Abstract— Vehicular Ad Hoc Networks (VANETs) are

widely considered as indispensable elements of the future

intelligent transportation systems that are aiming to apply

information and communications technologies to improve

transportation safety and quality of experience. We present our

take on a relatively unexplored problem, exploiting VANETs

for on-road surveillance. The proposal is inspired by multi-

agent systems intended for surveillance, e.g., a distributed

camera network. We propose a tracking system composed of

three operational modules, namely, localization, tracking data

collection and prediction of future locations of a target. Camera

equipped onboard units (OBUs) act as remote mobile sensors.

Tracking messages are communicated among the OBUs and

roadside units (RSUs). These messages are also triggered in the

possible locations of the target in a timely manner. Therefore, it

is imperative to scope the search to limit the number of OBUs

and RSUs involved in the tracking operation, thus, minimizing

the number of tracking messages. To this end, a movement

modeling technique utilizes the OBU-observations to classify

the target’s movement pattern to aid future trajectory

prediction. In our previous work, we proposed a Dirichlet-

multinomial (D-M) model under the Bayesian estimation

framework. In this paper, we present newly identified cues

towards improving the movement estimation model. The D-M

model is constrained to the assumption that all the choice sets

are identical across trials. We demonstrate that this is almost

never the case. The improved model exploits a choice model,

called the conditional logit. The conditional logit model is

attractive when choice sets vary across trials. Additionally, we

weight outcome of each trial according to the given choice sets

to achieve higher estimation accuracy. We evaluate the new

model by means of an experimental analysis and compare

results with the D-M model.

I. INTRODUCTION

The VANET [1] is an infrastructure enabling vehicles, in metropolitan and urban areas, to communicate with each other in an ad hoc manner. VANETs are widely considered as indispensable elements of the future intelligent transportation systems (ITSs) that aim to apply information and communication technologies (ICTs) to improve transportation safety, quality of experience and efficiency [2]. Possible VANET applications can be grouped in three major

* This research was partially supported by a scholarship from Salman

bin Abdulaziz University, Al-Kharj, Saudi Arabia. Tahsin Arafat Reza (corresponding author) and Michel Barbeau are with

the School of Computer Science, Carleton University, Ottawa, Ontario,

Canada (e-mail: treza@connect.carleton.ca, barbeau@scs.carleton.ca). Gilles Lamothe1is with the Department of Mathematics and Statistics,

University of Ottawa, Ottawa, Ontario, Canada (e-mail:

glamothe@uOttawa.ca). Badr Alsubaihi is with the School of Electrical Engineering and

Computer Science, University of Ottawa, Ottawa, Ontario, Canada,

affiliated with Salman bin Abdulaziz University, Al-Kharj, Saudi Arabia (e-mail: balsu075@uottawa.ca).

classes: 1. Safety and security, 2. Comfort and entertainment, and 3. Commercial [3]. In addition to vehicle-to-vehicle (V2V) communications, the latest Federal Communications Commission (FCC) amendment [4] also recommends vehicle-to-infrastructure (V2I) communications. The infrastructure could be a cellular base-station or simply a stationary roadside short range wireless access point, called a RSU. A vehicle equipped with a FCC recommended DSRC [1] compliant wireless communications device, capable of V2V and V2I (also vehicle-to-RSU or V2R) communications, is called an OBU. In VANET linguistics, the vehicle itself is commonly called the OBU. Often the term ego vehicle is used to address a vehicle that bears intelligent technologies.

The uncertainty associated with unplanned locomotion in a metropolitan road network makes vehicle tracking challenging. A metropolitan road network itself exhibits dynamic characteristics, such as different speed limits and time varying traffic congestion. The problem addressed in this paper is tracking an on the run vehicle that does not want to reveal its geographic location, communicate with other OBUs and RSUs, and be tracked. This problem scenario is analogous to chasing an on the run vehicle using police squad cars. We also consider the probabilistic measure of the target vehicle being situated in an urban location at a future point in time. The objectives are maximizing tracking success and to scope the search to limit the number of OBUs and RSUs involved in the tracking operation, thus, minimizing the number of tracking messages.

