# Deep Learning-based Cooperative LiDAR Sensing for Improved Vehicle
Positioning

Luca Barbieri Bernardo Camajori Tedeschini
Mattia Brambilla Monica Nicoli This work is financed by the European
Union—NextGenerationEU (National Sustainable Mobility Center CN00000023,
Italian Ministry of University and Research Decree n. 1033—17/06/2022, Spokes
6 and 9).
L. Barbieri, B. Camajori Tedeschini and M. Brambilla are with Dipartimento di
Elettronica, Informazione e Bioingegneria (DEIB), Politecnico di Milano, 20133
Milan, Italy (e-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>mattia.brambilla@polimi.it).M. Nicoli is with Dipartimento di Ingegneria
Gestionale (DIG), Politecnico di Milano, 20133 Milan, Italy (e-mail:
monica.nicoli@polimi.it).

###### Abstract

Accurate positioning is known to be a fundamental requirement for the
deployment of Connected Automated Vehicles (CAVs). To meet this need, a new
emerging trend is represented by cooperative methods where vehicles fuse
information coming from navigation and imaging sensors via Vehicle-to-
Everything (V2X) communications for joint positioning and environmental
perception. In line with this trend, this paper proposes a novel data-driven
cooperative sensing framework, termed Cooperative LiDAR Sensing with Message
Passing Neural Network (CLS-MPNN), where spatially-distributed vehicles
collaborate in perceiving the environment via LiDAR sensors. Vehicles process
their LiDAR point clouds using a Deep Neural Network (DNN), namely a 3D object
detector, to identify and localize possible static objects present in the
driving environment. Data are then aggregated by a centralized infrastructure
that performs Data Association (DA) using a Message Passing Neural Network
(MPNN) and runs the Implicit Cooperative Positioning (ICP) algorithm. The
proposed approach is evaluated using two realistic driving scenarios generated
by a high-fidelity automated driving simulator. The results show that CLS-MPNN
outperforms a conventional non-cooperative localization algorithm based on
Global Navigation Satellite System (GNSS) and a state-of-the-art cooperative
Simultaneous Localization and Mapping (SLAM) method while approaching the
performances of an oracle system with ideal sensing and perfect association.

###### Index Terms:

Connected Automated Vehicles, Cooperative LiDAR sensing, data association, 3D
object detection, Message Passing Neural Networks, positioning, SLAM.

##  I Introduction

The demand for highly-accurate localization in Cooperative Intelligent
Transportation Systems (C-ITS) has recently skyrocketed thanks to the
advancements in the development of Vehicle-To-Everything (V2X) communication
technologies [1, 2] which raised the attention to Connected Automated Vehicles
and associated use cases [3].

Nowadays, most of the proposed solutions rely on the largely-available Global
Navigation Satellite System (GNSS). However, even when augmented with inertial
sensors, differential corrections, or multi-constellations receivers, GNSS is
not able to satisfy the requirements of highly-accurate positioning services
[4, 5], as it is heavily affected by poor visibility conditions that may occur
in urban scenarios [6]. Novel design strategies (both from algorithmic and
technological points of view) are being considered to improve vehicle
positioning by integrating multiple onboard perception sensors [7, 8], side
information on the sensed environment [9] or exploiting V2X communication
technologies [10], rooted in 5G or beyond scenarios [11, 12, 13, 14, 15, 16].

Over the years, several positioning enhancements have been proposed to
overcome the GNSS degradation in urban environments. Among them, cooperative
algorithms based on centralized or distributed frameworks [17, 18, 19, 20, 21,
22] are gaining popularity as they improve vehicle positioning thanks to the
sharing of location-dependent information over V2X networks. Indeed, V2X links
allow aggregating the sensing information collected at multiple vehicles,
which act as mobile probes of a larger distributed sensing system with an
augmented view of the vehicular environment (compared to the ego vehicles)
that facilitates the detection of objects along roads [23].

###  I-A Related works

Cooperative localization algorithms for vehicular applications have been
proposed considering the exchange of GNSS [24, 25, 26] or other types of radio
measurements [27, 28, 29, 30, 31, 32, 33], and also with data fusion
approaches [34, 35, 36]. In [24], a cooperative localization framework is
proposed for correcting GNSS pseudoranges and improving the vehicle
positioning accuracy, while [25] integrates GNSS and measurements obtained
from Dedicated Short-Range Communications (DSRC) with a cubature Kalman
Filter. Authors in [26] analyze the theoretical performances of inter-vehicle
measurements extracted from GNSS observables. Besides GNSS-based solutions,
radio measurements can also be used for enhancing localization accuracy.
Methods exploiting angle measurements are proposed in [27, 28, 29], while [30,
31] use the multipath information available from the channel impulse response.
Other approaches, instead, focus on inter-distance measurements among vehicles
[32], or on the GNSS carrier phase [33]. Lastly, data fusion methods where
GNSS information and distances extracted from Ultra Wide Band (UWB) modules
are combined together are studied in [34, 35], whereas [36] combines distance
and angle measurements.

Besides relying on either GNSS, V2X radio measurements, or data fusion
approaches, cooperative localization systems can also be implemented by
exploiting imaging data coming from vehicle onboard perception sensors. A
fast-developing technology that has been shown to provide promising detection
and recognition capabilities for accurate environmental perception is LiDAR.
The integration of LiDAR sensors within cooperative positioning schemes is
therefore expected to bring significant advantages in terms of robustness and
accuracy. Despite the LiDAR potentials, few cooperative approaches based on
this technology have been studied [37, 38, 39, 40, 41, 42, 43, 44, 45]. The
works in [37, 38] investigate the association issue across multiple vehicles,
whereas [39] develops a decentralized cooperative localization method to fuse
LiDAR, GNSS and high-definition maps. In [40], a cooperative Simultaneous
Localization and Mapping (SLAM) approach is developed for vehicle pose
estimation, while [41] proposes a cooperative mapping technique to fuse
multiple LiDAR views into an improved unified map. Similarly, also [42]
develops a multi-vehicle cooperative scheme where vehicles share locally
processed maps to improve cooperative perception. Other studies focus on
collaborative Machine Learning (ML) methods where intermediate Neural Network
(NN) outputs are shared by vehicles [43, 44] and the road infrastructure [45].
Despite the competitive performances provided by the aforementioned methods,
they require the sharing of either raw or partially processed point clouds,
which may not be feasible for bandwidth-limited V2X applications, or they
assume the availability of maps, limiting their application in rural or poorly
visited areas.

In perception problems where passive, i.e., non-cooperative, targets are
present, algorithms handling Data association (DA) between measurements and
targets are needed. The pioneering Hungarian algorithm was proposed in [46]
for solving such problems. It was then extended and superseded by approaches
exploiting semantic information, which uniquely identifies the targets through
visual features, such as color, size, or movement patterns [47]. In case
measurements include only position-dependent parameters, such as distance or
angle, the association problem becomes non-trivial to be solved. Solutions
based on the Sum Product Algorithm (SPA) aim at efficiently computing the
marginal association probabilities through the use of message passing over
suitable factor graphs [48, 49], although they might suffer in case of cycle-
graphs and non-Gaussian noise models. To improve upon these limitations, some
works employ a double-loop algorithm, which forces the convergence of Gaussian
belief propagation, and non-walksummable models [50], which involve the use of
a preconditioner in an iterative method based on diagonal loading. Recent
works exploit the capabilities of NN over networks, also known as Message
Passing Neural Network (MPNN) [51, 52], which learn the correct association
directly from semantic data [38]. MPNNs can discern both linear and non-linear
relations between input and output data, they are time scalable similar to SPA
[53] and have demonstrated superior performance on loopy graphs, provided the
availability of sufficient training data [54, 55].

###  I-B Contributions

In this paper, we propose a novel data-driven cooperative localization method
for GNSS augmentation in connected driving scenarios and suited for both rural
and urban areas. The method builds on the Implicit Cooperative Positioning
(ICP) paradigm initially developed in [56] and later extended in [18] to
address DA. Compared to those former works that assumed point-like detections
obtained via generic sensing systems (e.g., LiDAR, camera, or radar), we here
introduce a data-driven framework for accurate environmental perception from
onboard LiDAR sensors at the vehicles. Furthermore, we also propose to solve
the DA problem via MPNNs to address the limitations of the SPA-based solution
in [18]. We refer to this proposed methodology as Cooperative LiDAR Sensing
with Message Passing Neural Network (CLS-MPNN).

In the proposed CLS-MPNN solution, each vehicle is equipped with a Deep Neural
Network (DNN), namely a 3D object detector, to efficiently process the LiDAR
point clouds so as to recognize and localize passive static objects in the
surroundings. Note that the proposed framework can easily accommodate other
types of sensors (e.g., cameras or radars) or multimodal solutions by properly
modifying the 3D object detectors. Poles are selected as reference objects to
be detected by vehicles as they are easily recognizable from the points
clouds, widespread on most roads, and fixed. Nevertheless, the proposed
framework is general enough to support other objects according to the scenario
(e.g., rural or urban environments). The individual detections made by the
vehicles are then exchanged with a centralized infrastructure, namely a Mobile
Edge Cloud (MEC), via Vehicle-To-Infrastructure (V2I) communications. The MEC
coherently combines the measurements provided by the vehicles by executing the
MPNN-based DA algorithm and then it runs the ICP method for refining both
objects and vehicle positions. We consider a MEC-centralized processing
architecture as it provides the highest performances and it can be implemented
at the road infrastructure, even if it has the drawback of being the critical
single point of failure of the system. The method is general enough to be
adapted to distributed architectures, following e.g., the approach in [18].

With respect to previous works that either rely on partially processed [43,
44, 45] or raw LiDAR sharing [40, 41], the proposed method foresees only the
exchange of the detected objects and vehicles positions, thereby substantially
limiting the communication overhead. Furthermore, the developed method does
not rely on maps of the driving environment, as in [39], making the
cooperative approach potentially applicable to any driving situation,
especially when high-definition maps are unavailable. The proposed solution
improves upon all our previous works, which provided an initial proof of
concept using only single-stage detectors [57, 58], or focused on studying the
DA problem alone [38, 37]. Herein, we provide a more complete and robust
solution that jointly addresses the DA problem and improves the localization
accuracy thanks to the cooperation among vehicles. Specifically, the main
contributions are as follows:

  * •

We embed the DA in a cooperative mechanism by extending the method in [38, 37]
to enable tracking over time.

