and transportation
mode detection. To make sure the framework work, PRNet+ develops a feature
extraction module to precisely learn local-, short- and long-term spatio-
temporal locality from heterogeneous MR samples. Extensive evaluation on eight
datasets collected at three representative areas in Shanghai indicates that
PRNet+ greatly outperforms state-of-the-arts.

##  1 Introduction

Recent years have witnessed unprecedented amounts of data generated by
telecommunication (Telco) cellular networks. For example, when mobile devices
make phone calls or access data services, measurement records (MRs) are
generated to report connection states, e.g., received signal strength of
mobile device during each call/session. In a modern urban city, Telco data
generated by Telco radio and core equipment account to 2.2TB per day [6].
Massive Telco historical data (e.g., MRs) have been widely used to understand
human mobility [3, 39] and facilitate applications such as urban planning and
traffic forecasting [4], due to the unique advantages – Telco data can be
collected cheaply, frequently, and on a global scale.

The key to model human mobility and the applications above is to capture
outdoor positions of mobile users. The position recovery problem, i.e.,
precisely localizing outdoor mobile devices from Telco historical data (e.g.,
MRs), has attracted intensive research interests. A simple approach adopted by
Google MyLocation 111http://www.google.com/mobile/maps is to approximate
outdoor locations by the positions of cellular towers connected to mobile
devices. This method suffers from median errors of hundreds and even thousands
of meters. More recently, by using the sparse geo-tagged MR samples as
training data, machine learning-based Telco localization approaches such as
Random Forest [43] and Hidden Markov Model (HMM) [14, 18, 21, 44] are
exploited to recover outdoor locations of mobile devices with the median
errors of tens of meters. Such HMM approaches usually divide the area of
interest into grid cells and treat the grid cells as hidden states and MR
signal features as observations. When people holding mobile devices are moving
around, these HMM-based works [14, 18, 21, 44] capture spatio-temporal
locality and frequently lead to better result than single point-based
approaches [43] which independently localize individual MR samples.

However, the HMM approaches above do not work well if we cannot precisely
capture the distribution of emission and transition probabilities on real MR
data. It is particularly true because MR data, if not geo-tagged, indicate
rather coarse location information and frequently exhibit heterogeneous
mobility patterns (e.g., caused by uneven distributions of the positions of MR
samples and mixed transportation modes of underlying mobile devices). For
example, due to the various timestamp intervals between neighbouring MR
samples, the spatial distance between two neighbouring MR samples with a time
interval of one minute could be much smaller than the one of ten minutes. Even
with the same time interval (e.g., one minute), the distance between two
neighbouring MR samples in the driving mode is significantly greater than the
one in the walking mode. If we still take the HMM approaches above for
illustration, the transition probabilities across hidden states (i.e., grid
cells) do not take into account the mixed transportation modes and various
timestamp intervals of MR samples, resulting in the poor localization
performance. Thus, these HMM approaches cannot precisely capture spatio-
temporal locality and there still exist significant potentials for better
accuracy.

In addition, understanding human transportation modes is helpful for many
applications such as urban planning, transportation management and precision
advertisement. Many existing methods [7, 27, 28, 42] exploit GPS trajectory
data to infer users’ transportation modes, and do not work well on Telco data
(e.g., MR samples). In addition, Telco data usually cover much higher
population and more areas, and it is meaningful to detect transportation modes
on Telco data for urban sensing. On the other hand, the transportation modes
of underlying mobile devices are helpful to capture moving speed and then
estimate the moving distance of mobile devices within a certain time period.
Thus, if the transportation modes are known, we have chance to improve outdoor
position recovery.

To this end, we propose a multi-task learning-based deep neural network (DNN)
framework, namely PRNet+, to incorporate the two tasks of outdoor position
recovery and transportation mode detection. To make sure the framework work,
PRNet+ develops a feature extraction module to precisely learn common local-,
short- and long-term spatio-temporal locality from heterogeneous MR samples,
with help of the power of a convolutional neural network (CNN), a recently
developed sequence learning model, i.e., long short-term memory cells (LSTM),
and attention mechanism. The learned features are then used to solve the two
tasks. Specifically, PRNet+ 1) allows the various-length sequences of MR
samples, such that the two components (CNN and LSTM) are able to capture
spatial locality from the samples within each MR sequence, 2) exploits two
attention mechanisms for the time-interval between neighbouring MR samples,
together with the one between neighbouring MR sequences, to capture temporal
locality, and 3) incorporates the detected transportation modes and predicted
locations of heterogeneous MR data into a joint loss for better result. As a
summary, we make the following contributions.

_1_) To the best of our knowledge, this is the first attempt to fully employ
the power of multiple DNN models to automatically learn spatio-temporal
features from heterogeneous MR samples. Compared to the existing work on HMM-
based localization, PRNet+ can train a spatio-temporal sequence prediction
model from heterogeneous MR data for accurate location recovery.

_2_) PRNet+ properly leverages a multi-task learning framework to solve the
two tasks of outdoor position recovery and transportation mode detection.
Since the two tasks share the same features learned from heterogeneous MR data
via the developed feature extraction module, we have chance to avoid high
overheads to learn features independently for each task.

_3_) We evaluate PRNet+ against state-of-the-art counterparts by using eight
datasets collected on three representative (core, urban and rural) areas in
Shanghai, China. Our evaluation indicates that PRNet+ significantly
outperforms these counterparts.

The rest of this paper is organized as follows. Section 2 first introduces
preliminaries. Section 3 then gives the problem setting and Sections 4-6
present the design. Next, Section 7 evaluates PRNet+ and Section 8 reviews
related works. Section 9 finally concludes the paper.

##  2 Preliminaries

TABLE I: 2G GSM MR Sample MRTime | 2018/4/23 9:20 | IMSI | xxx | SRNCID | 6188 | BestCellID | 26051 | LCS BIT | 300
---|---|---|---|---|---|---|---|---|---
RNCID_1 | 6188 | CellID_1 | 26051 | AsuLevel_1 | 27 | SignalLevel_1 | 4 | RSSI_1 | -74.5
RNCID_2 | 6188 | CellID_2 | 27394 | AsuLevel_2 | 10 | SignalLevel_2 | 3 | RSSI_2 | -84.88
RNCID_3 | 6188 | CellID_3 | 27377 | AsuLevel_3 | 18 | SignalLevel_3 | 4 | RSSI_3 | -85.13
RNCID_4 | 6188 | CellID_4 | 27378 | AsuLevel_4 | 12 | SignalLevel_4 | 4 | RSSI_4 | -85.87
RNCID_5 | 6182 | CellID_5 | 41139 | AsuLevel_5 | 8 | SignalLevel_5 | 3 | RSSI_5 | -88.88
RNCID_6 | 6188 | CellID_6 | 27393 | AsuLevel_6 | 9 | SignalLevel_6 | 3 | RSSI_6 | -90.22
RNCID_7 | 6182 | CellID_7 | 44754 | AsuLevel_7 | 9 | SignalLevel_7 | 3 | RSSI_7 | -95

Measurement Record (MR) Data: MR data measure the connection states between
mobile devices and neighbouring base stations. Table I gives an example of 2G
GSM MR collected by an Android phone. This sample contains a unique number
(known as IMSI, International Mobile Subscriber Identity), connection time
stamp (MRTime), up to 7 nearby base stations (RNCID and CellID), signal
measurements such as AsuLevel, SignalLevel, and RSSI (radio signal strength
indicator). The up to 7 base stations are frequently sorted by descending
order in signal level and strength. Thus, the base station with the order
index 1 (RNCID_1 and CellID_1) is with the strongest signal and typically
selected as the primary serving base station to provide communication and data
services for mobile devices. When a mobile device is moving out of the signal
coverage range of a primary serving base station, the _handoff_ between base
stations occurs to re-select a new primary serving base station for the mobile
device.

Telco Location Recovery: Existing works on Telco position recovery are
typically divided into three categories. Firstly, _measurement-based methods_
approaches localize mobile devices based on absolute point-to-point distance
or angles [20, 30, 32]. Triangulation localization, one of the widely used
measurement-based approach, usually does not work well for 4G LTE MR data
where frequently signal strengths of one or at most two cells are available.
Yet triangulation localization requires signal strength regarding three and
ideally four or more cells.

Secondly, _fingerprinting-based methods_ [15, 17, 19] usually have better
performance than measurement-based methods, by dividing an area of interest
into small grids and representing each grid by an associated fingerprint [17].
NBL [19], a recently proposed work, assumes that signal strengths of each
neighbouring cell tower in the grid follow a Gaussian distribution. The online
stage next adopts either Maximum Likelihood Estimation (MLE) or Weighted
Average (WA) to localize mobile devices.

Lastly, some recent works [25, 15, 19, 43, 36] adopt _machine learning (ML)
techniques_ such as Random Forest to build a localization model to maintain
the correlations between the features extracted from MR samples and associated
locations (e.g., GPS coordinates). The predicted locations could be either
spatial regions (grid cells) or numeric GSP coordinates. ML techniques then
train the corresponding multi-classifiers [15, 19, 25] or regression models
[43]. Recently, a deep neural network-based outdoor cellular localization
system, namely DeepLoc [25], has been proposed. DeepLoc mainly utilizes a data
augmentor to handle data noise issue and to provide more training samples, and
trains a deep learning model using the augmented samples for better
localization result.

Note that ML techniques differ from measurement- and fingerprinting-based
methods in terms of application scenarios. That is, ML techniques usually
exhibit better results because ML techniques can leverage the rich information
from various Telco data including (geo-tagged) MR data and configuration
parameters (e.g., GPS coordinates) of base stations, Web log data, and etc.
Instead, when measurement and fingerprinting-based methods work on frontend
mobile devices for active localization, they may not exploit the rich data as
ML-based localization and thus cannot achieve comparable accuracy.