Unfortunately, high-speed pursuits are prone to property damages and crash related injuries. A 2004 case study by Rivara and Mack [5], based on statistics from more than 1200 pursuits in Miami, Florida, Omaha, Nebraska and Aiken, South Carolina, exposed that pursuit related property damages occurred in 20%-40% of the incidents. Crashes resulting in injury or fatality in 12%-41% of all pursuits. The most alarming figures revealed in the study is that more than 30% of the victims were occupant of vehicles uninvolved in the pursuit. We believe, the aforementioned statistics justify that our proposal holds potential as an alternative, a supplementary measure to be the least, to high-speed pursuits.

The work presented in [26] is our first attempt towards exploring the addressed problem. The proposal is inspired by multi-agent systems intended for surveillance, e.g., a distributed camera network. We proposed a tracking system composed of three operational modules, namely, localization, tracking data collection and prediction of future locations of the target. Using cameras and image processing, OBUs can search and identify a target vehicle based on the license plate number (LPN) and record locations of observations. Tracking

Non-cooperating Vehicle Tracking in VANETs using the Conditional

Logit model

Tahsin Arafat Reza, Michel Barbeau, Gilles Lamothe, and Badr Alsubaihi

Proceedings of the 16th International IEEE Annual Conference onIntelligent Transportation Systems (ITSC 2013), The Hague, TheNetherlands, October 6-9, 2013

MoD4.1

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messages are communicated among the OBUs and the RSUs and are triggered in the possible locations of the target in a timely manner. Therefore, it is imperative to scope the search to limit the number of OBUs and RSUs involved in the tracking operation, thus, minimizing the number of tracking messages. To this end, a movement modeling technique utilizes the OBU-observations to classify the target’s movement pattern to aid future trajectory prediction. In [26], we have proposed a Dirichlet-multinomial (D-M) model under the Bayesian estimation framework. In this paper, we present newly identified cues toward further improving the movement estimation model. The D-M model is constrained to the property of multinomial distribution that all the choice sets are identical across trials. We demonstrate that, in reality, this is almost never the case. The improved model exploits a choice model, called the conditional logit. The conditional logit model is attractive when choice sets vary across trials. Additionally, we weight outcome of each trail according to the given choice sets achieve higher estimation accuracy.

The rest of the paper is organized in four sections. In Sect. II, related work relevant to the addressed problem is presented. In Sect. III, we summarize the VANET infrastructure and massage-passing model. In Sect. IV, we present the probabilistic movement estimation model. Experiments and results are documented in Sect. VI. Section VI concludes the paper and outlines future work.

II. RELATED WORK

In general, tracking refers to monitoring any phenomenon or observing context change in an object or a group of objects. Contextual information are typically collected via various sensor inputs [6]. Some popular moving target detection approaches are radar-based, laser-based, acoustic-based and camera-based [7]. Detection methods can be fused together to rip benefits of each technique [8]. A camera acquires data in a non-intrusive manner. The key advantage of a camera-based technique over the aforementioned techniques is the monetary cost. Our particular interest is tracking using a distributed camera network that includes non-stationary cameras. Computer vision based tracking considers detection and recognition, object’s special movements and gestures. Tasks include identifying and localizing, hence, keeping track of the object in a sequence of frames, as well as short-term prediction of object’s future position [9][10][11]. The Bayesian inference is used in [12] for tracking multiple persons through a network of distributed stationary cameras, with emphasize on re-identifying persons after large observation gaps. A non-linear/non-Gaussian tracking system based on the Bayesian filtering is proposed in [13]. The goal of this work is to increase coverage of a fixed surveillance infrastructure by introducing additional mobile cameras. The proposed technique decomposes the state space (2-D locations) into grid cells and calculates the probability of the target being in a cell at a given time. The mobile cameras are used to overcome the degeneracy problem where a predefined state transition function may lead to erroneous prior probability distribution function (PDF) at each state during the time period the target is out of stationary camera coverage. This work does not assume any motion model for the mobile target and uses a distance based exponential state transition function. The work presented in