  * •

We extend our frameworks in [37, 38, 57, 58] by integrating both single-stage
and double-stage 3D object detectors to provide a comprehensive cooperative
localization platform.

  * •

We introduce a comparison with state-of-the-art cooperative SLAM approaches to
show the benefits of the proposal in terms of positioning accuracy as well as
in reducing the communication overhead.

  * •

We study the generalization abilities of CLS-MPNN in new driving scenarios
where neither the 3D object detector nor the MPNN were trained on. Besides, we
also characterize the ability of CLS-MPNN to work with cheaper, lower-
resolution LiDAR sensors and its robustness against false alarms.

The overall goal is to provide the achievable performance of a cooperative
system that uses LiDAR sensing to detect static objects in the road
environment for vehicle positioning augmentation. For this reason, we assume
noisy detections neglecting false alarms or False Positives (i.e., undesired
objects that are either erroneously detected by the DNN model or generate
backscattering with high intensity). Experimental results show that CLS-MPNN
substantially outperforms an ego-vehicle positioning method based on GNSS
tracking for different traffic densities and LiDAR resolutions while
approaching the performances of an ideal cooperative LiDAR sensing system with
perfect DA that serves as a possible lower bound on the performances.
Additionally, the proposal is shown to be advantageous even when compared with
state-of-the-art cooperative SLAM algorithms and when the FPs are not removed.
Lastly, when testing is performed in a scenario different from the one used
for training, the cooperative approach still largely outperforms the ego GNSS
tracking one, even though more missed detections are observed.

The paper is organized as follows. Sec. II details the system model considered
throughout the paper. Sec. III presents the ML methods adopted for
environmental perception, while Sec. IV describes the Bayesian tracking
framework and the MPNN-based DA. Sec. V discusses potential implementation
challenges. Sec. VI highlights the performances of the 3D object detectors and
the MPNN, while Sec. VII presents the result characterizing the proposed
cooperative localization framework. Lastly, Sec. VIII draws conclusions.

(a)  (b)

Figure 1: Representation of vehicular sensing scenario with $N_{v}=3$ vehicles
and $N_{o}=9$ non-cooperative objects (poles). (a) Top view of a scenario
extracted from CARLA. (b) LiDAR point clouds captured by the vehicles.

##  II Vehicular scenario and models

In this section, we introduce the connected vehicular scenario and the main
assumptions used in the paper for the design of the cooperative localization
solution. More specifically, Sec. II-A defines the models for the vehicle
dynamics and the localization measurements available for cooperative
positioning refinement; whereas Sec. II-B presents the modeling of the DA
problem and the related variables.

###  II-A Localization model

The road scenario comprises a set $\mathcal{V}=\\{1,\ldots,N_{v}\\}$ of
$N_{v}$ vehicles moving over a 3D space. At discrete time $t$, each vehicle
$v\in\mathcal{V}$ is characterized by a 3D position
$\mathbf{u}_{v,t}^{(\text{V})}=[u_{v,x,t}^{(\text{V})}\,u_{v,y,t}^{(\text{V})}\,u_{v,z,t}^{(\text{V})}]^{\mathrm{T}}$
and a 3D velocity
$\mathbf{v}_{v,t}^{(\text{V})}=[v_{v,x,t}^{(\text{V})}\,v_{v,y,t}^{(\text{V})}\,0]^{\mathrm{T}}$,
which are collected into the time-varying state
$\mathbf{x}_{v,t}^{(\text{V})}=[\mathbf{u}_{v,t}^{{(\text{V})}^{\mathrm{T}}}\,\mathbf{v}_{v,t}^{{(\text{V})}^{\mathrm{T}}}]^{\mathrm{T}}$.
Additionally, each vehicle can establish a V2I communication link with a
centralized infrastructure, namely a MEC, for exchanging positioning and
sensing information. The vehicle state is assumed to evolve according to the
following first-order Markov model, namely the constant velocity [59]

$\mathbf{x}_{v,t}^{(\text{V})}=\mathbf{F}\mathbf{x}_{v,t-1}^{(\text{V})}+\mathbf{K}\mathbf{w}_{v,t-1}^{(\text{V})}\,,$
(1)

with
$\mathbf{F}\\!\\!=\\!\\![\mathbf{I}_{3},\\!T_{s}\mathbf{I}_{3};\\!\mathbf{0}_{3\times
3},\\!\mathbf{I}_{3}]$ and
$\mathbf{K}\\!\\!=\\!\\![0.5T_{s}^{2}\mathbf{I}_{2};\\!\mathbf{0}_{1\times
2};\\!T_{s}\mathbf{I}_{2};\\!\mathbf{0}_{1\times 2}]$, while
$\mathbf{w}_{v,t-1}^{(\text{V})}$ is a zero-mean Gaussian driving process
modeling the acceleration uncertainty with covariance
$\mathbf{Q}^{(\text{V})}_{v,t-1}=\sigma_{Q}^{2}\mathbf{I}_{2}$ and $T_{s}$ the
sampling interval. Besides vehicles, the scenario contains a set
$\mathcal{O}=\\{1,\ldots,N_{o}\\}$ of $N_{o}$ non-cooperative static objects
that can be detected by nearby vehicles. Ideally, ad-hoc objects should be
placed in the driving environment to facilitate their detection from the
imaging sensors of the vehicles. For this initial study, we select poles as
detectable objects since they are extremely common, easily recognizable and
fixed. Each pole is described by a position state
$\mathbf{x}_{k,t}^{(\text{O})}=[x_{k,x,t}^{(\text{O})}\,x_{k,y,t}^{(\text{O})}\,x_{k,z,t}^{(\text{O})}]^{\mathrm{T}}$
here assumed to be time-invariant:
$\mathbf{x}_{k,t}^{(\text{O})}=\mathbf{x}_{k,t-1}^{(\text{O})}$. A
visualization of a portion of the scenario from the software used for
simulation, i.e., CARLA [60], is provided in Fig. 1.

The vehicles are able to estimate their own position using navigation units,
e.g., GNSS, which are assumed to be always available. The GNSS measurement at
vehicle $v$ is modeled as

$\boldsymbol{\rho}_{v,t}^{(\text{V})}=\mathbf{T}\mathbf{x}_{v,t}^{(\text{V})}+\mathbf{n}_{v,t}^{(\text{V})}\,,$
(2)

where $\mathbf{T}=[\mathbf{I}_{2}\,\mathbf{0}_{2\times 4}]$, while
$\mathbf{n}_{v.t}^{(\text{V})}$ is a zero-mean Gaussian measurement error with
covariance
$\mathbf{R}_{v,t}^{(\text{V})}=\sigma_{\text{P}}^{(\text{V})^{2}}\mathbf{I}_{2}$
with $\sigma_{\text{P}}^{(\text{V})}$ denoting the GNSS position accuracy.

Each vehicle is also able to detect possible objects present in the
surroundings via LiDAR sensors. Specifically, the point cloud
$\mathbf{P}_{v,t}$ captured at time $t$ by vehicle $v$ is processed by a 3D
object detector, whose task is to generate a candidate set of bounding boxes
physically encapsulating the detected poles. Such set is denoted as
$\mathcal{O}_{v,t}=\\{k\in\mathcal{O}:\|\mathbf{u}_{v,t}^{(\text{V})}-\mathbf{x}_{k,t}^{(\text{O})}\|\leq
R_{s}\\}\subseteq\mathcal{O}$ with cardinality $|\mathcal{O}_{v,t}|$, where
$R_{s}$ is the LiDAR sensing range (here assumed to be equal for all
vehicles).

The 3D object detector provides two different types of measurements. The first
one refers to the 3D position of the bounding boxes’ centroids and is given by

$\displaystyle\boldsymbol{\rho}_{v,t}^{\text{(O)}}=\\{\boldsymbol{\rho}_{v,k,t}^{\text{(O)}}\\}_{k=1}^{|\mathcal{O}_{v,t}|},$
(3)

where $\boldsymbol{\rho}_{v,k,t}^{\text{(O)}}$, with
$k=1,\ldots,|\mathcal{O}_{v,t}|$, denotes the distance between the $k$-th
bounding box center and the $v$-th vehicle position at time $t$. The second
one, instead, represents the detected poles as a collection of eight corners

$\mathbf{z}_{v,t}^{\text{(O)}}=\left\\{\mathbf{z}_{v,k,t}^{\text{(O)}}\right\\}_{k=1}^{|\mathcal{O}_{v,t}|}=\left\\{\left[\mathbf{z}_{v,k,c,t}^{\text{(O)}}\right]_{c=1}^{8}\right\\}_{k=1}^{|\mathcal{O}_{v,t}|}\,,$
(4)

where $\mathbf{z}_{v,k,c,t}^{\text{(O)}}$ represents the 3D coordinate of a
corner point. We specifically represent objects as bounding boxes as they can
be easily obtained from the output provided by the 3D object detector (as
highlighted in Sec. III). Note that other choices can still be used by
converting the output of the 3D object detectors in an appropriate format. For
DA purposes, we also define the sets of estimated absolute locations of the
centroids and the bounding box corners as

$\displaystyle\overline{\boldsymbol{\rho}}_{v,t}^{\text{(O)}}$
$\displaystyle=\left\\{\overline{\boldsymbol{\rho}}_{v,k,t}^{\text{(O)}}\right\\}_{k=1}^{|\mathcal{O}_{v,t}|}=\left\\{\boldsymbol{\rho}_{v,k,t}^{\text{(O)}}+\widehat{\mathbf{u}}_{v,t}^{(\text{V})}\right\\}_{k=1}^{|\mathcal{O}_{v,t}|}\,,$
(5) $\displaystyle\overline{\mathbf{z}}_{v,t}^{\text{(O)}}$
$\displaystyle=\left\\{\overline{\mathbf{z}}_{v,k,t}^{\text{(O)}}\right\\}_{k=1}^{|\mathcal{O}_{v,t}|}=\left\\{\left[\mathbf{z}_{v,k,c,t}^{\text{(O)}}\right]_{c=1}^{8}+\widehat{\mathbf{u}}_{v,t}^{(\text{V})}\right\\}_{k=1}^{|\mathcal{O}_{v,t}|}\,,$
(6)

where $\widehat{\mathbf{u}}_{v,t}^{(\text{V})}$ is the predicted position of
vehicle $v$ at time $t$ from its previous state estimate
$\widehat{\mathbf{x}}_{v,t-1}^{(\text{V})}$ according to the motion model in
(1). The definition of the sets (5)-(6) is required to enable the coherent
fusion of the detected objects across vehicles by performing the DA step in a
common reference system. Specifically, set
$\overline{\mathbf{z}}_{v,t}^{\text{(O)}}$ is useful for solving the DA
problem as it represents the bounding boxes accounting for both orientation
and dimension. By contrast, set
$\overline{\boldsymbol{\rho}}_{v,t}^{\text{(O)}}$ enables to estimate the
absolute position $\widehat{\mathbf{x}}_{o,t}^{(\text{O})}$ of each object
$o\in\mathcal{O}_{v,t}$.