##  3 Problem Setting and Solution Overview

###  3.1 Problem Setting

Suppose that Telco operators have maintained a historical MR database. MR
samples usually do not contain the accurate locations of mobile devices
(identified by IMSI), and we expect to annotate MR samples with the accurate
locations of these mobile devices. There are various ways to acquire the
locations. For example, when mobile users are using vehicle navigation
services and switching on GPS receivers in the mobile devices, the GPS
coordinates of mobile devices are embedded in the URLs of mobile web logs. By
extracting the GPS coordinates from such URLs, we establish the linkage
between extracted GPS coordinates and MR samples in light of IMSI and
timestamp. In this way, MR samples are tagged by the linked GPS coordinates.

Nevertheless, mobile users frequently switch off GPS receivers on mobile
devices e.g., for energy saving, and mobile Web logs contain rather sparse GPS
coordinates. Thus, the majority of Telco MR data do not be tagged with the
associated GPS coordinates. To tackle this issue, we first train a machine
learning model by using the sparse geo-tagged MR samples as training data and
next recover outdoor locations for non-tagged MR samples (testing data).
Recall that single-point-based location recovery [43] may not capture spatio-
temporal locality of underlying mobile devices. We thus expect to recover a
trajectory of the locations predicted from a sequence of MR samples.

###### Definition 1

[MR Database $\mathcal{D}$] A database $\mathcal{D}$ of MR samples is
organized as follows. We first group the MR samples by IMSI and then sort the
samples in each group by timestamp. In this way, each IMSI is with a series of
sorted MR samples.

Suppose that every MR sample in $\mathcal{D}$ is with an associated GPS
position and transportation mode. Then for each IMSI, we have a series of
sorted MR samples and an associated trajectory of GPS positions. We are now
ready to define the position recovery problem.

###### Problem 1

[Position Recovery Problem] Given a database $\mathcal{D}$, by training a
multi-task learning-based framework $\mathds{R}$, the position recovery
problem aims to map a testing MR series to a GPS trajectory by $\mathds{R}$.

###  3.2 Challenges

A baseline approach to address Problem 1 is to exploit a sequence model such
as the popular RNN or LSTM model. For example, we might divide every MR series
into fixed-length windows of MR samples and then feed these windows of MR
samples into the LSTM network for trajectory recovery. However, the baseline
approach does not work well to capture spatio-temporal locality and suffers
from high localization errors, due to the following challenges caused by
heterogeneous MR samples.

1) _Mixed transportation modes_ : The simple assumption that the mobile device
regarding a given MR series always moves by a certain transportation mode
(e.g., walking) clearly does not hold. Depending on various transportation
modes, the spatial distance between neighbouring MR samples differs
significantly.

2) _Irregular MR sampling rate_ : Practically it is highly possible that the
time intervals of some neighbouring MR samples within a real world MR series
are very short (e.g., one minute) and yet those of other samples are rather
long (e.g., ten minutes). Thus, assuming fixed time intervals between
neighbouring MR samples is unreasonable.

3) _Uneven density of deployed base stations_ : Dense base stations are
frequently deployed in urban areas and yet spare ones in rural areas.
Consequently, the neighbouring MR samples within the MR series located in
urban and rural areas, even with exactly the same spatial distance and time
interval, could exhibit very different Telco signal handoff behavior between
base stations.

###  3.3 Solution Overview

Figure 1: The Architecture of PRNet+

To address above challenges, in Figure 1, we propose a multi-task learning-
based solution framework, namely PRNet+, which consists of three modules: _1)_
Feature Extraction Module to learn spatio-temporal features for an input MR
sequence (we will soon give the formal definition of MR (sub)sequence), _2)_
Position Recovery Module to recover a trajectory of outdoor positions for an
input MR sequence, and _3)_ Mode Detection Module to estimate the
transportation mode for each MR sample within the MR sequence. Here, the two
tasks of outdoor position recovery and transportation mode detection share the
learned spatio-temporal features for better efficiency.

The key of PRNet+ is to train a multi-task learning framework, where the tasks
of position recovery and transportation mode detection tasks share the same
learned features. As shown in Figure 1, given the input of PRNet+, i.e., one
MR _sequence_ $S$, the feature extraction module learns spatio-temporal
features, which are then fed into the two learning tasks (position recovery
and mode detection) to generate final predictions, respectively. To train the
multi-task learning framework, we design a join loss function consisting of
three individual loss functions. Thus, PRNet+ differs from the previous work
PRNet [37], i.e., a single-task learning approach of outdoor position
recovery. By incorporating both position recovery and mode detection tasks
into the multi-task learning framework, PRNet+ leads to much lower
localization errors than PRNet alone. It makes sense because the learned
transportation mode in PRNet+ directly indicates the moving speed constraint
for better localization result.

###  3.4 MR (Sub)sequence

It is not hard to find that the number of MR samples within a MR series varies
across the associated mobile devices. To capture the spatial locality from the
various-length MR series, we exploit the Telco signal _handoff_ between base
stations as follows. Let us consider the Telco signal coverage range of a
certain base station _bs_ , e.g., a circle with the radius around 1000 meters.
The MR samples using _bs_ as the primary serving base station exhibit spatial
locality because these samples are located within the circle. Thus, based on
the stations in MR samples, we define the following MR (sub)sequences.

###### Definition 2

[MR Sequence $\mathcal{S}$] Given a series of sorted MR samples regarding a
certain IMSI, we divide the MR series into multiple sequences by primary
serving base stations (_RNCID_1_ and _CellID_1_). The MR samples in each
sequence $\mathcal{S}$, sorted by timestamp, share the same primary serving
base station and IMSI.

Figure 2: Illustration of 6 MR Sequences

Figure 2 illustrates 6 MR sequences $S_{a1},S_{a2},...,S_{c1},S_{c2}$
generated from 3 MR series identified by the 3 mobile devices $a,b,c$ across
the coverage range of two primary serving base stations _bs_ 1 and _bs_ 2. For
a mobile device say $a$, the _handoff point_ $h_{a}$ divides its MR series
into two sequences $S_{a1}$ and $S_{a2}$.

Beyond MR sequence, we define the following MR subsequences.

###### Definition 3

[MR Subsequence] By the first non-serving base station (RNCID$\\_2$ and
CellID$\\_2$), we divide a certain MR sequence $\mathcal{S}$ into multiple MR
subsequences $S^{s}$. The MR samples in each $S$ share exactly the same non-
serving base station (RNCID$\\_2$ and CellID$\\_2$), primary serving base
station and IMSI.

Given the MR subsequences above, we expect that the MR samples within these
subsequences exhibit spatio -temporal locality. In this way, PRNet+ has chance
to capture the corresponding locality from these MR (sub)sequences for better
localization and mode detection results. Note that the amount of MR samples
within each MR sequence varies, depending upon the coverage radius of a base
station, sampling rate, and transportation mode. In case a certain MR sequence
contains very sparse samples, we could adaptively merge multiple neighbouring
MR sequences into a single one which contains at least $\tau$ samples.

##  4 Feature Extraction Module

In this section, we first introduce the data model of feature extraction
module in PRNet+. For convenience, in the rest of this paper, we denote
scalars by lowercase letters e.g., $a$, vectors by bold lowercase letters
e.g., $\bm{a}$, matrices by bold upper-case letters e.g., $\bm{A}$, and
tensors by bold upper-case letters e.g., $\mathbf{A}$. Specifically, we
represent each MR sample by a matrix $\bm{X}\in\mathbb{R}^{F\times N}$, where
$N$ is the number of base stations in this MR sample and $F$ is the number of
MR features of each base station. For the 2G MR sample in Table I, we have
$N=7$ stations (from the primary serving one to the 7-th station) and $F=7$
features (i.e., RNCID, CellID, latitude and longitude of the station
identified by RNCID/CellID, ASULevel, SignalLevel, and RSSI).

We represent each MR sequence $\mathcal{S}$ by a sequence of MR feature
matrices $\mathbf{X}=$
$\\{\bm{X}_{1,1},...,\bm{X}_{i,j},...,\bm{X}_{q,|S_{q}}|\\}$, where
$\bm{X}_{i,j}\in\mathbb{R}^{F\times N}$ is the MR feature matrix of the $j$-th
MR sample in the $i$-th subsequence $S_{i}$ with $1\leq i\leq q$ and $1\leq
j\leq|S_{q}|$, where $q$ is the number of MR subsequences within $S$ and
$|S_{i}|$ is the amount of MR samples in a MR subsequence $S_{i}$. Given the
input MR sequence, we will learn a corresponding sequence of feature vectors
$\bm{V}=\\{\bm{v}_{1,1},...,$ $\bm{v}_{1,|S_{1}|},...,\bm{v}_{q,|S_{q}}|\\}$.

Figure 3: Network Structure of Feature Extraction Module

Figure 3 gives the overview of Feature Extraction Module, consisting of two
main components.

_1)_ Local Single-Point Predictor takes each individual matrix $\bm{X}_{i,j}$
as input and generates a corresponding hidden vector $\bm{p}_{i,j}$ as the
output. The local predictor is composed of a convolution layer and a recurrent
layer to capture the local dependencies from the MR features in
$\bm{X}_{i,j}$.

_2)_ Global Recurrent Predictor takes a sequence of generated hidden vectors
$\bm{P}=\\{\bm{p}_{1,1},...,\bm{p}_{i,j},...,$ $\bm{p}_{q,|S_{q}|}\\}$ as
input and generates a sequence of shared feature representation vectors
$\bm{V}$. This predictor consists of three layers: a bottom recurrent layer to
learn short-term dependencies within each subsequence, an upper recurrent
layer to capture the long-term dependencies among subsequences, and an output
layer to mix the short- and long-term dependencies in order to generate the
shared feature representation vectors of the input MR sequence.