[14] considers a pursuit-evasion scenario. A probabilistic path planning algorithm for tracking a moving ground target using camera equipped UAVs (unmanned aerial vehicles) and UGVs (unmanned ground vehicles) is presented. The target state is modeled using the dynamic occupancy grid and target motion is represented using a second-order Markov chain. The probability of the target location is updated using the Bayesian filtering. Vision occlusion due to obstacles is also considered in this work. A mechanism for tracking in sparsely deployed WSN that does not require overlapping sensing regions is presented in [15]. Through formulating a Quadratic Constrained Linear Programming Problem (QCLP), a target is tracked by estimating the traveled distance on the basis of time spent in the vicinity of the sensors. Constant velocity of the target is assumed in this work. Connected dominating set (CDS) is used in [16] for tracking fast-paced mobile nodes in the VANET. The proposal enables location update of high-mobility nodes by some dominator in the CDS. The work does not consider tracking a non-cooperative node and the CDS assumptions make it incompatible for our problem. Reference [29] presents use of Bayesian Occupancy Filter (BOF) for tracking the evolution of the environment, in the context of mobile autonomous systems which consider data association and occlusion. A cooperative path prediction algorithm for safety applications in VANETs is presented in [18], which considers position, velocity, acceleration, heading and yaw rate measurements. Beacons contain dynamic status of a transmitting vehicle. The algorithms uses unscented Kalman filter (UKF), and constant turn rate and tangential acceleration (CTRA) motion model is assumed [18]. The prediction is both short-distance and short-term and only works when the target is within the sensing range of the ego vehicle. The Gaussian Mixture Model (GMM) is used in [19]. This work assumes availability of kinematics as in [18]. Future trajectory prediction in the road network is presented in [20] and [17]. Reference [17] utilizes non-linear support vector machine (SVM). The proposal does not presume any motion model but the large dataset required for SVM training can become a bottleneck for online prediction [21]. Robust Extended Kalman Filter (REKF) is used in [22] to estimate the mobile user’s trajectory to improve connection reliability and bandwidth efficiency. Gaussian Process Regression (GPR) is used in [21] for long term trajectory prediction of moving objects and allows online training using small size deterministic dataset. Kinematics used in this work are not available in our problem scenario. In [27], a multivariate logit model is used for modeling human mobility. The model accounts for the subjects’ social and geographic contexts. The so-called Socially and Geography Aware (SAGA) mobility model clusters users with similar features, such as average time in a cell, speed and pause time. The model aims to preserve heterogeneous nodes’ spatial density, creating and maintaining clusters and accounting for different node’s popularity and transitivity, thus solving limitations exhibited by Random-Waypoint and mobility models that solely depend on pure preferential attachments. Multinomial logit discrete choice model is used for modeling mobility of pedestrians and vehicles in [28]. Travel decision includes modeling of user trip sequence and movement path selection. Trip sequence is modeled after popularity among the population. The proposal borrows techniques from

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transportation planning and uses the classical STOCH algorithm to estimate path selection probability. The vehicle mobility also considers road traffic volume. The proposal addresses dynamic movement where speed and directions change over time.