###  II-B Data association model

A fundamental step required to coherently aggregate the bounding box
measurements generated by each vehicle is the DA, which enables the
identification of bounding boxes relating to the same object across multiple
vehicles. This operation is typically affected by several errors. Examples
include the intrinsic error on the point clouds (in the order of centimeters),
the error introduced by the object detection process (for some reference
values please see the analysis provided in Sec. VI), and the accuracy of the
onboard positioning system (e.g., GNSS), which represents the highest source
of error (in the order of meters).  Overall, the combination of these noise
sources makes solving the DA problem non-trivial. To address these
shortcomings, we propose to employ MPNNs, as detailed hereafter.

Given the set
$\mathcal{Z}_{t}=\bigcup_{v=1}^{N_{v}}\overline{\mathbf{z}}_{v,t}^{(\text{O})}$
comprising all the bounding box corners generated by all vehicles at time $t$,
the MPNN input is modeled starting from $\mathcal{Z}_{t}$ so as to obtain a
directed graph $\mathcal{G}=(\mathcal{N},\mathcal{E})$, where $\mathcal{N}$
and $\mathcal{E}$ are the sets of nodes and edges, respectively. The graph
$\mathcal{G}$ is obtained via a mapping function
$\Phi_{t}:\mathcal{N}\rightarrow\mathcal{Z}_{t}\times\mathcal{V}$ such that
each bounding box $k=1,\dots,|\mathcal{O}_{v,t}|$ of vehicle $v$ is associated
to a graph node $n\in\mathcal{N}$, while the edge $(n,m)\in\mathcal{E}$, with
$n\neq m$, denotes a potential association between the bounding boxes encoded
by nodes $n$ and $m$. Additionally, we introduce the association variable
$\mathtt{a}_{n\to m}\in\\{0,1\\}$, where $\mathtt{a}_{n\to m}=1$ denotes the
existence of the edge $(n,m)$, or equivalently that the bounding boxes
associated with nodes $n$ and $m$ refer to the same object, while
$\mathtt{a}_{n\to m}=0$ indicates that no edge exists between nodes $n$ and
$m$. The goal of the MPNN is to infer the association variables
$\widehat{\mathtt{a}}_{n\to m}\in\\{0,1\\}$ by considering all the potential
bounding box combinations for all vehicles. To avoid associating two (or more)
bounding boxes estimated by the same vehicle, we impose
$\widehat{\mathtt{a}}_{n\to m}=0$ whenever the mappings $\Phi_{t}(n)$ and
$\Phi_{t}(m)$ refer to the same vehicle.

Besides the measurement-to-measurement association variable $\mathtt{a}_{n\to
m}$, we also define the binary vector
$\boldsymbol{\alpha}_{t}=[\alpha_{v,o,t}]_{v\in\mathcal{V},o\in\mathcal{O}_{t}}$
collecting all the measurement-to-object association variables of all vehicles
at time $t$, where $\mathcal{O}_{t}=\bigcup_{v=1}^{N_{v}}\mathcal{O}_{v,t}$ is
the set of indexes of all detected objects at time $t$. Given the output of
the MPNN, another step is required to pair the (associated) measurements with
the objects and obtain an estimate of the measurement-to-object association
variable $\widehat{\boldsymbol{\alpha}}_{t}$. This step will be detailed in
Sec. IV-A.

##  III Deep learning-based lidar sensing

In this section, we detail the strategies used for enabling each vehicle to
perceive the driving environment. In particular, Deep Learning (DL)-based 3D
object detectors are used to efficiently process the LiDAR point clouds and
obtain the position of the static objects in the vehicles’ surroundings. Given
the ego-vehicle LiDAR data, the 3D object detectors provide at the output a
set $\mathscr{B}=\\{1,\ldots,N_{B}\\}$ of $N_{B}$ candidate bounding boxes
physically encapsulating the detected objects. Each bounding box is compactly
described as
$\widehat{\mathbf{b}}_{j}=[\widehat{\mathbf{u}}_{j}^{(\text{B})}\,\widehat{\mathbf{d}}_{j}\,\widehat{\gamma}_{j}]^{\mathrm{T}}$
with $j=1,\dots,N_{B}$, where
$\widehat{\mathbf{u}}_{j}^{(\text{B})}~{}=~{}[\widehat{u}_{x,j}^{(\text{B})}\,\widehat{u}_{y,j}^{(\text{B})}\,\widehat{u}_{z,j}^{(\text{B})}]$
is the estimated object’s centroid,
$\widehat{\mathbf{d}}_{j}=[\widehat{\ell}_{j}\,\widehat{w}_{j}\,\widehat{h}_{j}]$
contains the object’s dimensions, namely the length, width and height, while
$\widehat{\gamma}_{j}$ is the yaw angle. The outputs provided by the detectors
can then be suitably converted to obtain the measurements defined in (3)-(4).
Besides, each bounding box is associated with a score probability, ranging
from 0 up to 1, that indicates the (soft) confidence of the detector. Herein,
we assume that all bounding boxes provided by the 3D object detectors refer
only to poles present in the driving environment, namely all FPs are filtered
out. Nevertheless, the score probability can be used to suppress the FPs as
analyzed in Sec. VII-A.

To design the cooperative localization framework, we employ two state-of-the-
art 3D object detection methods with increasing complexity, namely
PointPillars and Part-$\text{A}^{2}$ that are based on the single-stage and
double-state paradigms, respectively [61]. In the following, we initially
describe the inner workings of PointPillars (Sec. III-A) and then present the
Part-$\text{A}^{2}$ method (Sec. III-B).

###  III-A PointPillars

PointPillars is a single-stage object detector that processes the input point
cloud and extracts important features organized in pillars through the
employment of PointNet [62] modules. The encoded features are then processed
by a standard Region Proposal Network (RPN) to obtain the final predictions.
In the following, we explain its inner working principles.

Starting from a single-vehicle point cloud
$\mathbf{P}=[\mathbf{p}_{1}\cdots\mathbf{p}_{N_{\ell
p}}]^{\mathrm{T}}\triangleq\mathbf{P}_{v,t}$111 We remove the dependency on
the vehicle and time indexes to simplify the disclosure in this section.of
$N_{\ell p}$ points, PointPillars converts it into an image-based
representation. Specifically, $\mathbf{P}$ is discretized into an evenly-
spaced $x$-$y$ grid of $\mathcal{P}$ non-empty pillars, each containing
$N_{p}$ points222This is done by padding pillars with zeros until they have
exactly $N_{p}$ points or randomly removing points from pillars having more
than $N_{p}$ points.. The output is then fed to a simplified PointNet
architecture as presented in [63] to obtain a 2D pseudo-image of size $C\times
H\times W$, with $C$, $H$ and $W$ denoting the number of channels, height and
width of the canvas, respectively. The pseudo-image is used by a RPN to
estimate the 3D bounding boxes. Specifically, the RPN is composed by a
backbone, whose task is to compute important features, and a detection head
that uses the backbone’s features to generate the final predictions. In
PointPillars, the Single Shot Detector (SSD) head with pre-defined anchor (or
prior) boxes is used. The matching strategy [64] used by PointPillars assigns
a positive match to the predicted bounding box having the highest 2D
Intersection over Union (IoU) with the ground-truth box or a
$\text{2D}\,\text{IoU}>0.5$. On the other hand, predicted boxes with
$\text{2D}\,\text{IoU}<0.35$ are deemed as negative samples. All other anchors
are ignored for the loss computation. During inference, an axis-aligned Non-
Maximum Suppression (NMS) stage [64] with an IoU threshold of 0.5 is applied
to filter out overlapping boxes that refer to the same object. Finally, the NN
parameters of PointPillars are updated according to the losses presented in
[63] using the same configuration parameters.

###  III-B Part-$A^{2}$

Part-$A^{2}$ is a double-stage 3D object detector that introduces the concept
of intra-object part estimation and aggregation. It extends PointRCNN [65] to
concurrently learn segmentation masks for discerning foreground points,
classify their position inside the bounding box and generate 3D proposals,
i.e., rough bounding box estimates. The proposals are then fed into a part-
aggregation network that generates the final predictions, exploiting also the
intra-object part information produced in the preceding stage. Note that we
use in our experiments the Part-$\text{A}^{2}$-Anchor, which uses prior boxes
for the proposal generation process. In the following, we briefly describe the
overall architecture and how the bounding boxes are estimated.

In contrast to PointPillars, Part-$\text{A}^{2}$ process the single-vehicle
point cloud $\mathbf{P}$ using voxelization. In particular, a regular 3D grid
is computed starting from $\mathbf{P}$, and the points associated with each
grid point are grouped and averaged, leading to a new point cloud
representation. Then, a UNet-based encoder-decoder [66] segments the
foreground points, i.e., points belonging to the ground truth bounding boxes,
from all the other points. Concurrently, an additional module is responsible
for learning the intra-object part information. Then, a RPN is appended for
generating the 3D proposals (with pre-defined prior boxes). The matching
strategy uses bounding boxes with $\text{3D}\,\text{IoU}>0.5$ as positive
anchors, while boxes having $\text{3D}\,\text{IoU}<0.35$ are deemed as
negative. All other proposals are neglected during loss computation. After
this step, only $64$ positive and $64$ negative anchor boxes are retained for
further refinement.