###  4.1 Local Predictor

Each MR sample contains the signal measurements of up to 7 base stations.
Thus, in Figure 4, the convolution layer in the local predictor captures the
local dependencies among the $F$ MR features from the input MR feature matrix
$\bm{X}_{i,j}$ and generates an output feature vector $p_{i,j}$. Intuitively,
the MR sample can be alternatively treated as a sequence of the $N$ base
stations sorted by the associated signal measurements. Thus, the recurrent
layer captures the local dependencies from the sequence.

Figure 4: Network Structure of Local Predictor

####  4.1.1 Local Convolution Layer

Given an input $F\times N$ matrix $\bm{X}_{i,j}$, the convolution layer
captures the local dependencies between MR features. Thus, the convolution
layer adopts multiple one-dimensional filters with size $F\times 1$ where the
height of each filter is equal to the number $F$. Since the size of the
convolution filter is consistent with that of the feature vector of a certain
base station in $\bm{X}_{i,j}$, the convolution operation can extract the
local dependencies among multiple features of the base station. The output
vector of the $k$-th filter throughout the input matrix $\bm{X}_{i,j}$ is:

$\displaystyle\bm{h}^{c}_{i,j,k}=ReLU(\bm{W}_{k}^{c}\circ\bm{X}_{i,j}+\bm{b}_{k}^{c}),$
(1)

where $\circ$ denotes a convolution operation and $ReLU(\cdot)$ is the
activation function. The superscript $c$ indicates the convolution layer. We
set the stride of convolution operation to one and ensure that each output
vector $\bm{h}^{c}_{i,j,k}$ has the size $N$.

Given $K$ filters, the output of the local convolution layer is a $K\times N$
matrix. For the $n$-th base station ($1\leq n\leq N$) within $\bm{X}_{i,j}$,
the $K\times N$ output matrix has an associated row vector
$\bm{x}_{i,j,n}\in\mathbb{R}^{K\times 1}$, treated as the latent feature
vector of the $n$-th base station.

####  4.1.2 Local Recurrent Layer

Given a $K\times N$ matrix above, the local recurrent layer treats it as a
sequence of $N$ latent feature vectors. The intuition is that the order of
these latent feature vectors indicates the inherent correlations among the $N$
base stations in an input MR sample. Thus, this local recurrent layer extracts
the local dependencies from the latent feature vectors regarding $N$ base
stations. We implement the local recurrent layer by LSTM [11] and compute the
hidden state of the LSTM cells for the latent vector $\bm{x}_{i,j,n}$ as
follows.

$\displaystyle\bm{z}_{i,j,n}^{r}$
$\displaystyle=\tanh(\bm{W}_{z}^{r}[\bm{h}_{i,j,n-1}^{r};\bm{x}_{i,j,n}]+\bm{b}_{z}^{r}),$
(2) $\displaystyle\bm{f}_{i,j,n}^{r}$
$\displaystyle=\sigma(\bm{W}_{f}^{r}[\bm{h}_{i,j,n-1}^{r};\bm{x}_{i,j,n}]+\bm{b}_{f}^{r}),$
$\displaystyle\bm{g}_{i,j,n}^{r}$
$\displaystyle=\sigma(\bm{W}_{g}^{r}[\bm{h}_{i,j,n-1}^{r};\bm{x}_{i,j,n}]+\bm{b}_{g}^{r}),$
$\displaystyle\bm{c}_{i,j,n}^{r}$
$\displaystyle=\bm{f}_{i,j,n}^{r}*\bm{c}_{i,j,n-1}^{r}+\bm{g}_{i,j,n}^{r}*\bm{z}_{i,j,n}^{r},$
$\displaystyle\bm{o}_{i,j,n}^{r}$
$\displaystyle=\sigma(\bm{W}_{o}^{r}[\bm{h}_{i,j,n-1}^{r};\bm{x}_{i,j,n}]+\bm{b}_{o}^{r}),$
$\displaystyle\bm{h}_{i,j,n}^{r}$
$\displaystyle=\bm{o}_{i,j,n}^{r}*\tanh\bm{c}_{i,j,n}^{r},$

where $*$ denotes element-wise multiplication and $\bm{h}_{i,j,n}$ is the
hidden state of the $n$-th base station in $\bm{X}_{i,j}$. The superscript $r$
denotes a local recurrent layer. The output of this layer,
$\bm{p}_{i,j}\in\mathbb{R}^{(N\times d_{l})\times 1}$, is the concatenation
result of all hidden states, where $d_{l}$ denotes the number of hidden units
in this local recurrent layer.

With the local predictor, Feature Extraction Module encodes each individual MR
feature matrix $\bm{X}_{i,j}$ into a hidden feature vector $\bm{p}_{i,j}$.
When an entire matrix sequence $\mathbf{X}$ is processed, the local predictor
generates a sequence $\bm{P}=\\{\bm{p}_{1,1},...,\bm{p}_{i,j},...,$
$\bm{p}_{q,|S_{q}|}\\}$, which is fed into the global recurrent predictor to
generate the sequence of shared feature representation vectors.

###  4.2 Global Recurrent Predictor

Figure 5 gives the neural network structure of our global recurrent predictor.
Inspired by the hierarchical deep neural network for document classification
problem [34], the global recurrent predictor first employs a _bottom recurrent
layer_ with time interval attention to extract the short-term latent
dependencies among MR samples within a subsequence. An _upper recurrent layer_
is then exploited to learn the long-term dependencies among MR subsequences to
generate subsequence attention. Finally, an _output layer_ merges the hidden
state of bottom recurrent layer and generated subsequence attention of upper
recurrent layer to produce the final output of this module.

Figure 5: Network Structure of Global Recurrent Predictor

####  4.2.1 Bottom Recurrent Layer

The bottom recurrent layer adopts LSTM cells to capture the short-term
dependencies among the hidden vectors
$\bm{p}_{i,1},...,\bm{p}_{i,|S_{i}^{s}|}$ within a certain subsequence
$S_{i}^{s}$. However, a standard LSTM model ignores the difference of time
intervals between the neighbouring cells. The length of time interval
indicates the relevance from the previous cell to the current one. For
instance, if the time interval increases, the contribution of previous cell
becomes weak. Thus, we utilize the time-interval attention mechanism to
address this issue.

Figure 6: Time-interval Attention in LSTM Cells

Time-interval attention: Figure 6 gives the LSTM cell structure with time
interval attention. Specifically, the attention acts on the forget gate and
input gate, respectively. We construct the time interval attention via a
linear perceptron by referring to the time interval between the current state
and the previous one with:

$\displaystyle a_{i,j}$ $\displaystyle=\tanh(w^{a}\Delta t_{i,j}+b^{a}),$ (3)

where $w^{a}$ and $b^{a}$ are learnable parameters and $\Delta t_{i,j}$ is the
timestamp difference between the current MR sample w.r.t $\bm{p}_{i,j}$ and
the previous one. We denote the time interval attention weight by $a_{i,j}$ to
update the forget and input gates of LSTM cell as:

$\displaystyle\bm{z}_{i,j,n}^{b}$
$\displaystyle=\tanh(\bm{W}_{z}^{b}[\bm{h}_{i,j,n-1}^{b};\bm{x}_{i,j,n}]+\bm{b}_{z}^{b}),$
(4) $\displaystyle\bm{f}_{i,j,n}^{b}$
$\displaystyle=\sigma(\bm{W}_{f}^{b}[\bm{h}_{i,j,n-1}^{b};\bm{x}_{i,j,n}]+\bm{b}_{f}^{b})\cdot
a_{i,j}$ $\displaystyle\bm{g}_{i,j,n}^{b}$
$\displaystyle=\sigma(\bm{W}_{g}^{b}[\bm{h}_{i,j,n-1}^{b};\bm{x}_{i,j,n}]+\bm{b}_{g}^{b})\cdot(1-a_{i,j}),$
$\displaystyle\bm{c}_{i,j,n}^{b}$
$\displaystyle=\bm{f}_{i,j,n}^{b}*\bm{c}_{i,j,n-1}^{b}+\bm{g}_{i,j,n}^{b}*\bm{z}_{i,j,n}^{b},$
$\displaystyle\bm{o}_{i,j,n}^{b}$
$\displaystyle=\sigma(\bm{W}_{o}^{b}[\bm{h}_{i,j,n-1}^{b};\bm{x}_{i,j,n}]+\bm{b}_{o}^{b}),$
$\displaystyle\bm{h}_{i,j,n}^{b}$
$\displaystyle=\bm{o}_{i,j,n}^{b}*\tanh\bm{c}_{i,j,n}^{b},$

where superscript $b$ indicates the bottom recurrent layer. The time attention
$a_{i,j}$ first acts on the forget gate and models a temporal decay to discard
the information from the previous cell state. Next, since the latest state
mainly determines the output of the current input, the attention $(1-a_{i,j})$
is thus applied to the input gate.

####  4.2.2 Upper Recurrent Layer

After the bottom recurrent layer has extracted the short-term temporal
dependencies among the MR samples within a subsequence, the upper recurrent
layer next captures the long-term dependencies between MR subsequences with
the following input:

$\displaystyle\bm{p}_{i}=\sum_{j}{\bm{h}_{i,j}^{b}},$ (5)

where $\bm{h}_{i,j}^{b}$ denotes the $j$-th hidden state of the $i$-th
subsequence acquired from the bottom recurrent layer. Since the upper
recurrent layer is to capture the correlations among subsequences, the input
of this layer, $\bm{p}_{i}$, needs to consider the latent characteristics of
all elements in the $i$-th subsequence. Thus, we compute the input
$\bm{p}_{i}$ by the sum of the hidden states in the $i$-th subsequence.