III. THE VANET INFRASTRUCTURE

In this section, we summarize the VANET infrastructure

and message-passing model used in this work, originally

presented in [26]. We utilize a VANET composed of OBUs

and RSUs for tracking the on the run vehicle. An OBU could

be any type of vehicle, equipped with an array of cameras

covering a 360o field of view (FOV). An installed license

plate identification application (LPIA) can identify the target

by LPN, given the target is within the camera FOV. The

metropolitan road network is subdivided into logical units,

called a zone. A zone zi has the following attributes: ID i,

length li, type typi=(ZA, ZB or ZC), speed-limit sli=(vmin, vmax)

and RSU list RSUi. Z is the finite set of zones in the road

network. A zone is essentially a highway, a road or a street

segment. The concept of zone allows us to represent 2-D

location information as 1-D location identifiers, i.e., zone

IDs. In the exchanged messages, only zone IDs are used,

eliminating exchange of large amount of location related

data. An OBU has access to a digital map incorporating the

zone information and the RSU topology. We assume the

existence of a real-time Traffic Information Service (TIS)

for the metropolitan area. The TIS maintains historical

traffic data and can infer the traffic level at a future time.

Traffic is classified in three levels, namely, TA, TB and TC,

signifying no, moderate and high traffic congestion

respectively. The tracking procedure initiates when RSUs

broadcast the request to track messages (TREQ) with the

target’s LPN. Upon receiving a TREQ, an OBU activates the

tracking mode and starts collecting visuals of its

surroundings. Tracking information are communicated

among OBU’s by means of exchanging TREQs containing

the 2-tuple (z, t) where z is the latest known zone of the

target and t is the time of observation. There are three types

of TREQs: INIT (initial), BCST (broadcast) and RBCST (re-

broadcast). Based on the tracking activity, an OBU can be a

primary observer (OBUprm) or a secondary observer

(OBUsec). The OBUs forward accumulated tracking data to

the RSUs, as TDAT messages, either directly or in a multi-

hop manner. After predicting the possible future location(s)

of the target, the RSUs broadcast TREQs in the appropriate

zone(s) in a timely manner so that OBUs can accurately

localize the target. The infrastructure proposal also

incorporates mechanisms for efficient message propagation

and congestion control. Details are available in [26].

IV. PREDICTING FUTURE LOCATION OF THE TARGET

It is impossible to guarantee that the target will always be within OBUs’ camera FOV. Although, continuous citywide TREQ broadcast until the target is confiscated, is a potential solution; it would be very inefficient [26]. In order to scope the search and limit the number of OBUs and RSUs involved

in tracking, we propose a probabilistic model to predict the future trajectories of the target. The objectives are to overcome the effect of vision occultation and false positive detections, and enhance tracking efficiency by broadcasting TREQs only in the probable zones where the target may be situated at a given time, thus, minimizing the number of transmitted messages. In the remaining of the paper, on several occasions, we will refer to two functions, namely, getPathsByDistance and getPathsByTime. Because of space limitations, the algorithms that implement these functions are not provided in this paper.

Let us assume that vehicle X is the target. From TDAT received by the RSUs, we construct a set S of zone ID-timestamp pairs. Here, S={(zi, ti), (zi+1, ti+1), …, (zj-1, tj-1), (zj, tj)} where ti< ti+1 … < tj-1< tj. zj is X’s latest known location. S also represents X’s trajectory for the interval tj-ti.

First, we propose a method to model X’s movement behaviour. The entries in S revels information regarding X’s locomotion in the road network. For example, the headed direction from an intersection and zone type. From the TIS, we can retrieve the traffic level for a zone ID-timestamp pair (z, t)∈S. We model the movement behaviour using three attributes: direction, zone type and traffic level. We consider four directions, namely, North (N), South (S), East (E) and West (W). In an observed trajectory, we label each zone and their adjacent zones using a 3-tuple (DIR, TYP, TRF), referring to direction, zone type and traffic level respectively. The domains are defined as DIR∈{N, S, E, W}, TYP∈{ZA, ZB, ZC} and TRF∈{TA, TB, TC}.