Once the proposals have been generated, a second network is responsible for
improving the detection accuracy. This module takes as input the intra-object
part locations estimated before, together with the proposals and the
associated learned features, and refines the estimated bounding boxes. At
first, the points falling within each proposal are transformed into a
canonical coordinate system where the $x$ and $y$ axes are approximately
parallel to the ground plane, while the $z$ axis is the same as the input
point cloud. This reduces the impact of different rotation angles and
locations of the proposals, leading to a better bounding box regression. Then,
a Region of Interest (RoI)-aware pooling strategy is used to aggregate the
features produced during the previous stage as in [67]. Finally, the pooled
features are fed to sparse convolutional layers whose outputs are used by two
separate branches for bounding box regression and classification. The
confidence scores are assigned by a 3D IoU guided scoring strategy [67]. A
confidence of 0 is assigned to boxes having $\text{3D}\,\text{IoU}<0.25$,
while for boxes with $\text{3D}\,\text{IoU}>0.75$ the confidence is set to 1.
In all other cases, the confidence is computed as $2\text{IoU}-0.25$. During
inference, a rotational NMS strategy with IoU threshold of 0.7 is applied to
filter out overlapping boxes that refer to the same object.
Part-$\text{A}^{2}$ is trained in an end-to-end manner by exploiting the
losses presented in [67].

Both DNN detectors are trained in a centralized manner and then deployed at
the vehicles. In this way, each vehicle $v$ can estimate the bounding boxes
from the point cloud $\mathbf{P}_{v,t}$ and obtain the corresponding sets
$\boldsymbol{\rho}_{v,t}^{\text{(O)}}$ and $\mathbf{z}_{v,t}^{\text{(O)}}$.

##  IV Cooperative lidar positioning

LiDAR point cloudGNSSDNN modelDNN modelDNN model measurement aggregation at
vehicle measurement aggregation at vehicle measurement aggregation at vehicle
MEC data aggregationData associationCooperative Bayesian localization
Vehicle/object state estimate Vehicle/object state prediction Figure 2: Block
scheme of the proposed CLS-MPNN localization framework. Each vehicle processes
its local LiDAR point cloud via 3D object detectors to localize passive
objects. The GNSS and the bounding box measurements are aggregated and shared
with the MEC, which performs DA and cooperatively tracks both objects and
vehicle states.

In this section, we present the CLS-MPNN localization framework employed for
cooperatively localizing both objects and vehicles and tracking their states
across time. Sec. IV-A introduces the Bayesian tracking solution, then we
describe how the DA problem is addressed. In particular, we solve the DA
problem in two steps: the first one enables the estimation of the measurement-
to-measurement association variable via the MPNN (Sec. IV-B), while the second
one estimates the measurement-to-target associations (Sec. IV-C). The overall
block scheme of the CLS-MPNN positioning framework is summarized in Fig. 2.

###  IV-A Bayesian tracking solution

We assume that at each time $t$ all vehicles $v\in\mathcal{V}$ are able to
send to the road infrastructure via V2I links their position measurements
$\boldsymbol{\rho}_{v,t}^{\text{(V)}}$ together with the sets
$\mathbf{z}_{v,t}^{\text{(O)}}$ and $\boldsymbol{\rho}_{v,t}^{\text{(O)}}$ of
detected poles. The MEC is then in charge of cooperatively tracking the state
evolution of the vehicles and the objects over consecutive time instants. To
do so, we resort to a Bayesian approach where we are interested in computing
the joint posterior probability density function (pdf) of vehicles and
objects, namely
$p(\boldsymbol{\theta}_{t}|\boldsymbol{\rho}_{1:t}^{(\text{V})},\boldsymbol{\rho}_{1:t}^{(\text{O})})$,
where
$\boldsymbol{\theta}_{t}=[\mathbf{x}_{t}^{(\text{V})^{\text{T}}}\,\mathbf{x}_{t}^{(\text{O})^{\text{T}}}]^{\text{T}}$
collects all the vehicles $\mathbf{x}_{t}^{(\text{V})}$ and object
$\mathbf{x}_{t}^{(\text{O})}$ states, while
$\boldsymbol{\rho}_{1:t}^{(\text{V})}$ and
$\boldsymbol{\rho}_{1:t}^{\text{(O)}}$ aggregate all the measurements
$\boldsymbol{\rho}_{v,t}^{(\text{V})}$ and
$\boldsymbol{\rho}_{v,t}^{\text{(O)}}$, respectively, of all vehicles up to
time $t$. The overall state can be then estimated using the Minimum Mean
Square Error (MMSE) criterion, leading to

$\widehat{\boldsymbol{\theta}}_{t}=\int\boldsymbol{\theta}_{t}\,p(\boldsymbol{\theta}_{t}|\boldsymbol{\rho}_{1:t}^{(\text{V})},\boldsymbol{\rho}_{1:t}^{(\text{O})})\,\mathrm{d}\boldsymbol{\theta}_{t}\,.$
(7)

Such estimation process entails computing
$p(\boldsymbol{\theta}_{t}|\boldsymbol{\rho}_{1:t}^{(\text{V})},\boldsymbol{\rho}_{1:t}^{(\text{O})})$,
which needs to be evaluated after the DA is resolved. By conditioning with
respect to the association variable $\boldsymbol{\alpha}_{t}$, the posterior
is rewritten as

$\displaystyle
p(\boldsymbol{\theta}_{t}|\boldsymbol{\rho}_{1:t}^{(\text{V})},\boldsymbol{\rho}_{1:t}^{\text{(O)}})=\sum_{\boldsymbol{\alpha}_{t}}p(\boldsymbol{\theta}_{t}|\boldsymbol{\alpha}_{t},\boldsymbol{\rho}_{1:t}^{(\text{V})},\boldsymbol{\rho}_{1:t}^{\text{(O)}})\,p(\boldsymbol{\alpha}_{t}|\boldsymbol{\rho}_{1:t}^{(\text{V})},\boldsymbol{\rho}_{1:t}^{\text{(O)}})\,.$
(8)

where
$p(\boldsymbol{\theta}_{t}|\boldsymbol{\alpha}_{t},\boldsymbol{\rho}_{1:t}^{(\text{V})},\boldsymbol{\rho}_{1:t}^{\text{(O)}})$
is evaluated according to the mathematical formulation in [18], while
$p(\boldsymbol{\alpha}_{t}|\boldsymbol{\rho}_{1:t}^{(\text{V})},\boldsymbol{\rho}_{1:t}^{\text{(O)}})$
is obtained by solving the DA. Specifically, we split the computation of
$p(\boldsymbol{\alpha}_{t}|\boldsymbol{\rho}_{1:t}^{(\text{V})},\boldsymbol{\rho}_{1:t}^{\text{(O)}})$
into two steps. The first one uses the MPNN to pair bounding boxes
hypothesized to refer to the same object while the second evaluates the
measurement-to-target association, providing as output the pdf
$p(\boldsymbol{\alpha}_{t}|\boldsymbol{\rho}_{1:t}^{(\text{V})},\boldsymbol{\rho}_{1:t}^{\text{(O)}})$,

###  IV-B Measurement-to-measurement association

The MPNN takes as input the pole measurements $\mathbf{z}_{v,t}^{\text{(O)}}$
and $\boldsymbol{\rho}_{v,t}^{\text{(O)}}$, and constructs the input graph
$\mathcal{G}$ as detailed in Sec. II-B. The aim of the MPNN is to learn the
correct association among the pole measurements by operating on the graph
$\mathcal{G}$ with an iterative message passing scheme. The overall process is
composed by $I$ message passing iterations and for each iteration
$i~{}=~{}1,\dots,I$ the node and edge embeddings, denoted as
$\mathbf{h}_{n}^{(i)}$ and $\mathbf{m}_{n\to m}^{(i)}$, are used to spread the
information throughout $\mathcal{G}$. More specifically, at iteration $i=0$,
the node and edge embeddings are initialized as

$\displaystyle\mathbf{m}_{n\to m}^{(0)}$
$\displaystyle=g_{\text{e}}^{\text{enc}}\left(\overline{\mathbf{z}}_{v,k,1,t}^{\text{(O)}}-\overline{\mathbf{z}}_{v^{\prime},k^{\prime},1,t}^{\text{(O)}},\overline{\mathbf{z}}_{v,k,8,t}^{\text{(O)}}-\overline{\mathbf{z}}_{v^{\prime},k^{\prime},8,t}^{\text{(O)}}\right)\,,$
$\displaystyle\forall(n,m)\in\mathcal{E}:\Phi_{t}(n)=\\{k,v\\}\land\Phi_{t}(m)=\\{k^{\prime},v^{\prime}\\},v\neq
v^{\prime},$ (9) $\displaystyle\mathbf{h}_{n}^{(0)}$
$\displaystyle=g_{\text{n}}^{\text{enc}}\left(\overline{\mathbf{z}}_{v,k,t}^{\text{(O)}}\right)\,,\quad\forall
n\in\mathcal{V}:\Phi_{t}(n)=\\{k,v\\},$ (10)

where, $g_{\text{n}}^{\text{enc}}(\cdot)$ and
$g_{\text{e}}^{\text{enc}}(\cdot)$ are two Multi Layer Perceptrons at the node
and edge, respectively, whose goal is to extract the feature embeddings from
the bounding boxes. The MPNN then further encodes the node and edge embeddings
using three additional MLPs at each node, namely $g_{\text{n}}(\cdot)$,
$g_{\text{n}}^{\text{out}}(\cdot)$ and $g_{\text{n}}^{\text{in}}(\cdot)$,
while an additional MLP $g_{\text{e}}(\cdot)$ is used at each edge. The role
of each MLP is detailed in [38]. At iteration $i$, the MLP at each edge is
used to update the edge embeddings as

$\mathbf{m}_{n\to
m}^{(i)}=g_{\text{e}}\left(\mathbf{h}_{n}^{(i-1)},\mathbf{h}_{m}^{(i-1)},\mathbf{m}_{n\to
m}^{(i-1)}\right)\,,\ \forall m~{}\in~{}\mathcal{N}_{n}\,,$ (11)

where $\mathcal{N}_{n}$ is the set of neighbors of node
$n~{}\in~{}\mathcal{V}$, while the node embeddings are updated as

$\mathbf{h}_{n}^{(i)}=g_{\text{n}}\left(\sum_{m~{}\in~{}\mathcal{N}_{n}}\mathbf{m}_{m\to
n}^{\text{in},(i)},\sum_{m~{}\in~{}\mathcal{N}_{n}}\mathbf{m}_{n\to
m}^{\text{out},(i)}\right),$ (12)

where

$\displaystyle\mathbf{m}_{m\to n}^{\text{in},(i)}$
$\displaystyle=g_{\text{n}}^{\text{in}}\left(\mathbf{h}_{i}^{(i-1)},\mathbf{m}_{m\to
n}^{(i)}\right)\,,\quad$ $\displaystyle\forall m~{}\in~{}\mathcal{N}_{n},$
(13)

and

$\displaystyle\mathbf{m}_{n\to m}^{\text{out},(i)}$
$\displaystyle=g_{\text{n}}^{\text{out}}\left(\mathbf{h}_{n}^{(i-1)},\mathbf{m}_{n\to
m}^{(i)}\right)\,,\quad$ $\displaystyle\forall m~{}\in~{}\mathcal{N}_{n}.$
(14)

are the incoming and outgoing edge embeddings, respectively.