Subsequence attention: In the upper recurrent layer, we again leverage the
LSTM cells to capture the long-term dependency by a subsequence attention
mechanism to adaptively select meaningful hidden states (subsequences) across
all subsequences ($i=1,...,q$). Specifically, the attention weight of the
$i$-th hidden state $\bm{h}^{u}_{i}$ regarding the $i$-th subsequence (denoted
by $\bm{p}_{i}$) is computed as:

$\displaystyle u_{i}$
$\displaystyle=(\bm{v}^{u})^{\mathsf{T}}\tanh(\bm{W}^{u}\bm{h}_{i}^{u}+\bm{b}^{u}),$
(6) $\displaystyle\beta_{i}$
$\displaystyle=\frac{\exp(u_{i})}{\sum_{m=1}^{q}\exp(u_{m})},$

where $\bm{v}^{u}$, $\bm{W}^{u}$ and $\bm{b}^{u}$ are learnable parameters.
The attention weight $\beta_{i}$ represents the importance of the $i$-th
hidden state $\bm{h}_{i}^{u}$ for the prediction, where superscript $u$ refers
to the upper recurrent layer. Based on the weight $\beta_{i}$, the upper
recurrent layer generates a weighted context vector
$\bm{s}_{i}=\beta_{i}\bm{h}_{i}^{u}$ as the output.

####  4.2.3 Output Layer

The output layer is a fully connected (FC) layer to merge the outputs of the
bottom and upper recurrent layer. The output layer takes the hidden state of
bottom layer at time step $j$ of the $i$-th subsequence (denoted by
$\bm{h}_{i,j}^{b}$) and the context vector of upper layer of the $i$-th
subsequence (denoted by $\bm{s}_{i}$) as input. The final output of this
module $\bm{v}_{i,j}\in\mathbb{R}^{d_{f}}$, where $d_{f}$ indicates the
dimension of the learned feature vector, can be formulated as:

$\displaystyle\bm{v}_{i,j}=\tanh(\bm{W}^{o}_{b}\bm{h}_{i,j}^{u}+\bm{W}^{o}_{u}\bm{s}_{i}+\bm{b}^{o}),$
(7)

$\bm{W}^{o}_{b}$, $\bm{W}^{o}_{u}$ and $\bm{b}^{o}$ are learnable parameters
of this layer, and the entire Feature Extraction Module can be treated as a
shared encoder to learn common latent feature representation among different
tasks automatically.

##  5 Details of Two Learning Tasks

In this section, we present the details of two learning tasks (outdoor
position recovery and transportation mode detection) to process the learned
features above.

###  5.1 Outdoor Position Recovery Task

Figure 7: Outdoor Position Recovery Task

As shown in Figure 7, the outdoor position recovery task contains a Full
Connection (FC) layer with two hidden units. Given the learned feature vector
$\bm{V}$, the position recovery task generates a corresponding trajectory of
MR positions $\bm{Y}$ where $\bm{y}_{i,j}\in\bm{Y}$ is a predicted GPS
position of $v_{i,j}\in\bm{V}$. The output $\bm{y_{i,j}}$ can be formulated
as:

$\displaystyle\bm{y}_{i,j}=\sigma(\bm{W}^{p}\bm{v}_{i,j}+\bm{b}^{p})$ (8)

where $\bm{W}^{p}$ and $\bm{b}^{p}$ are learnable parameters, and superscript
$p$ indicates the task of position recovery. Due to the two dimensional GPS
latitude and longitude coordinates, the output $\bm{y}_{i,j}$ is a $2\times 1$
vector $\bm{y}_{i,j}$ with respect to one input MR sample $\bm{X}_{i,j}$ (or
the learned vector $\bm{v}_{i,j}$ of $\bm{X}_{i,j}$).

###  5.2 Transportation Mode Detection Task

In Figure 8, the transportation mode detection task still takes the shared
feature vector $\bm{V}$ as input and generates a certain transportation mode
for an input MR sample via a DNN classifier. The hidden layers of in the DNN
classifier consist of $T$ stacked FC layers. Slightly different from the
position recovery task, the transportation mode detection task requires deeper
network structure to perform the transportation mode estimation. In this task,
the output $\bm{h}_{i,j,m}^{t}$ of the $m$-th hidden FC layer can be written
as:

$\small\left\\{\begin{aligned}
\bm{h}_{i,j,m}^{t}&=\sigma(\bm{W}^{t}_{m}\bm{v}_{i,j}+\bm{b}^{t}_{m}),\quad
m=1\\\
\bm{h}_{i,j,m}^{t}&=\sigma(\bm{W}^{t}_{m}\bm{h}_{i,j,m-1}^{t}+\bm{b}^{t}_{m}),\quad
m=\\{2,...,T\\}\\\ \bm{m}_{i,j}&=Softmax(\bm{h}_{i,j,m}^{t}),\quad
m=T\end{aligned}\right.$ (9)

Figure 8: Transportation Mode Detection Task

where $\bm{W}^{t}_{m}$ and $\bm{b}^{t}_{m}$ are the learned parameters by FC
layers, and superscript $t$ denotes the task of transportation mode detection.
$\bm{m}_{i,j}\in\mathbb{R}^{|\mathcal{C}|}$ denotes the output of the final
hidden layer with Softmax activation function, where $\mathcal{C}$ is a
category set containing the possible transportation modes, e.g., walking,
cycling, and driving in our datasets. In this way, we classify a
transportation mode $\bm{m}_{i,j}$ per MR sample, differing from the previous
works Monitor [2], and MonoSense [1] which generate a certain mode for an
entire window of MR samples. It is not hard to find that, in a fine-grained
manner, our approach can process the heterogeneous MR samples with mixed
transportation modes within an input MR (sub)sequence.

##  6 Model Training

In this section, before giving the joint loss of the entire learning
framework, we first introduce the individual loss involving of two learning
tasks, and then present the training detail.

###  6.1 Individual Loss

First, since the outdoor position recovery problem is to predict numeric GPS
coordinates, we model the problem as a regression task and compute the
regression loss $\mathcal{L}^{\textbf{W}}_{loc}(S)$ with model parameters W on
input $S$ as:

$\displaystyle\mathcal{L}^{\textbf{W}}_{loc}(S)=\sum_{i=1}^{q}\sum_{j=1}^{|S_{i}|}||\bm{y}_{i,j}-\bm{y}^{true}_{i,j}||$
(10)

where $\bm{y}^{true}_{i,j}$ is the ground truth location coordinates of the
$j$-th input MR sample in the $i$-th subsequence $S_{i}$.

Second, we model the transportation mode detection problem as a classification
task. Thus, to define the loss function $\mathcal{L}^{\textbf{W}}_{mode}$ of
this task, we need to accumulate the mean cross-entropy for each MR sample in
a certain MR sequence $S$ as follows

$\displaystyle\mathcal{L}^{\textbf{W}}_{mode}(S)$
$\displaystyle=\sum_{i=1}^{q}\sum_{j=1}^{|S_{i}|}\sum_{c=1}^{|\mathcal{C}|}\delta_{i,j}^{c}\log
m_{i,j}^{c}$ (11)

In the equation above, $m_{i,j}^{c}$ denotes the predicted probability that
the $j$-th input MR sample in the $i$-th subsequence $S_{i}$, and
$\delta_{i,j}^{c}$ is the ground truth probability (0 or 1) of the input MR
sample being the $c$-th transportation mode.

Figure 9: Speed Probability Distribution of Driving Mode

Third, we note that the mobility features such as moving speed captured from
predicted outdoor positions should be consist with the corresponding
transportation mode. To this end, we introduce the speed constraint loss
$\mathcal{L}^{\textbf{W}}_{speed}(\mathcal{S})$ to associate the recovered
outdoor positions with detected transportation modes.

$\displaystyle\scriptsize\mathcal{L}^{\textbf{W}}_{speed}(\mathcal{S})$
$\displaystyle=\sum_{i=1}^{q}\sum_{j=2}^{|S_{i}|}-\log(1+P_{\bm{m}_{i,j}}(\hat{v}_{i,j})),$
(12) $\displaystyle\hat{v}_{i,j}$
$\displaystyle=\frac{||\bm{y}_{i,j}-\bm{y}_{i,j-1}||}{t_{i,j}-t_{i,j-1}}$

In the speed-constraint loss above, the item $P_{\bm{m}_{i,j}}(\hat{v}_{i,j})$
indicates the likelihood that the speed $\hat{v}_{i,j}$ follows the
transportation mode $\bm{m}_{i,j}$. Here, we estimate the speed
$\hat{v}_{i,j}$ via the Euclidean distance $||\bm{y}_{i,j}-\bm{y}_{i,j-1}||$,
between two predicted neighbouring positions $\bm{y}_{i,j}$ and
$\bm{y}_{i,j-1}$. After that, given a speed probability distribution of a
certain transportation mode, the item $P_{\bm{m}_{i,j}}(\hat{v}_{i,j})$
indicates the likelihood of the estimated speed $\hat{v}_{i,j}$ following such
a transportation mode. For example, Figure 9 gives the speed probability
distribution of the driving mode in one of our dataset. Given an estimated
speed $\hat{v}_{i,j}=4m/s$, with the help of the speed probability
distribution, we then have the probability
$P_{\bm{m}_{i,j}}(\hat{v}_{i,j})=0.238$, indicating that this speed
$\hat{v}_{i,j}$ follows the driving mode by the probability $0.238$. From the
equation above, if the predicted positions are more likely to follow the
predicted transportation modes, we have a smaller negative loss
$\mathcal{L}^{\textbf{W}}_{speed}$, which will next minimize our joint loss
$\mathcal{L}^{\textbf{W}}$.