In general, each vehicle on the road has an ultimate objective that is not transparent to other vehicles. The objective could be a target destination or a road trip along the coastal highway. A vehicle on the run is no different and most likely to have similar objectives. If not interrupted, we are actually allowing the target to materialize its original intentions. The locomotion pattern of the target is very much likely to reflect its original objective(s). By observing the movement behaviour, we may be able to hypothesize the locomotion pattern of the target. An example hypothesis is: the target is avoiding high traffic zones and heading to the North. A hypothesis can be characterized by constituting movement behaviour features. In the above example, two relevant features are direction and traffic level. Based on this conception, we theorize a movement modeling technique called feature hypothesis (FH). The feature space F is composed of independent features, the domains of DIR, TYP and TRF. Each element of DIR, TYP and TRF is called a primitive feature hypothesis (PFH) e.g., (ZB) and (TA). Multiple PFHs assemble a composed feature hypothesis (CFH), e.g., (ZB, TA) and (W, ZB, TA). The movement behavior is expected to converge to one to multiple PFH(s) and/or CFH(s). In this paper, we only use the PFHs.

Let G=(V, E) be the graph underlying the road network where V is the set of nodes, E is the set of edges and T is the time horizon. Each node and edge represents an intersection and a zone respectively. The location of X at time t∈T is Xt. If the location of X at time t=1 is i∈V then the initial state probability πi=P(X1=i). Assuming that at each time step X can only travel to a neighboring node, at time t+1 X’s location Xt+1=j∈NBi where NBi={j∈V: (i,j)∈E}, the set of

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neighbors of i. Hence, the trajectory evolution on G is Markovian such that, P(Xt+1=j|Xt=i):=Pi,j for all t∈T and the transition probability matrix Pt=[Pi,j]. For each i,

1, iNBj jiP and Pi,j=0 for jNBi [23]. In the addressed

problem, each Pi,j depends on the property of the edge (i,j) (i.e., a zone) which is realized by the 3-tuple (DIR, TYP, TRF). Since, we do not presume any motion model for X, we compute [Pi,j] from S. First, each zone in S and their neighboring zones are labeled using the 3-tupe (DIR, TYP, TRF). Assuming no U-turn is made at an intersection, X may have one to three transition alternatives. Fig. 1 (a) presents this idea with an example. Transiting from z1, X has three alternatives.

A. Motivation behind the improved model

In [26], we proposed a Dirichlet-multinomial model

under the Bayesian estimation framework and calculated the

selection probability of the PFHs using the Baye’s rule under

the squared error loss [24]. In the context of the addressed

problem scenario, one limitation of using the Dirichlet-

multinomial distribution is that it assumes that choice sets

are uniform in each trial. More specifically, at each

intersection (which is equivalent to a trial), the target is

assumed to be presented with all three possible zone types,

traffic alternatives and four directions. In reality, the

likelihood of the choice sets being uniform is impossible.

Fig. 1 shows three examples of choices sets at three different

intersections. Another shortcoming of the previous model is

that it does not account for the avoidance behavior. No

distinction is made between, when a PFH is avoided and

when it is not present at a trial.

Our aim is to develop a computational model that

addresses limitations of the D-M model. A model that takes

varying choice sets into consideration and segregates

avoidance behavior from absence of a PFH. Furthermore, we

are interested in achieving fine-grained classification of

behavioral components. If an alternative is chosen from a

larger choice set compared to a case with a smaller set, it

should be regarded highly compared to the other. For

example, let us assume that in Fig. 1 (a), z4 is chosen and in

(b), z6 is chosen. In both cases the selected TRF is TB. In Fig.

1 (a), there are three TRF alternatives while in (b), there are

two. Since, in Fig. 1 (a), TB is chosen in presence of higher

number of alternatives than in (b), the trial in (a) should

impact the selection likelihood at a higher degree compared

to the one in (b). Consequently, in Fig. 1 (c), transiting from

z8, there is only one choice to make. The latter should not

have any impact.

B. A conditional logit based movement estimation model

The improved model is based on conditional logits,

originally proposed by McFadden in 1973 [25]. Conditional

logit is an attractive technique when the choice among

alternatives is a function of the characteristics of the

alternatives. This feature of conditional logit makes it a

powerful tool for modeling behavioural estimations. Here,

an alternative refers to a PFH. A trial takes place at an

intersection where the target is presented with varying

number of alternatives.