This procedure is repeated for $I$ message passing iterations and the
association variable $\widehat{\mathtt{a}}_{n\to m}$ is obtained by applying a
thresholding operation (with threshold $\Gamma$) to the output of an edge
classifier, called $g_{\text{e}}^{\text{class}}(\cdot)$, operating over the
edge embeddings as $\widehat{\mathtt{a}}_{n\to
m}^{(I)}=g_{\text{e}}^{\text{class}}\left(\mathbf{m}_{n\to
m}^{(I)}\right)\geq\Gamma$. Other strategies can be used for obtaining
$\widehat{\mathtt{a}}_{n\to m}^{(I)}$, such as the Hungarian algorithm. Table
I summarizes the layers used by each encoder in the MPNN architecture. Note
that after each linear layer, a dropout operation and a ReLU activation
function are added.

The MPNN is trained using a weighted binary cross-entropy loss computed after
each iteration $i$ as

$\displaystyle\mathcal{L}_{\text{MPNN}}=$
$\displaystyle\frac{-1}{|\mathcal{E}|}\sum_{i=1}^{I}\sum_{(n,m)~{}\in~{}\mathcal{E}}\\!\\!\\!\\!(1-{\mathtt{a}}_{n\to
m})\text{log}(1-\widehat{\mathtt{a}}_{n\to m}^{(i)})$
$\displaystyle+w\,{\mathtt{a}}_{n\to m}\text{log}(\widehat{\mathtt{a}}_{n\to
m}^{(i)})\,,$ (15)

where $w$ is a weight given to the positive class to compensate for the class
unbalances, which is computed as the ratio between the number of 0-class and
1-class edges.

TABLE I: MPNN architecture $g_{n}^{(enc)}$ | $g_{e}^{(enc)}$ | $g_{n}$ | $g_{e}$ | $g_{e}^{(class)}$ | $g_{e}^{(in)}=g_{e}^{(out)}$
---|---|---|---|---|---
Layer type | Output | Layer type | Output | Layer type | Output | Layer type | Output | Layer type | Output | Layer type | Output
Input | $24\times 1$ | Input | $6\times 1$ | Input | $64\times 1$ | Input | $96\times 1$ | Input | $16\times 1$ | Input | $48\times 1$
Linear | $72\times 1$ | Linear | $18\times 1$ | Linear | $32\times 1$ | Linear | $80\times 1$ | Linear | $8\times 1$ | Linear | $56\times 1$
Linear | $32\times 1$ | Linear | $18\times 1$ |  |  | Linear | $16\times 1$ | Sigmoid | $1\times 1$ | Linear | $32\times 1$
|  | Linear | $16\times 1$ |  |  |  |  |  |  |  |

###  IV-C Measurement-to-target association

Once the association variable $\widehat{\mathtt{a}}_{n\to m}$ is estimated, we
can distinguish which set of bounding boxes from different vehicles have been
generated by the same object. This is done by extracting the connected
components of the graph $\mathcal{G}$ with only the positive-classified edges,
i.e., $\widehat{\mathtt{a}}_{n\to m}^{(I)}>\Gamma$. We define with
$\mathcal{A}_{\widehat{o},t}=\\{(v,k):\Phi_{t}(n)=\\{k,v\\}\land\widehat{\mathtt{a}}_{n\to
m}^{(I)}>\Gamma\\}$ the set of vehicle-measurements tuples that are related to
the same target with unknown identification $\widehat{o}$. The goal now is to
associate each $\widehat{o}$ to the indexes $o\in\mathcal{O}_{t-1}$.

From the mean of the associated bounding boxes, we estimate the object
position by computing the centroid averaging over the eight corners as

$\widehat{\mathbf{x}}_{\widehat{o},t}^{\text{(O)}}=\dfrac{1}{8\,|\mathcal{A}_{\widehat{o},t}|}\sum_{c=1}^{8}\sum_{(v,k)\in\mathcal{A}_{\widehat{o},t}}\overline{\mathbf{z}}_{v,k,c,t}^{(O)}\,,\quad\forall\,\widehat{o}.$
(16)

Motivated by the fact that $\widehat{\mathbf{x}}_{\widehat{o},t}^{\text{(O)}}$
holds a good approximation of the real bounding boxes positions, we solve this
second association step by setting $\alpha_{v,o,t}=1$ according to the maximum
likelihood criterion over the distance
$d_{\widehat{o},o,t}=\|\widehat{\mathbf{x}}_{\widehat{o},t}^{\text{(O)}}-\widehat{\mathbf{x}}_{o,t-1}^{(\text{O})}\|_{2}$,
constrained to $d_{\widehat{o},o,t}<\Delta$, being $\Delta$ a given threshold.
Otherwise, $\alpha_{v,o,t}=0$ indicates the detection of a newly-observed
object.

##  V Implementation aspects

This section highlights potential challenges that can arise in the
implementation of the proposed cooperative approach in real systems.
Specifically, we discuss about the limitations of LiDAR sensors in Sec. V-A,
while in Sec. V-B we detail strategies to limit the impact of inaccurate
synchronization, network reliability and signal interference. Privacy and
security issues are covered in Sec. V-C.

###  V-A LiDAR sensing technology limitations

Despite the highly-accurate environmental sensing, LiDAR sensors are impaired
by noise, occlusion, and adverse weather conditions that require specific
countermeasures. For example, ML-based methodologies could be designed to
reduce the point cloud noise (see e.g., [68]). Similarly, data-driven
strategies could be utilized to predict objects that are partially occluded
(see e.g., [69]), reducing the degradation due to blockage. Under rain, fog,
or snow conditions, the environmental sensing obtained by LiDAR may not be
sufficiently accurate, and the integration of multiple imaging sensors (e.g.,
camera, radar, and LiDAR) is suggested to provide a reliable localization
system under all weather conditions (for example, by drawing inspiration from
[70]).

###  V-B Synchronization, network reliability and signal interference

The performance of our cooperative localization system can be degraded by the
impairments of the communication channel such as poor synchronization,
communication delays, unreliable networks, and signal interference. All these
aspects need to be handled by dedicated protocols or processing strategies. In
particular, synchronization between vehicles and the road infrastructure could
be guaranteed by dedicated protocols, such as the Precision Time Protocol
version 2 (PTPv2) [71], or by using synchronization signals extracted from the
onboard GNSS receivers of the vehicles. Communication delays introduced by the
network must be handled by temporally realigning the measurements received by
the infrastructure as discussed in [56]. Alternatively, the asynchronicity of
measurements can be statistically accounted for within the tracking algorithm
[72]. For what concerns unreliable networks, vehicles could implement
retransmission schemes or the infrastructure could modify the fusion strategy
to take into account packet drops. Signal interference among connected
vehicles could be reduced by introducing ad-hoc scheduling strategies [73] or
resource allocation policies [74].

###  V-C Privacy and security considerations

From a privacy and security perspective, the proposed approach could leak
information about the area where vehicles are currently located. This may be
inferred from the information sent by the vehicles to the MEC. Additionally,
unauthorized entities are able to tamper with the communications to modify the
exchanged vehicles and/or object positions, jeopardizing the CLS-MPNN
positioning performances. All these situations must be avoided by introducing
ad-hoc security schemes. For example, the communication can be encrypted by
adopting blockchain technologies as discussed in [75]. On the other hand, the
impact of malicious vehicles entering the cooperative process can be limited
by employing authentication protocols [76].

##  VI Neural networks training and evaluation

This section details the strategies adopted for training the LiDAR-based 3D
object detectors and the MPNN and their respective performances. In
particular, Sec. VI-A provides the results obtained by the 3D object
detectors, while Sec VI-B focuses on the MPNN DA performances.

###  VI-A LiDAR-based object detection

This section focuses on the evaluation of the detection performances of
PointPillars and Part-$\text{A}^{2}$. We are interested in characterizing
their ability to correctly estimate the bounding boxes of the poles from the
LiDAR point clouds to evaluate the overall error introduced by the detection
process while assuming the vehicle position to be exactly known.

For training the 3D object detectors, we generated a synthetic dataset from
CARLA [60], an advanced driving simulator that allows flexible configuration
of realistic vehicular layouts and sensor specifications. The dataset is
collected in the urban map Town02 of CARLA, that spans roughly a
$200\\!\times\\!200$ $\text{m}^{2}$ area, where a single LiDAR-equipped
vehicle moves in the environment for 5000 timestamps sampled at $T_{s}=0.2$ s.

The LiDAR sensor is placed on the roof of the vehicle and is configured to
have 64 planes covering an elevation angle between $-25$° and $15$°, a sensing
range of $70$ m and to output 1 million point clouds per second, on average,
with a $\pm 2$ cm accuracy. For a more realistic simulation, we randomly
remove $20\%$ of the points for each captured frame and apply an additional
dropping strategy where points having a reflectance value $r_{j}<0.8$ are
randomly dropped. The ground truth data consists of 3D bounding boxes
physically enclosing the poles for each captured LiDAR frame. Note that we
consider only ground-truth boxes with at least 10 points inside. The
performances of the object detector are evaluated over a held-out portion of
the dataset composed by $1000$ examples, while the remaining $4000$ ones are
used for training.

Both detectors are implemented relying on the open-source repository in [77].
PointPillars is configured to have $\mathcal{P}=16000$ pillars of $N_{p}=32$
points each, while the output image dimensions obtained after scattering back
the learned features are set to $C=64$, $H=432$ and $W=496$. On the other
hand, Part-$\text{A}^{2}$ utilizes 16000 voxels. The prior boxes width,
length, and height are selected as 1.1 m, 1.1 m, and 7.67 m, respectively, for
both detectors. PointPillars is trained over $160$ epochs with batches of $6$
examples using an Adam optimizer [78] with learning rate $\eta=0.01$, momentum
parameters $\beta_{1}=0.95$ and $\beta_{2}=0.85$, and a weight decay factor of
0.01. A cosine annealing strategy [79] without warm restarts is used to
schedule the learning rate. Similarly, Part-$\text{A}^{2}$ is trained using
the same optimizer and learning rate scheduler but considering a maximum
number of epochs of $80$ and with a batch size of $2$ examples.