###  6.2 Joint Loss

A simple joint loss is to directly sum the three loss functions above.
However, such a joint loss does not work well due to the significantly
difference scale of the three loss functions. To tackle this issue in a multi-
task learning framework, we follow the previous work [16] to compute the
weighted joint loss function via the so-called homoscedastic uncertainty to
learn a weight for each task. Here, such an uncertainty is a quantity which
stays constant for all input data and varies from tasks in Bayesian modelling.

Note that the two learning tasks in PRNet+ predict the outputs consisting of
numeric GPS coordinates (i.e., continuous values) $\bm{Y}$ and a
transportation mode (i.e., a discrete value) $\bm{M}$, respectively. Following
the work [16], we model such continuous and discrete values as a Gaussian
likelihood and a Softmax likelihood, and thus have the following loss function
with model parameters W on input $S$ and two outputs $\bm{Y}$ and $\bm{M}$ for
the two tasks:

$\displaystyle\mathcal{L}^{\textbf{W}}(\mathcal{S})=$ $\displaystyle-\log
p(\bm{Y},\bm{M}|\textbf{f}^{\textbf{W}})$ (13) $\displaystyle=$
$\displaystyle-\log\mathcal{N}(\bm{Y};\textbf{f}^{\textbf{W}},\sigma_{1}^{2})\cdot
Softmax(\bm{M};\textbf{f}^{\textbf{W}},\sigma_{2}^{2})$ $\displaystyle\approx$
$\displaystyle\frac{1}{2\sigma_{1}^{2}}\mathcal{L}^{\textbf{W}}_{loc}(\mathcal{S})+\frac{1}{2\sigma_{2}^{2}}\mathcal{L}^{\textbf{W}}_{mode}(\mathcal{S})+\log\sigma_{1}+\log\sigma_{2}$

where $\textbf{f}^{\textbf{W}}$ denotes the sufficient statistic to derive a
joint loss function by maximizing the Gaussian likelihood and $\sigma_{1}$,
$\sigma_{2}$ are learnable parameters which can be treated as the task weights
[16].

Besides the two loss functions with respect to the two learning tasks, we have
the speed-constraint loss and then incorporate the speed-constraint loss into
the final joint loss as follows.

$\displaystyle\mathcal{L}^{\textbf{W}}(\mathcal{S})=$
$\displaystyle\frac{1}{2\sigma_{1}^{2}}\mathcal{L}^{\textbf{W}}_{loc}(\mathcal{S})+\frac{1}{2\sigma_{2}^{2}}\mathcal{L}^{\textbf{W}}_{mode}(\mathcal{S})+$
(14)
$\displaystyle\alpha\mathcal{L}^{\textbf{W}}_{speed}(\mathcal{S})+\log\sigma_{1}+\log\sigma_{2}$

where $\alpha$ is a pre-defined hyper-parameter (e.g., $\alpha=0.05$ in one of
our used datasets) for speed constraint in the joint loss. Note that we do not
define a homoscedastic uncertainty weight for the speed-constraint loss
$\mathcal{L}^{\textbf{W}}_{speed}(\mathcal{S})$. It is mainly because
$\mathcal{L}^{\textbf{W}}_{loc}(\mathcal{S})$ and
$\mathcal{L}^{\textbf{W}}_{mode}(\mathcal{S})$ are those loss functions with
respect to the two learning tasks with certain outputs and yet
$\mathcal{L}^{\textbf{W}}_{speed}(\mathcal{S})$ not.

###  6.3 Training Detail

To train the two-task learning framework of PRNet+, we split the training data
into mini-batches and pad MR sequences (both feature and label sequences) with
a certain value e.g., -1. In this way, we make sure that they have the same
length (mainly because the length of MR sequence with respect to IMSI differs
in our datasets). In order to reduce the negative effect of the padding
operation, we define a mask matrix $\mathcal{M}$ where the matrix member
$\mathcal{M}_{i,j}$ is defined as:

$\small\mathcal{M}_{i,j}=\left\\{\begin{aligned}
0&,&\bm{y}_{i,j}^{true}=[-1,-1],\\\
1&,&\bm{y}_{i,j}^{true}\neq[-1,-1].\end{aligned}\right.$ (15)

where $\bm{y}_{i,j}^{true}=[-1,-1]$ indicates that $X_{i,j}$ is a padding
item. Thus, we then update the aforementioned loss functions.

$\displaystyle\mathcal{L}^{\textbf{W}}_{mode}(S)$
$\displaystyle=\sum_{i=1}^{q}\sum_{j=1}^{|S_{i}|}\sum_{c=1}^{|\mathcal{C}|}\mathcal{M}_{i,j}\delta_{i,j}^{c}\log
m_{i,j}^{c}$ (16) $\displaystyle\mathcal{L}^{\textbf{W}}_{loc}(S)$
$\displaystyle=\sum_{i=1}^{q}\sum_{j=1}^{|S_{i}|}\mathcal{M}_{i,j}||\bm{y}_{i,j}-\bm{y}^{true}_{i,j}||$
$\displaystyle\mathcal{L}^{\textbf{W}}_{cons}(\mathcal{S})$
$\displaystyle=\sum_{i=1}^{q}\sum_{j=2}^{|S_{i}|}-\mathcal{M}_{i,j}\log(1+P_{\bm{m}_{i,j}}(\hat{v}_{i,j}))$

Until now, we give the training steps in Algorithm 1. Here, we take an Adam
Optimizer to optimizing the model parameters.

Input: Training set $\mathcal{D}$, Position recovery and mode detection ground
truth: $\bm{Y}^{true}$ and $\bm{M}^{true}$, Training steps $T$, Batches $B$,
Hyper-parameter $\alpha$

Output: Model parameters

1 Initialize Model params W, $\sigma_{1}$, $\sigma_{2}$;

2 for  _$t=1$ $\rightarrow$ $T$_ do

3 for  _$i=1$ $\rightarrow$ $B$_ do

4 $\bm{V}_{b_{i}}\leftarrow$ FeatureExtract($\mathcal{D}_{b_{i}}$);

5 $\bm{Y}_{b_{i}}\leftarrow$ PositionRecoveryTask($\bm{V}_{b_{i}}$);

6 $\bm{M}_{b_{i}}\leftarrow$ ModeDetectionTask($\bm{V}_{b_{i}}$);

7 $\mathcal{L}^{\textbf{W}}\leftarrow$
JointLoss($\bm{Y}_{b_{i}},\bm{M}_{b_{i}},\bm{Y}^{true}_{b_{i}},\bm{M}^{true}_{b_{i}},\alpha$);

8 $\textbf{W},\sigma_{1},\sigma_{2}\leftarrow$
ADAM($\mathcal{L}^{\textbf{W}},\textbf{W},\sigma_{1},\sigma_{2}$);

9

10

11Return W, $\sigma_{1}$ and $\sigma_{2}$;

Algorithm 1 PRNet+ Training Procedure TABLE II: Statistics of Used Data Sets | Jiading-1 | Jiading-2 | Jiading-3 | Siping | Xuhui
---|---|---|---|---|---
Num. of samples (2G/4G) | 17354/12245 |  8444/$-$ |  $-$/150288 | 6723/4953 | 14680/10455
Route len (2G/4G) in km | 96.5/60.3 |  62.35/$-$ |  $-$/1347.6 | 24.6/15.5 | 29.3/15.9
Sampling rate (sec) | 3 | 1 | 10 | 3 | 2
Area size (km2) | 1.67 | 1.58 | 20.38 | 0.862 | 0.57
% of MRs with walking/cycling/driving | 60.1/25.2/14.1 | 58.8/31.1/10.1 | unknown | 63.8/36.2/- | 58.5/-/41.5
Num. of Serving BS per km2 (2G/4G) | 26.34/29.43 |  18.99/$-$ |  $-$/24.92 | 27.16/34.67 | 28.18/37.12
Num. of serving BSs (2G/4G) | 62/38 |  30/$-$ |  $-$/508 | 51/72 | 28/16

##  7 Experiments

###  7.1 Experimental Setup

1) Data Sets: As shown in Table II, we evaluate PRNet+ using the data sets
collected in three representative areas in Shanghai, China: a core business
area _Xuhui_ , an urban area _Siping_ and a rural area _Jiading_. The
geographical distances between _Jiading_ and _Siping_ , between _Jiading_ and
_Xuhui_ , and between _Siping_ and _Xuhui_ are around 31 km, 37 km and 15 km,
respectively. We have three datasets in _Jiading_ and instead only one dataset
in _Siping_ and _Xuhui_ , respectively. The _Xuhui_ and _Jiading-3_ datasets
were provided by one of the largest Telco operators in China, and the data
sets for _Jiading-1 $\sim$2_ and _Siping_ were collected by our developed
Android mobile app. When mobile users are moving around in outdoor road
networks to collect MR samples, we switch on GPS receivers on Android mobile
phones to collect current GPS coordinates. Since the collected GPS coordinates
may contain noises, we further employ the map-matching technique [38, 12] to
mitigate the effect of noises. To protect user privacy, all sensitive
information such as IMSI has been anonymized.

Table II summarizes the used data sets. For each dataset, we have collected 2G
GSM and (or) 4G LTE MR samples and the associated GPS coordinates. Due to the
limitations of the Android APIs in the 4G networks, each 4G MR sample in
_Jiading-1_ and _Siping_ contains only one (serving) base station without the
information about other neighboring base stations. Yet each 4G MR sample in
_Xuhui_ and _Jiading-3_ still contains up to 7 base stations. The
transportation mode ground truth of MR samples in _Jiading-1 $\sim$2_,
_Siping_ and _Xuhui_ datasets has been labelled. However, the Telco operator
does not provide the label information of transportation modes of _Jiading-3_
dataset due to the large size of _Jiading-3_ dataset.