Data augmentation strategies are used to improve the performances of both
detectors. During training, each point cloud is augmented by applying a random
rotation of [-90°, +90°], a random scaling of [0.95,1.05], and a random
horizontal flip. Additionally, ground-truth sampling [80] is used, where at
most $10$ bounding boxes are added to each point cloud example. For
Part-$\text{A}^{2}$, an additional augmentation strategy is adopted, whereby
the ground-truth sampling is applied by adding noise to the bounding boxes.
Specifically, two types of noise are considered: a translational noise which
moves the bounding box on the horizontal plane, and a rotational noise, which
adds a random rotation in the interval [-45°, +45°].

As performance metric we use the Average Precision (AP) as presented in [81].
For object detection tasks, the AP requires the computation of the IoU to
discern positive and negative predictions. Given a pair
$\\{\mathbf{b}_{j},\widehat{\mathbf{b}}_{j}\\}$ of ground-truth and predicted
bounding boxes, the IoU is the ratio of the volume of the intersection and the
volume of the union between $\mathbf{b}_{j}$ and $\widehat{\mathbf{b}}_{j}$.
Thus, the IoU is

$\text{IoU}(\mathbf{b}_{j},\widehat{\mathbf{b}}_{j})~{}=~{}\dfrac{\text{volume}(\mathbf{b}_{j}\cap\widehat{\mathbf{b}}_{j})}{\text{volume}(\mathbf{b}_{j}\cup\widehat{\mathbf{b}}_{j})}\,,$
(17)

and $\widehat{\mathbf{b}}_{j}$ is deemed as positive if the IoU is greater
than a threshold $\varepsilon$. The AP is evaluated considering two recall
levels $L=11$ and $L~{}=~{}40$ as recently suggested in [82].

As an additional performance metric, we evaluate the localization error of the
predicted bounding boxes with respect to the ground truths, neglecting any
FPs. We consider the centroid of the bounding box to assess how accurate and
precise are the predictions with respect to the ground truths. For this
purpose, we evaluate the Circular Error Probable (CEP) at $9$5% confidence of
the location error cumulative distribution function (CDF) over each axis
separately. Both performance metrics are evaluated on the validation dataset.

TABLE II: 3D object detection performance Detector | $\text{AP}_{\text{BEV}}$ | $\text{AP}_{\text{3D}}$
---|---|---
$L~{}\\!=\\!~{}11$ | $L~{}\\!=\\!~{}40$ | $L~{}\\!=\\!~{}11$ | $L~{}\\!=\\!~{}40$
$\varepsilon~{}\\!=\\!~{}0.25$ | $\varepsilon~{}\\!=\\!~{}0.50$ | $\varepsilon~{}\\!=\\!~{}0.70$ | $\varepsilon~{}\\!=\\!~{}0.25$ | $\varepsilon~{}\\!=\\!~{}0.50$ | $\varepsilon~{}\\!=\\!~{}0.70$ | $\varepsilon~{}\\!=\\!~{}0.25$ | $\varepsilon~{}\\!=\\!~{}0.50$ | $\varepsilon~{}\\!=\\!~{}0.70$ | $\varepsilon~{}\\!=\\!~{}0.25$ | $\varepsilon~{}\\!=\\!~{}0.50$ | $\varepsilon~{}\\!=\\!~{}0.70$
PointPillars | 97.27 | 97.21 | 90.35 | 98.75 | 98.61 | 95.99 | 97.16 | 96.24 | 89.35 | 98.74 | 98.32 | 95.45
Part-$\text{A}^{2}$ | 89.54 | 89.41 | 75.64 | 94.49 | 92.31 | 76.10 | 89.49 | 89.22 | 75.08 | 92.67 | 92.38 | 75.96

Table II reports the AP for PointPillars and Part-$\text{A}^{2}$ considering
IoU thresholds $\varepsilon~{}=~{}\\{0.25,0.50,0.70\\}$ and recall levels
$L~{}=~{}\\{11,40\\}$. The AP is evaluated over the Bird’s Eye View (BEV)
projection, denoted as $\text{AP}_{\text{BEV}}$, which projects the
predictions onto the $x$-$y$ plane and in the 3D space, referred to as
$\text{AP}_{\text{3D}}$. Comparing the results, the $\text{AP}_{\text{BEV}}$
and $\text{AP}_{\text{3D}}$ metrics show that PointPillars provides more
accurate detections compared to Part-$\text{A}^{2}$ for all values of $L$ and
IoU thresholds $\varepsilon$. Indeed, the AP of PointPillars is, on average,
$5\%$ higher than the one obtained by Part-$\text{A}^{2}$ until
$\varepsilon\leq 0.50$, while for more stringent thresholds, i.e.,
$\varepsilon~{}=~{}0.7$, the gap between the two detectors becomes even
larger. Focusing on the results under different recall levels $L$, one can
notice that $L~{}=~{}11$ provides a lower value compared to $L~{}=~{}40$. This
should be expected since $L~{}=~{}11$ generally leads to an underestimation of
the actual performances compared to $L~{}=~{}40$ as relying only on 11 recall
values compared to 40.

Figure 3: Bounding box location error CEP95 over the three axes.

To further characterize the performance of the 3D object detectors, in Fig. 3
we report the CEP95 of the location error obtained by PointPillars and
Part-$\text{A}^{2}$ over the three axes. The results confirm the findings of
the previous analysis: PointPillars provides more accurate detections when
compared with Part-$\text{A}^{2}$. More specifically, the two methods have
similar CEP95 over the $x$ and $y$ axes, while for the $z$ axis PointPillars
achieves a location error lower than $13$ cm in 95% of the cases, while
Part-$\text{A}^{2}$ attains a much larger value of $29$ cm.

###  VI-B MPNN data association

The MPNN is trained over the same CARLA map used for training the 3D object
detectors. In particular, a new dataset is generated in Town02 where 20 LiDAR-
equipped vehicles, with LiDAR sensors configured as in Sec. VI-A, move in the
environment for $1000$ timestamps, again with sampling time
$T_{s}~{}=~{}0.2$s. The database is constructed by firstly running the
PointPillars model on the point cloud data acquired by each vehicle
individually to obtain the set of estimated bounding boxes. We specifically
select PointPillars in this stage due to its more accurate detection
performances compared to Part-$\text{A}^{2}$ as highlighted in the previous
analysis. To make the MPNN-based DA strategy more resilient to the errors
discussed in Sec. II-B, we add Gaussian noise to the bounding boxes provided
by PointPillars. The noise standard deviation is set to $1$ m. Then, the input
graphs containing the true associations among the poles detected by the
vehicles are used as ground-truth information for training the MPNN. We use
$700$ examples for training and the remaining $300$ for validation. The MPNN
is trained considering a batch size of $20$ examples for 50 epochs and using
the Adam optimizer with learning rate $\eta=0.001$ and momentum parameters
$\beta_{1}=0.9$ and $\beta_{2}=0.999$.

1.000.990.980.970.961197531$I$AccuracyPrecisionRecall Figure 4: DA task
validation performances reached after 50 epochs of training as a function of
the number of message passing iterations $I$.

To tune the hyper-parameter $I$, we analyze the accuracy, precision, and
recall performance metrics in the validation dataset by varying the number of
message passing iterations, whose results are reported in Fig. 4. The error
bars are computed using the mean values and standard deviation as
uncertainties. Results show that the optimal number of iterations $I$ is
between 5 and 7. Indeed, $I<5$ prevents effective feature extractions and
elaboration, while $I>7$ may lead to over-complicated models and potential
overfitting. That is, when $I$ is too large, the model might start learning
noise or outliers in the training data, rather than the underlying patterns.
Therefore, for the following analyses we set $I=5$.

##  VII Cooperative localization results

This section analyzes the performances of the proposed cooperative
localization approach in two realistic driving scenarios. The goal is to
comprehensively assess the DA approach and the overall cooperative system as
compared to ideal and state-of-the-art solutions. The first one is again based
on the map Town02 of CARLA but with new trajectories and vehicle interactions
(Sec. VII-A). The second one instead is a brand new environment where the NNs
have been not trained on (Sec. VII-B). Finally, Sec.VII-C discusses the
communication overhead of CLS-MPNN.

###  VII-A Town02 results

We initially assess the proposed method considering the Town02 map of CARLA
where twenty vehicles move in the area following different trajectories
compared to the ones of Sec. VI. Unless stated otherwise, we assume that the
onboard GNSS receiver provides a position estimate with accuracy
$\sigma_{\text{P}}^{(\text{V})}=5$ m all over the map. The same parameters
used in Sec. VI are reused to configure the LiDAR sensors onboard the
vehicles. The motion model (1) is calibrated according to the vehicles’
motion, with $\sigma_{\text{Q}}=0.5$ m/${\text{s}^{2}}$, while the accuracy of
the object detectors is as in Fig. 3. The overall simulation lasts for $300$
seconds and comprises $1500$ snapshots each sampled at $T_{s}=0.2$ s.

TABLE III: Detection Performances Analysis in Town02 Method | Correct detections | Missed detections | False positives
---|---|---|---
[%] | [%] | [%]
PointPillars | 95.93 | 4.07 | 12.59
Part-$\text{A}^{2}$ | 94.30 | 5.70 | 16.72

(a)  (b)  (c)  (d)

(e)  (f)

Figure 5: Spatial RMSE of vehicle positions over the Town02 simulation map:
(a) GNSS-KF. (b) O-CLS-MPNN (perfect DA and LiDAR sensing) (c) CLS-MPNN with
PointPillars, (d) CLS-MPNN with Part-$\text{A}^{2}$, (e) C-SLAM, (f)
comparison of the CEP95 of the vehicle location error for all the
methodologies.

In the following, we assess the performances provided by the following
positioning solutions:

  * •

The proposed CLS-MPNN tool integrating the detections provided by the 3D
object detectors and the MPNN-based DA strategy. We will show results
considering separately the detections obtained by PointPillars and
Part-$\text{A}^{2}$.

  * •

An oracle version of the proposed method, referred to as O-CLS-MPNN, with
perfect DA and LiDAR sensing where all poles present in the field of view of
the LiDAR sensor are detected.

  * •

A state-of-the-art cooperative SLAM approach [40] that requires vehicles to
exchange their positions and the raw LiDAR point clouds, denoted as C-SLAM.