The data sets contain heterogeneous MR samples due to mixed transportation
modes and uncertain timestamp intervals between neighbouring samples. In
particular, though we set a fixed sampling rate to collect MR data, the
timestamp intervals between neighbouring samples vary significantly. For
example, in the _Jiading_ -1 2G data set, the timestamp intervals vary from 1
to 125 seconds (see Table III), mainly due to (1) the uncertain delay of
Android threads scheduled by Android OS to collect MR samples and (2) noisy MR
samples (e.g., those samples having empty or zero signal measurements or empty
base station IDs, and we have to clean the noise). Given the heterogeneous
samples, we will study the effect of transportation modes and time intervals
between neighboring MR samples in Section 7.4.

TABLE III: Time Intervals in _Jiading-1_ 2G Dataset Intervals (s) | [1,3] | (3,5] | (5,10] | (10,30] | (30,60] | (60,125]
---|---|---|---|---|---|---
Ratio | 71.32% | 17.08% | 8.14% | 1.77% | 1.34% | 0.35%

Besides, we acquire the GPS longitude and latitude coordinates of every base
station provided by Telco operators, and use them as additional features of MR
samples. However, the parameters such as antenna height and angle are
unavailable due to the limited information provided by the database. We
believe that these parameters, if available, will further improve PRNet+.

TABLE IV: Counterparts Counterpart | Description | Approach
---|---|---
NBL |  Recent fingerprinting method [19] | Single Point
DeepLoc |  3-layer neural network [25] | Single Point
RaF |  1-layer Random Forest regression [43] | Single Point
CCR |  2-layer Random Forest regression [43] | Implicit Sequence
HMM |  HMM + particle filtering [21] | Sequence
SeqtoSeq |  a LSTM-based seq. to seq. model [29] | Sequence
ConvLSTM |  a convolutional LSTM [24] | Sequence
PRNet |  a hierarchical neural network [37] | Sequence
PRNet+ |  an improvement on PRNet | Sequence

2) Counterparts: We compare PRNet+ against 8 counterparts in Table IV from the
following aspects:

_(a)_ Depending upon the location recovery result, the counterparts are either
single point- (NBL [19], RaF [43], CCR [43] and a very recent work DeepLoc
[25]), or sequence-based approaches (HMM [21], SeqtoSeq [29], ConvLSTM [24],
PRNet [37] and PRNet+). In [43], the location recovery model can be either
only a single-layer Random Forest (RaF), or a two-layer Random Forests (CCR)
which can be treated as an implicit sequence-based approach due to the
contextual features acquired from the predicted result of the 1st layer.

_(b)_ In terms of the used models, the counterparts can be either the
fingerprinting-based (NBL), or traditional machine learning-based (RaF, CCR
and HMM), or DNN-based models (SeqtoSeq, ConvLSTM, DeepLoc, PRNet and PRNet+).

Given the MR samples above, we follow the previous work [9, 23] to adopt the
$k$-fold ($k=10$) cross validation by choosing 80% training and 20% testing
data from each data set to avoid over-fitting. We compute the prediction error
by the Euclidian distance between recovered locations and ground truth (i.e.,
the real GPS coordinates of MR samples), we choose median error, mean error,
and top $90\%$ error (by sorting prediction errors in ascending order) as
evaluation metrics. Since the transportation modes of _Jiading-3_ dataset are
unavailable, we exploit the previous transportation mode detection approach on
GPS data [42] to predict the transportation modes of training MR samples in
_Jiading-3_ dataset, and then the training MR samples of _Jiading-3_ dataset
with the predicted transportation modes are together used to train PRNet+
module for position recovery.

3) Key Parameters: Table V lists the parameters used in our experiments. We
use default values in the baseline experiment, and vary the values within
allowable ranges for multi-task learning and sensitivity study. Due to the low
sampling rate and short length of user trajectories in _Jiading-3_ dataset, we
thus treat an entire user trajectory as an MR sequence.

TABLE V: Key Parameters Parameter | Range | Default Val.
---|---|---
Parameter $\alpha$ in Joint Loss | 0.01, 0.05, 0.1 | 0.05
Timestamp Interval (s) | 3–120 | 3
Base Station Density | 25% - 100% | 100%
Learning Rate of PRNet+ | 0.005, 0.001, 0.0005, 0.0001 | 0.0005

###  7.2 Baseline Study

TABLE VI: Baseline Experiment: Localization Errors of Nine Approaches Methods | NBL | DeepLoc | RaF | CCR | HMM | SeqtoSeq | ConvLSTM | PRNet | PRNet+
---|---|---|---|---|---|---|---|---|---
Jiading-1 (2G) | Median | 53.4 | 35.1 | 38.3 | 34.1 | 36.5 | 25.4 | 28.5 | 15.8 | 15.2
Mean | 67.2 | 47.6 | 48.3 | 43.2 | 52.3 | 50.6 | 59.3 | 37.8 | 34.3
90% | 300.9 | 250.3 | 168.9 | 142.3 | 172.8 | 85.3 | 129.3 | 63.2 | 59.6
Jiading-1 (4G) | Median | 59.7 | 40.2 | 38.5 | 30.2 | 42.1 | 24.2 | 27.3 | 18.4 | 18.1
Mean | 72.3 | 53.9 | 47.2 | 44.5 | 53.6 | 50.1 | 58.1 | 40.6 | 37.4
90% | 318.6 | 280.6 | 158.9 | 145.9 | 188.4 | 81.7 | 124.5 | 66.5 | 62.3
Jiading-2 (2G) | Median | 54.3 | 36.2 | 37.5 | 36.1 | 37.3 | 27.3 | 29.6 | 19.4 | 17.3
Mean | 68.2 | 49.3 | 48.9 | 44.0 | 52.4 | 49.5 | 57.6 | 41.3 | 37.9
90% | 291.4 | 255.7 | 166.4 | 147.8 | 168.2 | 88.4 | 127.6 | 70.4 | 64.7
Jiading-3 (4G) | Median | 55.3 | 44.7 | 44.3 | 40.3 | 51.8 | 33.7 | 34.5 | 31.5 | 28.9
Mean | 64.7 | 54.2 | 53.6 | 51.1 | 56.2 | 54.1 | 57.4 | 49.5 | 47.8
90% | 296.6 | 247.0 | 166.9 | 154.2 | 167.0 | 157.1 | 149.1 | 135.2 | 131.7
Siping (2G) | Median | 42.8 | 33.5 | 41.1 | 37.5 | 37.2 | 23.4 | 27.7 | 15.3 | 14.9
Mean | 63.0 | 44.7 | 47.3 | 42.8 | 51.4 | 48.9 | 57.3 | 34.2 | 32.3
90% | 298.3 | 219.9 | 158.8 | 139.5 | 160.3 | 84.9 | 120.4 | 60.2 | 58.4
Siping (4G) | Median | 43.2 | 38.7 | 35.1 | 29.5 | 30.7 | 22.7 | 25.6 | 17.4 | 17.2
Mean | 64.9 | 49.6 | 44.4 | 40.6 | 48.2 | 47.3 | 55.7 | 37.7 | 35.3
90% | 256.7 | 267.5 | 105.8 | 101.2 | 145.6 | 83.5 | 117.2 | 63.4 | 60.1
Xuhui (2G) | Median | 45.9 | 31.2 | 35.6 | 30.0 | 35.3 | 22.5 | 25.3 | 15.7 | 15.2
Mean | 59.0 | 40.5 | 43.4 | 40.2 | 42.7 | 43.2 | 52.5 | 34.4 | 31.1
90% | 240.7 | 210.5 | 137.7 | 125.2 | 148.0 | 84.7 | 113.2 | 62.5 | 58.4
Xuhui (4G) | Median | 32.2 | 27.4 | 32.2 | 20.0 | 28.6 | 21.9 | 24.4 | 13.7 | 13.4
Mean | 52.7 | 400.1 | 41.5 | 34.1 | 39.1 | 42.9 | 50.6 | 31.2 | 28.3
90% | 191.2 | 211.9 | 104.4 | 98.3 | 129.5 | 81.8 | 107.8 | 59.3 | 57.1

In Table VI, we compare the prediction errors (median, mean, and 90% errors)
of the nine approaches on the eight datasets from three areas (Jiading,
Siping, and Xuhui). From Table VI, we have the following findings.

_1_) PRNet+ offers the least error among these nine approaches on all MR
datasets. For example, in _Jiading-1_ 2G data set, PRNet+ reduces the median
error by 56.7% compared with the recent outdoor Telco position recovery
approach, DeepLoc. It is mainly because DeepLoc is a single point-based
prediction method, which does not capture contextual dependencies. In
addition, PRNet+ outperforms the two deep neural network-based approaches
(i.e. SeqtoSeq and ConvLSTM). Such results indicate that PRNet+ outperforms
both the state-of-the-arts and alternative DNN-based approaches.

_2_) We compare the top-90% errors among the nine approaches. Still on
_Jiading-1_ 2G dataset, PRNet+ outperforms CCR with 58.1% lower top-90% error.
Similar results are applicable to other datasets. These numbers indicate that
PRNet+ has fully employed the power of hierarchical deep neural network,
sequence model, attention mechanism and joint loss together to effectively
mitigate the outliers among predicted locations.

_3_) We compare the results of the five sequence-based approaches against four
single-point-based ones. For example, a simple sequence model, HMM, still
outperforms DeepLoc by 31.0% smaller 90% error on _Jiading-1_ 2G data set. In
addition, though CCR and RaF are both Random Forest-based approaches, CCR
leverages the contextual features such as moving speed and leads to better
result than RaF by 10.9% smaller median error. Such results verify that the
sequence models, no matter they implicit or explicit use of contextual
features, could lead to better results than the original single-point-based
approaches.

_4_) Among the five deep neural network-based approaches, ConvLSTM suffers the
highest errors. It might be mainly because ConvLSTM is typically used to solve
flow prediction (e.g., precipitation nowcasting [24] and traffic accident
[35]) for the time series data involving explicit spatio-temporal information.
However, MR samples do not contain accurate locations, which are just our
objective (note that the GPS locations of base stations are used as additional
features, but not the locations of MR samples). Thus, ConvLSTM may not
properly solve our problem though ConvLSTM also utilizes the power of both CNN
and LSTM. SeqtoSeq is slightly better than ConvLSTM, but still incomparable
with PRNet+.

_5_) Table VI is consistent with results reported in the previous works CCR
and NBL: for the same area e.g., _Xuhui_ , 4G MR samples typically lead to
better result than 2G samples; and for the same Telco networks, the results of
the _Xuhui_ 2G dataset are better than those of _Siping_ and _Jiading-1
$\sim$2_ 2G datasets. We have the finding that higher base station deployment
density in 4G networks and core areas (see Table II) can achieve better result
than those in 2G and rural areas. We also note that due to only one base
station per MR sample in _Jiading-1_ and _Siping_ 4G datasets, their errors
are even higher than those 2G datasets. Such result verifies the importance of
multiple base stations for precise location recovery.

_6)_ Among the datasets in _Jiading_ area, the localization errors of
_Jiading-3_ 4G data set are higher than the other datasets. It is mainly
caused by the lowest sampling rate among all datasets and more sparse base
station density within the area covered by _Jiading-3_ data set. In addition,
the localization errors of _Jiading-2_ 2G data set are slightly higher than
_Jiading-1_ 2G data set. It is mainly because _Jiading-2_ data set has a
higher percentage of MR samples collected by driving and cycling (see Table
II). We will discuss the effect of transportation modes in Section 7.4.

Due to space limitation, we choose _Jiading-1_ and _Jiadng-2_ 2G datasets (the
two datasets contain the greatest number of MR samples labelled by
transportation modes) to evaluate PRNet+ in the rest of this section.

###  7.3 Evaluation of Multi-Task Learning Framework

In this section, we are interested in how the two individual learning tasks
independently work against the entire multi-task learning framework of PRNet+.
In Table VII, the first two rows indicate the performance result of an
individual task alone, the third row involves those of the multi-task learning
models with man-made uniform weights in the joint loss, and the rest rows give
those with task uncertainty weighted loss functions.

TABLE VII: Multi-Task Learning in PRNet+. Loss | Task (Loss item) Weights | Jiading-1 2G Data | Jiading-2 2G Data
---|---|---|---
Pos. Recover. | Mode Detect. | Pos. Recover. | Mode Detect.
Speed Const. | Pos. Recover. | Mode Detect. | 50% Error: meters | Accuracy | 50% Error: meters | Accuracy
Pos. Recovery Task alone | / | 1 | 0 | 15.8 | / | 16.7 | /
Mode Detect. Task alone | / | 0 | 1 | / | 0.754 | / | 0.761
Uniform weights | 1 | 1 | 1 | 28.7 | 0.682 | 31.4 | 0\. 679
2-task uncertainty weights | / | $\surd$ | $\surd$ | 17.1 | 0.775 | 17.9 | 0.752
2-task uncertainty weights | 0.01 | $\surd$ | $\surd$ | 16.8 | 0.781 | 17.2 | 0.760
2-task uncertainty weights | 0.1 | $\surd$ | $\surd$ | 17.4 | 0.781 | 18.1 | 0.766
2-task uncertainty weights | 0.05 | $\surd$ | $\surd$ | 15.4 | 0.784 | 16.2 | 0.773

Table VII clearly illustrates the benefit of the multi-task learning with much
better performing results than an individual task alone. For example, using
the multi-task learning framework, PRNet+ in the bottom row improves the
classification accuracy from 75.4% to 78.4% in _Jiading-1_ 2G dataset and the
position recovery error (median error) from 15.8 meters to 15.2 meters. In
addition, we compare the uncertainty weights against the manual weights in the
joint loss. Using a uniform weighting results in rather poor performance, even
worse than the results of an individual task alone. Next, the 4-th row (i.e.,
the loss regarding to the speed constraint is missed in the joint loss) cannot
compete the bottom row, i.e., the 2-task uncertainty weights with the pre-
defined parameter $\alpha=0.05$ for the speed constraint loss. It is mainly
because using the speed constraint can effectively link the predicted
positions with detected modes for better results.

|
---|---
Figure 10: Transportation Mode Detection: (a) Counterparts (b) Localization
Improvement, (c) Sequence Model (from left to right).

###  7.4 Sensitivity Study

(1) Transportation Mode: Due to the mixed transportation modes of MR samples,
we are interested in how these modes affect the performance of PRNet+.

Firstly, Figure 10 evaluates the detection accuracy of PRNet+ with two other
approaches Monitor [2] and MonoSense [1]. From this figure, we find that
PRNet+ performs consistently better than Monitor and MonoSense. Since Monitor
and MonoSense predict a certain transportation mode for entire MR samples
within a time window, they do not work well when such MR samples involves
mixed transportation modes within a time window. In addition, the detection
accuracy of either walking or driving mode is significantly higher than the
one of cycling. It is mainly because in our datasets collected in a campus,
fast (resp. slow) cycling speed is close to the driving (resp. walking) speed,
thus blurring the features w.r.t the cycling mode from those of either driving
or walking modes.

Secondly, Figure 10 studies the benefit of transportation mode detection on
position recovery. Specifically, we calculate how much localization error
reduction is gained when the speed constraint loss is incorporated into the
joint loss of PRNet+. We find that the reduction of the mean and 90% errors of
PRNet+ is rather significant. Such result indicates that transportation mode
detection greatly improves the outliers of predicted positions.

Finally, under various transportation modes, Figure 10 compare PRNet+ against
three other sequenced-based approaches PRNet, SeqtoSeq and HMM). From this
figure, we find that the walking mode leads to the best prediction accuracy.
It is mainly because the MR samples in the walking mode exhibit higher spatial
locality compared to cycling and driving, i.e., more MR samples within every
MR (sub)sequence. Moreover, among all transportation modes, PRNet+ still
performs best. In particular, the errors of both SeqtoSeq and HMM grow
significantly on the MR samples collected by the driving mode. When these MR
samples are rather spare in terms of their locations and uneven timestamp
intervals, these two models are hard to precisely capture spatio-temporal
locality.

(2) Timestamp Intervals: In this experiment, we study the effect of timestamp
intervals (used by Equation 3 of time-interval attention in Section 4.2.1) on
localization errors. From the MR samples of the _Jiading-1_ and _Jiading-2_ 2G
datasets, we randomly select MR samples to make sure that the timestamp
difference between neighbouring MR samples in MR sequences is smaller than a
certain time interval, and we vary the time intervals from 3 seconds to 120
seconds. From Figure 11(a), we have the following result. Firstly, a higher
time interval (and thus more sparse data samples) leads to the higher
prediction errors of all four sequence models. Secondly, the growth trends of
median errors regarding PRNet+ and PRNet are rather smooth. It is mainly
because PRNet module can capture temporal dependencies even from sparse
samples. In addition, HMM suffers from much higher errors than SeqtoSeq,
indicating that the deep sequence models including SeqtoSeq, PRNet and PRNet+
are better to capture long-term dependencies than the first-order HMM model.
Then, even with high timestamp intervals from 30 to 120 seconds, PRNet+ and
PRNet can still perform well, mainly due to the time interval and subsequence
attention mechanism in PRNet/Feature Extraction module.

(3) Base Station Density: We now study how the density of base stations
affects the prediction errors of PRNet+ by varying the percentage of base
stations from 25%-100%. Specifically, among all base stations in a MR dataset,
we randomly remove some base stations from MR samples. If a certain MR sample
contains a removed base station, then the signal measurements regarding this
base station are dropped from the sample. Figure 11(b) indicates that PRNet+
leads to a competitive accuracy even if we drop 50% base stations.
Nevertheless, a lower base station density means higher errors. The reason is
that sparse base stations incur spatial ambiguity of MR samples. More base
stations in MR samples alternatively lead to more discriminative MR features
and lower errors.

|  |
---|---|---
Figure 11: Sensitivity Study. (a)Time Interval, (b) Base Station Density, (c)
Ablation Study (from left to right).

(4) Ablation Study of PRNet+: To study the importance of each component in
PRNet+ for localization, we design the following variants. 1) PRNetl using the
local predictor of Feature Extraction Module alone (which can be treated as a
single-point-based predictor to process MR samples individually): we need to
add an additional dense layer to produce the final outputs; 2) PRNetg using
the global predictor of Feature Extraction Module alone: we need to reshape
the original input matrix $\bm{X}_{i,j}\in\mathbb{R}^{F\times N}$ of a MR
sequence into a column vector $(F\times N)\times 1$, which is directly fed
into the global predictor; 3) PRNet without Transportation Mode Detection
Module. As shown in Figure 11(c), PRNetl incurs a high growth of localization
errors, indicating the significant contribution offered by the global
predictor to capture the temporal dependencies of the entire sequence.
Instead, PRNetg could reduce the top 90% errors, when compared to PRNetl. It
mainly because that the dependencies among neighbouring MR samples can
mitigate the prediction of outliers. Not surprisingly, PRNet with the local
and global predictors can lead to the lowest localization errors among PRNet
and its two variants. Since PRNet+ utilizes the detected transportation modes
of MR samples by Transportation Mode Detection module and the shared feature
representations to improve the performance of PRNet module, PRNet+ has the
slightly lower prediction errors than PRNet.