  * •

A non-cooperative GNSS-based tracking tool where a Kalman Filter (KF)
integrates the positions provided by the GNSS units, referred to as GNSS-KF.

The main difference between O-CLS-MPNN and CLS-MPNN is that CLS-MPNN is
subject to missed detections while O-CLS-MPNN is not as all detectable poles
are always correctly recognized, provided they fall inside the field of view
of the LiDAR sensor. The detection performances of PointPillars and
Part-$\text{A}^{2}$ are reported in Table III which highlights the percentages
of correct detections, missed detections, and false positives obtained by the
two detectors. The results indicate that PointPillars provides more robust
results as its missed detection and false positive percentages are lower when
compared with the ones attained by Part-$\text{A}^{2}$.

####  VII-A1 Cooperative localization performances

Fig. 5 shows the spatial Root Mean Square Error (RMSE) of the vehicle location
estimate computed all over the map for GNSS-KF (Fig. 5a), O-CLS-MPNN (Fig.
5b), the proposed CLS-MPNN method considering the detections provided by
PointPillars (Fig. 5c), Part-$\text{A}^{2}$ (Fig. 5d) and C-SLAM (Fig. 5e).
Additionally, Fig. 5f reports the CEP95 of the vehicle location error for all
the compared methodologies. Analyzing the results, CLS-MPNN substantially
outperforms GNSS-KF on all map positions, regardless of the detector employed,
while approaching the performances attained by O-CLS-MPNN. The improvement
brought by CLS-MPNN is nearly constant all over the map apart from a few spots
in the leftmost road where a decreased level of cooperation is observed due to
a lower number of vehicles driving in that area. The developed method also
provides more accurate results compared to the ones achieved by C-SLAM as its
location RMSE is largely reduced both for PointPillars and
Part-$\text{A}^{2}$. Looking at the CEP95 of the vehicle location error in
Fig. 5f, they further confirm the superiority of the proposed cooperative
localization framework. Indeed, the location error of CLS-MPNN that integrates
the detections provided by PointPillars and Part-$\text{A}^{2}$ is lower than
0.99 m and 1.17 m in 95% of the cases, respectively, while GNSS-KF and C-SLAM
attain 6.36 m and 1.36 m, respectively. Therefore, CLS-MPNN enhances the
localization accuracy in the considered scenario compared to GNSS-KF and
C-SLAM. Besides obtaining more accurate position estimates, CLS-MPNN is more
communication-efficient compared with C-SLAM as only the estimated positions
of vehicles and objects bounding boxes are exchanged with the MEC while C-SLAM
requires vehicles to share also the raw LiDAR point cloud. Focusing on the
comparison between O-CLS-MPNN and CLS-MPNN, some performance loss is
experienced. This should not be surprising as O-CLS-MPNN detects all possible
poles recognizable by the LiDAR sensors while also carrying out perfect DA.
Nevertheless, the gap between CLS-MPNN implemented using the detections
provided by PointPillars and O-CLS-MPNN is only $6$ cm.

Figure 6: CEP95 values of CLS-MPNN and GNSS-KF vs GNSS accuracy. Figure 7:
CEP95 values of the vehicle location error vs the number of vehicles.

####  VII-A2 Impact of GNSS accuracy

To complement the analysis shown before, we here evaluate the impact of
varying the GNSS positioning uncertainty $\sigma_{\text{P}}^{(\text{V})}$.
Fig. 6 reports the vehicle location error CEP95 attained by CLS-MPNN and GNSS-
KF when $\sigma_{\text{P}}^{(\text{V})}$ ranges from 0.1 m up to 5 m. The
results show that CLS-MPNN is particularly useful for enhancing the
positioning performances when the GNSS is highly inaccurate. Indeed, when
$\sigma_{\text{P}}^{(\text{V})}<1$ m the average improvement brought by CLS-
MPNN with respect to GNSS-KF is 57%, while for
$\sigma_{\text{P}}^{(\text{V})}\geq 1$ m the same improvement is roughly 87%.
Besides, the analysis highlights that CLS-MPNN is advantageous even when the
GNSS accuracy is high.

####  VII-A3 Impact of number of vehicles

In Fig. 7, we analyze how the CEP95 of the vehicle location error is
influenced by the number of vehicles in the scenario. We compare the results
for the CLS-MPNN using PointPillars and Part-$\text{A}^{2}$ when $N_{v}$
ranges from $2$ up to $20$. The achieved results show a diminishing return in
terms of positioning accuracy as the number of connected vehicles decreases:
the localization error is more than doubled when passing from $N_{v}=20$ to
$N_{v}=2$. Nevertheless, even when $N_{v}=2$, the proposed approach is still
able to largely outperform GNSS-KF regardless of the detector employed.

Figure 8: CEP95 values of the vehicle location error and percentage of correct
detection vs LiDAR resolution.

####  VII-A4 Impact of LiDAR resolution

We here analyze how the resolution of the LiDAR (i.e., number of channels)
affects the localization performances of CLS-MPNN. In the left panel of Fig. 8
we report the CEP95 values of vehicle location accuracy when using LiDARs with
$16$, $32$, and $64$ channels, while the right panel highlights the percentage
of correct detections obtained by PointPillars and Part-$\text{A}^{2}$. Note
that the 3D object detectors are not retrained to account for the lower LiDAR
resolution. We observe that as the number of channels decreases, the
positioning accuracy decreases as well, regardless of the detector employed.
This should be expected since a lower resolution makes the detection process
more difficult, leading to fewer objects detected and a consequent increase of
the CEP95 value. To improve the object detection performances, super-
resolution methods could be adopted [83]. We remark that CLS-MPNN still
outperforms GNSS-KF even when using low-resolution LiDAR sensors.

TABLE IV: Analysis on the impact of false positives  Detector | Original | Strategy | Strategy | Strategy
---|---|---|---|---
false positives | 1 | 2 | 3
[%] | [%] | [%] | [%]
PointPillars | 12.59 | 0.88 | 0.48 | 0.18
Part-$\text{A}^{2}$ | 16.72 | 3.13 | 1.75 | 0.38

####  VII-A5 Impact of false positives

Even though the proposed method is not formulated to deal with FPs, we here
highlight how the detections can be filtered to minimize the false alarms
without heavily impacting the performances of CLS-MPNN. To reduce the number
of FPs, we employ three filtering strategies. The first one (Strategy 1)
retains only bounding boxes detected by multiple vehicles at the same time
instant, whereas the other two take as input the output of the first one and
remove boxes having a score probability less than 0.15 (Strategy 2) and 0.25
(Strategy 3). Table IV and Fig. 9 report the percentage of FPs and the vehicle
location error CEP95 of CLS-MPNN before and after applying the three filtering
strategies for both PointPillars and Part-$\text{A}^{2}$, respectively.
Analyzing the results, the first strategy heavily limits the number of FPs
without reducing the final accuracy. On the other hand, the other two policies
introduce marginal accuracy drops but allow to almost completely cancel out
the false alarms, i.e., the FPs are less than 1% of all the detections.
Indeed, removing bounding boxes that have a score lower than 0.25 reduces the
percentage of FPs to $0.18$% and to $0.38$% for PointPillars and
Part-$\text{A}^{2}$, respectively. This in turn makes CLS-MPNN slightly less
accurate, increasing its CEP95 to 1.19 m and 1.46 m for PointPillars and
Part-$\text{A}^{2}$, respectively.

Figure 9: CEP95 values attained by CLS-MPNN after applying the filtering
strategies of FPs.

(a)  (b)

Figure 10: Execution time (a) and memory (b) required to run the proposed
approach as a function of the number of vehicles.

####  VII-A6 Computational requirements

We analyze the computational complexity for executing the proposed method by
reporting in Fig. 10a the computational time and in Fig. 10b the associated
memory utilization, with a breakdown on the individual contributions from the
detector, DA algorithm and cooperative tracker. Results show that the most
time-consuming stages for running the developed approach are the DA step and
the 3D object detection process. For what concerns the memory utilization
instead, a large memory portion should be devoted to storing the detectors.
The figures also show that the times/memory required for running the DA and
the cooperative tracking steps increase as the number of connected vehicles
grows. This is reasonable since, as opposed to the object detection process
which is performed onboard the vehicles, a larger number of vehicles leads to
a more complex cooperation among vehicles.

Figure 11: Impact of packet drops on the vehicle location error CEP95.

####  VII-A7 Impact of network reliability

We here evaluate the robustness of CLS-MPNN against unreliable networks by
introducing packet drop events in the cooperative framework. They are assumed
to be independent across vehicles and we consider that if a packet drop occurs
between the $v$-th vehicle and the MEC all the transmitted information (i.e.,
the position of the $v$-th vehicle and the poles bounding boxes detect by it)
is lost. Herein, we do not rely on V2X networking simulators as we want to
benchmark CLS-MPNN under extreme conditions. Such conditions are likely not to
be encountered when utilizing V2X simulation frameworks but are useful to
highlight the potential limits of the proposed approach. Fig. 11 shows the
location error CEP95 achieved by CLS-MPNN when the packet drop probability
ranges from 0% (i.e., no packet drops) to 40%. The results show that the CLS-
MPNN is negligibly affected if the packet drop probability is lower than 10%
regardless of the detector considered. For larger packet drop occurrences, a
strong reduction on the accuracy is experienced.

####  VII-A8 Impact of LiDAR sensing range

Fig. 12 compares the performances on vehicle positioning obtained by CLS-MPNN
integrating the PointPillars and Part-$\text{A}^{2}$ detections with the ones
achieved by O-CLS-MPNN considering different LiDAR sensing ranges $R_{s}$
ranging from $20$ m up to $70$ m, i.e., the case considered previously.
Comparing the results, PointPillars achieves a lower CEP95 compared with
Part-$\text{A}^{2}$ in nearly all cases. This should be expected since, in
this scenario, PointPillars detects more poles compared to Part-$\text{A}^{2}$
(as highlighted in Table III). Comparing the results for different values of
$R_{s}$, the performances of all methods do not deteriorate too much for
$R_{s}\geq 40$ m, while for $R_{s}<40$ m a large performance drop occours.
Therefore, the proposed approach could be employed with lower-grade LiDAR
sensors provided that $R_{s}\geq 40$ m.

Figure 12: CEP95 values of vehicle location error in Town02 for O-CLS-MPNN and
CLS-MPNN with PointPillars and Part-$\text{A}^{2}$ for different LiDAR sensing
ranges.  Figure 13: CEP95 of pole location error for different localization
methodologies.

####  VII-A9 Object position accuracy

As a final analysis, we evaluate the positioning accuracy of poles, comparing
the proposed approach with an ego-sensing solution. In the latter, vehicles
obtain their positions via the GNSS-KF approach and use this information
jointly with the LiDAR detections to localize the poles in a global reference
frame. The results of this comparison are highlighted in Fig. 13 considering
the detections provided by PointPillars and Part-$\text{A}^{2}$ detectors. The
CEP95 location error of CLS-MPNN is largely reduced compared to the one
attained by the ego sensing solution for both detectors. This highlights the
benefits of employing CLS-MPNN to also improve the localization performances
of the poles with respect to non-cooperative sensing schemes.

###  VII-B Town10 results

In this section, we evaluate CLS-MPNN in a new scenario where the NNs have not
been trained on. This new evaluation is instrumental for characterizing the
developed method under unseen conditions. For this scope, we employ the Town10
map of CARLA, a more complex environment comprising an overpass and roads with
multiple lanes, where 20 LiDAR-equipped vehicles move in the environment. The
same calibration and LiDAR parameters employed in Sec. VII-A and in Sec. VI
are also used here. The simulation lasts $300$ seconds and comprises $1500$
snapshots each sampled at $T_{s}=0.2$ s. As done before, we report in Table V
the percentages of correct detections, missed detections, and FPs attained by
PointPillars and Part-$\text{A}^{2}$. For this map, Part-$\text{A}^{2}$ is
observed to generalize better as it provides fewer missed detections compared
to PointPillars, despite detecting a larger number of false positives. This is
in line with the results provided in [84] as they show that double-stage
detectors (e.g., Part-$\text{A}^{2}$) outperform single-stage ones (i.e.,
PointPillars) when the testing conditions change. Compared with the values
provided in Table III, FPs and missed detections are higher, indicating that
fine-tuning the detectors on this new map may help improve the performances.

TABLE V: Detection Performances Analysis in Town10 Method | Correct detections | Missed detections | False positives
---|---|---|---
[%] | [%] | [%]
PointPillars | 83.59 | 16.40 | 9.21
Part-$\text{A}^{2}$ | 87.89 | 12.11 | 14.26

(a)  (b)  (c)  (d)

(e)

Figure 14: Spatial RMSE of vehicle positions over the Town02 simulation map:
(a) GNSS-KF. (b) O-CLS-MPNN (perfect DA and LiDAR sensing) (c) CLS-MPNN with
PointPillars, (d) CLS-MPNN with Part-$\text{A}^{2}$, (e) comparison of the
CEP95 of the location error for all methods. Figure 15: Vehicle location error
CEP95 in Town10 for O-CLS-MPNN and CLS-MPNN with PointPillars and
Part-$\text{A}^{2}$ for different LiDAR sensing ranges.

Fig. 14 shows the spatial RMSE computed all over the map for GNSS-KF (Fig.
14a), O-CLS-MPNN (Fig. 14b), the proposed CLS-MPNN method considering the
detections provided by PointPillars (Fig. 14c) and by Part-$\text{A}^{2}$
(Fig. 14d), while Fig. 14e shows the CEP95 of the location error obtained by
all methods. The results of this analysis are in line with the findings of the
previous section: CLS-MPNN largely outperforms GNSS-KF regardless of the
detector considered while it approaches the performances of O-CLS-MPNN. Again,
some spots can be noticed where the improvement brought by CLS-MPNN is only
marginal due to a low cooperation level between vehicles. With respect to the
previous case, the CEP95 of the location error is generally lower for all
methods. This is related to the fact that a larger number of poles is present
on this map with respect to the ones present in Town02 that can be exploited
for cooperative vehicle positioning refinement. Another difference with
respect to the previous results is that the performance gap between CLS-MPNN
and O-CLS-MPNN is higher, possibly due to the larger number of missed
detections. Nevertheless, CLS-MPNN is shown to generalize to this new scenario
as it provides accurate vehicle positioning. Contrarily to before, now the
detections provided by Part-$\text{A}^{2}$ should be chosen for maximizing the
vehicle position accuracy.

To conclude the analysis, we report in Fig. 15 the CEP95 of the location error
obtained by CLS-MPNN implemented with the detections provided by PointPillars
and Part-$\text{A}^{2}$ and the one achieved by O-CLS-MPNN for varying LiDAR
sensing ranges. Under this map, the predictions provided by
Part-$\text{A}^{2}$ lead to a lower positioning error compared to the ones
provided by PointPillars for nearly all sensing ranges. Therefore, despite
Part-$\text{A}^{2}$ providing less accurate performances in Town02, it should
be preferred compred to PointPillars as it generalizes to unseen scenarios and
attain higher localization accuracy when integrated with CLS-MPNN.
Notwithstanding this aspect, it is advisable to partially retrain or fine-tune
the models to enhance even more the positioning accuracy as the performance
gap between O-CLS-MPNN and CLS-MPNN is higher when compared to the same gap
shown in Fig. 12.

###  VII-C Considerations on the communication overhead

We here compare the communication overhead of the proposed CLS-MPNN with the
one required by C-SLAM. An upper bound on the communication overhead (in bits)
required by each vehicle to run CLS-MPNN is
$N_{vd}E_{v}+N_{od}N_{c}N_{o}E_{o}$. The first term encodes the number of bits
used for exchanging the 3D vehicle position, where $N_{vd}=3$ and $E_{v}$
denotes the number of bits encoding the position, while the second refers to
the exchange of the detected objects, where $N_{c}=8$ is the number of 3D
corners of the bounding box, $N_{od}=3$, and $E_{o}$ is the number of bits
used for encoding the information. A typical value for $E_{v}$ and $E_{o}$ is
32 bits. On the other hand, the communication overhead of C-SLAM is upper
bounded by $N_{vd}E_{v}+N_{pd}N_{\ell p}E_{\ell p}$. The first term is the
same as before, while the second highlights the bits required for sharing the
raw point cloud, with $N_{pd}=3$ and $E_{p}$ denotes the number of bits for
representing a single point of the cloud. Clearly, CLS-MPNN is advantageous
over C-SLAM when $N_{pd}N_{\ell p}E_{\ell p}\gg N_{od}N_{c}N_{o}E_{o}$. This
is typically verified considering LiDAR sensors with at least 16 channels.
Indeed, on average, such sensors output $N_{\ell p}=300000$ points for each
frame [85], thus, the term $N_{pd}N_{\ell p}E_{\ell p}$ corresponds to 0.28
Mbits (assuming that point clouds are compressed using G-PCC). To get the same
communication overhead for CLS-MPNN, $N_{o}$ should be at least 375, which is
far beyond the maximum number of output objects from 3D detectors (limited to
50). In this condition, the communication overhead of CLS-MPNN is reduced by
7.5 times compared to C-SLAM.

##  VIII Conclusion

In this paper, we proposed a novel data-driven cooperative localization and
sensing framework, referred to as CLS-MPNN, for GNSS augmentation in complex
urban environments. The framework leverages a NN, i.e., a 3D object detector,
at the vehicles for recognizing and localizing static objects in the
surroundings. The detections are then aggregated at a centralized unit, namely
a MEC, that performs a MPNN-based data association procedure to coherently
combine the measurements provided by multiple vehicles and referring to a same
object. Once the data association is solved, the MEC employs a cooperative
Bayesian tracking algorithm to improve the objects’ localization accuracy and
implicitly refines the vehicle positioning as well.

We employed two synthetically-generated, yet realistic, urban scenarios to
assess the proposed cooperative method. The first one is used to assess the
performances of the employed single-stage/double-stage object detectors, the
MPNN data association accuracy, and, finally, to evaluate the performances of
the overall cooperative localization framework. The second one, instead, is
utilized to characterize the ability of the developed technique to generalize
to new unseen conditions. The results show that CLS-MPNN is able to
substantially outperform a conventional non-cooperative solution based on
stand-alone GNSS and a state-of-the-art cooperative SLAM approach.
Furthermore, when the scenario is modified with respect to the one used during
training, a marginal performance loss is experienced by CLS-MPNN due to more
missed detections. Nevertheless, CLS-MPNN is still able to substantially
reduce the positioning errors with respect to the ego positioning solution
while approaching the performances of an oracle system that perfectly
associates and detects all objects present in the surroundings of the
vehicles. The analysis also shows that double-stage 3D object detectors are to
be preferred compared to single-stage ones as they show better generalization
performances to new scenarios.

Future research activities will target the assessment in real-world driving
scenarios as well as the development of end-to-end cooperative learning
strategies where 3D object detection and data association tasks are carried
out by a single NN possibly designed to also support fully distributed
implementations. Besides, the MPNN-based data association strategy could be
extended to deal with the false positives.

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  *[C-ITS]: Cooperative Intelligent Transportation Systems
  *[V2X]: Vehicle-To-Everything
  *[GNSS]: Global Navigation Satellite System
  *[DSRC]: Dedicated Short-Range Communications
  *[UWB]: Ultra Wide Band
  *[SLAM]: Simultaneous Localization and Mapping
  *[ML]: Machine Learning
  *[NN]: Neural Network
  *[DA]: Data association
  *[SPA]: Sum Product Algorithm
  *[MPNN]: Message Passing Neural Network
  *[MPNNs]: Message Passing Neural Network
  *[ICP]: Implicit Cooperative Positioning
  *[CLS-MPNN]: Cooperative LiDAR Sensing with Message Passing Neural Network
  *[DNN]: Deep Neural Network
  *[MEC]: Mobile Edge Cloud
  *[V2I]: Vehicle-To-Infrastructure
  *[FPs]: False Positive
  *[DL]: Deep Learning
  *[RPN]: Region Proposal Network
  *[SSD]: Single Shot Detector
  *[IoU]: Intersection over Union
  *[NMS]: Non-Maximum Suppression
  *[pdf]: probability density function
  *[MMSE]: Minimum Mean Square Error
  *[MLPs]: Multi Layer Perceptron
  *[MLP]: Multi Layer Perceptron
  *[PTPv2]: Precision Time Protocol version 2
  *[AP]: Average Precision
  *[CEP]: Circular Error Probable
  *[CDF]: cumulative distribution function
  *[BEV]: Bird’s Eye View
  *[NNs]: Neural Network
  *[O-CLS-MPNN]: Oracle CLS-MPNN
  *[KF]: Kalman Filter
  *[RMSE]: Root Mean Square Error