(5) Learning Rate: Table VIII shows the effect of different learning rates on
PRNet+. Learning rate determines whether the objective (loss) function can
converge to a local minimum and how fast it converges. Compared to the SGD
optimizer utilized by PRNet, Adam optimizer is quite robust for the selection
of model parameters. Thus, we adopt Adam optimizer instead of SGD optimizer in
PRNet+, and vary the learning rate from 0.005 to 0.0001 under the same
training epoches. The table shows that lowering the learning rate to (0.0005)
makes the training more reliable. This is because lowering the learning rate
makes the optimizer step towards the minimum slowly which prevents
overshooting it.

TABLE VIII: Effect of Learning Rate Learning Rate | 0.005 | 0.001 | 0.0005 | 0.0001
---|---|---|---|---
Jiading-1 (2G) | Median Err. (meters) | 16.4 | 15.5 | 15.2 | 15.5
Mean Err. (meters) | 38.2 | 36.5 | 34.3 | 35.1
90% Err. (meters) | 63.7 | 61.2 | 59.6 | 60.8
Jiading-2 (2G) | Median Err. (meters) | 18.8 | 17.6 | 16.4 | 17.2
Mean Err. (meters) | 38.2 | 37.8 | 37.1 | 37.9
90% Err. (meters) | 66.4 | 65.8 | 64.7 | 65.2

###  7.5 Visualization

Finally, Figure 12 visualizes the position recovery results of PRNet+ and
three Telco location recovery approaches (PRNet, HMM, and DeepLoc) on a
randomly selected small area from the _Jiading-1_ 2G data set. As shown in
this figure, the trajectory predicted by PRNet+ is the closest to the ground
truth in terms of horizontal moving directions and vertical shift out of road
segments. Yet DeepLoc leads to the most shift in both horizontal and vertical
directions. The median localization errors of HMM, and DeepLoc are very close,
but HMM leads to a smoother trajectory of visualization results. It is mainly
because HMM first utilized Hidden Markov Model for extracting the contextual
dependencies between neighboring MR samples and next the filtering technique
for post-processing.

With help of the road network, we next perform the map-matching technique [41]
on the predicted trajectories of the aforementioned approaches (denoted as
PRNet+_M, PRNet_M, HMM_M, and DeepLoc_M, respectively) and plot the map-
matching results in this figure. This post-processing technique greatly
improves DeepLoc to generate smooth trajectories. However, the map-matching
technique cannot fully overcome the overall shift along the horizontal moving
direction, and Figure 12 has clearly visualized this issue.

Consistent with the result in Section 7.2, both PRNet+ and PRNet lead to
acceptable results, even without this post-processing step. The results in
Table 6 indicates the slight improvement of PRNet+ on PRNet (the 90% error is
reduced by 3.6 meters in Jiading-1 2G dataset), thus it make senses that there
is no significant visualization difference between the results of PRNet+ and
PRNet. However, PRNet+ can realize accurate fine-grained transportation mode
detection for MR data and while slightly improve the performance of outdoor
position recovery, which is meaningful for more urban computing scenarios.

(a) PRNet+ |  (b) PRNet+_M |  (c) PRNet |  (d) PRNet_M |  (e) HMM |  (f) HMM_M |  (g) DeepLoc |  (h) DeepLoc_M
---|---|---|---|---|---|---|---
Figure 12: Visualization (Map Scale 1.5:10000). Red: Ground Truth; Green:
Predicted Location; Blue: Map-matching location.

##  8 Related work

Trajectory Recovery: Unlike single point-based localization, the sequence-
based localization, namely trajectory recovery problem, frequently exhibit
much lower localization errors. For example, AT&T researchers [21] proposed an
outdoor localization approach, which first exploits the hidden markov model
(HMM) for trajectory recovery and then applies particle filters to generate
smooth trajectories. CCR [43] designed temporal and spatial contextual
features such as moving speeds and time gap via domain expert knowledge and
feature engineering expertise to greatly improve prediction accuracy. A recent
work [44], though achieving rather precisely localization result, requires
massive third-party GPS trajectories as the prior to precisely estimate the
HMM emission probability. In addition, the work [31] proposed a regularization
framework to reconstruct mobile trajectories from sparse location fingerprints
by enforcing two properties including spatial and temporal smoothness. Similar
to [31], map-matching techniques and their variants [38, 12] attempt to
recover an entire trajectory from a set of (sparse) locations, e.g., GPS
coordinates. These works, with help of road network constraints, project the
locations onto road networks to correct outlier locations (e.g., noisy GPS
points) and recover an entire trajectory. Unlike [31, 31], our work does not
require the availability of either sparse location points within input
trajectories or road networks.

Deep Learning for Localization Systems: Recently, deep neural networks have
been used in indoor or outdoor localization systems. Firstly, in dynamic
indoor environment, the Deep Belief Network (DBN) and Gaussian-Bernoulli
Restricted Boltzmann Machines have been utilized in fingerprinting-based
indoor localization to increase estimation accuracy and reduce generalization
error [8]. In addition, to process the RSS time-series acquired from wireless
local area network (WLAN) access points, the previous work [13] leveraged a
convolutional neural network (CNN) which is fed with RSS feature matrices for
indoor localization by extracting the temporal dependencies between the last
RSS readings. DeepFi [33] is another deep-learning-based indoor fingerprinting
system based on channel state information (CSI) rather than RSS for indoor
localization. DeepFi explores the features of wireless channel data and
obtains the optimal weights of DNN as fingerprints which effectively describe
the characteristics of CSI for each location and help reduce noise. These
fingerprint-based approaches typically require sufficient samples to construct
fingerprint database, and do not work well for our problem with heterogenous
samples. Finally, for outdoor Telco localization, DeepLoc [25] employs a data
augmentation technique to tackle the challenges of noisy data and insufficient
training samples. In summary, all of these DNN-based works typically perform
single-point-based localization though they improve localization result via
various contextual spatio-temporal features [13] and instead we focus on a
sequence-based DNN model.

Transportation Mode Detection: Many literature works have studied the problem
of transportation mode detection on GPS trajectory data. For example, the
previous works [28, 42] first extract the features such as velocity and then
train a machine learning-based detection model. Some works employ deep
learning techniques for transportation mode detection, e.g., the CNN-based and
LSTM-based detection [7, 27]. Instead of GPS data, some works perform
transportation mode detection via the readings from accelerators and
gyroscopes [5, 10].

Similar to our work, Monitor [2], and MonoSense [1] detect transportation
modes on the data generated by cellular networks with help of base station IDs
and the associated received signal strength (RSSI) to extract statistical
features such as velocity. Nevertheless, our work exploits learned features
rather than statistical features for better accuracy. Some works [26, 22]
incorporate cellular data and other sensor data collected from mobile devices
to detect transportation mode. CellTrans [40] infers that mobile users take
either public transportation tools or private car at urban scale by extracting
meaningful mobility features from cellular data. Such features are computed by
the positions of connected base stations from Mobile flow records (MFRs) at a
coarse-grained level (each trip of a user is tagged with a certain mode).
Instead, we perform fine-grained transportation mode detection with one mode
per MR sample.

##  9 Conclusion

In this paper, we proposed a multi-task learning framework called PRNet+.
PRNet+ first ensembles the power of CNN, LSTM, and two attention mechanisms to
properly leverage all of the local, short- and long-term spatial and temporal
dependencies to learn MR features. On the learned MR features, PRNet+ performs
two learning tasks (outdoor location recovery and transportation mode
detections) with help of a joint loss function. Our extensive evaluation shows
that PRNet+ greatly outperforms state-of-the-art localization approaches and
alternative variants of PRNet+ on the datasets collected in three
representative areas in Shanghai. The promising result of PRNet+ inspires
future studies on issues such as how to use the recovered trajectories from
Telco MR data for human mobility analysis and the potentials of applying
PRNet+ to indoor localization and forthcoming 5G networks.

Acknowledge: This work is partially supported by National Natural Science
Foundation of China (Grant No. 61972286, No. 61772371).

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|  Yige Zhang is a PhD student in School of Software Engineering, Tongji
University, China since Sept 2016, and received the B.Sc degree of Software
Engineering from Tongji University in July 2016. Her research interests focus
on mobile computing and machine learning.
---|---
|  Weixiong Rao received his Ph.D degree from The Chinese University of Hong
Kong in 2009. After that, he worked for Hong Kong University of Science and
Technology (2010), University of Helsinki (2011-2012), and University of
Cambridge Computer Laboratory Systems Research Group (2013) as Post-Doctor
researchers. He is a full Professor in School of Software Engineering, Tongji
University, China (since 2014). His research interests include mobile
computing and spatiotemporal data science, and is a member of CCF, ACM and
IEEE.
---|---
|  Kun Zhang is an associate professor in the philosophy department and an
affiliate faculty member in the machine learning department at Carnegie Mellon
University. He received his Ph.D. degree from The Chinese University of Hong
Kong in 2005. His research interests lie in machine learning and artificial
intelligence, especially in causal discovery, causality-based learning, and
general-purpose artificial intelligence. He coauthored a best student paper at
UAI 2010, received the best benchmark award of the causality challenge 2008,
and coauthored a finalist best paper at CVPR 2019. He has served as an area
chair or senior program committee member for major conferences in machine
learning or artificial intelligence, including NeurIPS, UAI, ICML, AISTATS,
AAAI, and IJCAI, and has organized various academic activities to foster
interdisciplinary research in causality.
---|---
|  Lei Chen is a full professor in the Department of Computer Science and
Engineering, Hong Kong University of Science and Technology. His research
interests include crowdsourcing over social media, social media analysis,
probabilistic and uncertain databases, and privacy-preserved data publishing.
The system developed by his team won the excellent demonstration award in VLDB
2014. He got the SIGMOD Test-of-Time Award in 2015. He is a member of the VLDB
endowment and ACM Distinguished Scientist.
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