Figure 1. Examples of avalable atlernatives at three different

intersections, namely, n1, n2 and n3. Zones are labeled using the 3-tupe (DIR, TYP, TRF).

Let us assume, i is the set of possible alternatives at the

ith

trial, J is the total number of possible alternatives and

ij is the jth

alternative. ],,[ 1 J is the

corresponding parameter vector for the characteristics of the

alternatives in the ith

trial. ij is a parameter of the system,

an observable covariate associated with the alternative j.

According to the conditional logit model, the probability that

the jth

alternative is chosen in the ith

trial is

i

j

j

j

je

eP

.

The conditional logit model is known to be related to the

log-linear model.

We use a Bayesian nonparametric computational

technique to estimate the PFH selection probability sP of a

category alternative. For a sample ST over the time horizon

T, the posterior distribution of is )()()|( PLSP T

where )(P is the prior density and )(L is the likelihood

function. After k trials (i.e., observations at k intersections),

the likelihood of the k choices is

k

j i

j

j

e

eL

)( . The

rational objective of a choice would be to maximize this

likelihood function. We assume a prior on with a Gaussian

distribution, ),(~ N with mean 0 and a scalar

covariance matrix I2 where I is the identity matrix.

The variance 2 is a scaling parameter regulating uncertainty

of the prior. A PFH selection probability sP is the posterior

distribution of the associated conditional logit parameter.

We describe the likelihood function using an example.

For simplicity, we consider only the traffic level (TRF) of

four consecutive intersections from a sample trajectory

(Table I).

TABLE I. A SAMPLE OF SIZE FOUR SHOWING ALTERNATIVES

Intersection Alternatives Chosen Alternative

1 A, B, C A

2 A,B A

3 A,C C

4 A,B,C A

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CBA

A

CA

C

BA

A

CBA

A

eee

e

ee

e

ee

e

eee

eL

)(

is the likelihood and the prior is

)]2/()(exp[)( 2222 CBAP . Since, we are

using a Gaussian prior on the conditional logit parameter ,

then the posterior distribution of is not a known

distribution. However, we can approximate it with a Gaussian distribution. Since, the mean of a Gaussian distribution is also the mode of the distribution; hence, the mode of the posterior is an approximation of the mean of the posterior. We are using the mode, since we can compute it numerically using the Nelder-Mead algorithm. The mode of the prior is =(0, 0, 0), while the mode of the posterior after Bayesian updating is =(1.13, -1.54, 0.41), when the scaling

parameter 2 is equal to 10.

The latest known location of X is zj at time tj. We would like to predict X’s locations after P units of time at time tk. Here, P=tk-tj. Tjk={tj, tj+1, …, tk-1, tk} is the time horizon. The function getPathsByTime(zj, P) returns a set

PATHs={PATH1, …. , PATHℤ+} containing all possible

unique paths X may travel on in P units of time. A path PATHy={zj, …, z1, z2, z3, …, zk} where each zx∈Z and zk is the furthest zone reachable in P units of time. During the interval tk-tj, at any time instance in Tjk, X should be in one of the zones in any path PATHy∈PATHs. First, all the zones in PATHs are labeled using the 3-tuple (DIR, TYP, TRF). We calculate the zone probability zP of each zone, which is the product of the selection probabilities of the three constituting

PFHs, DIR, TYP and TRF.TRFTYPDIR sPsPsPzP . Next,

for each path PATHy, we calculate the path probability pP,

which is the product of zP of all zx∈PATHy.x

m

x

zPpP

1

where |PATHy|=m. Unfortunately, pP is not an ideal metric for comparing different paths, because the paths are likely to contain varying number of zones. Since, zP ≤ 1, a path containing a higher number of zones would yield a smaller pP value compared to a path with a lower number of zones, regardless of the individual zone probabilities (unless, all zones have zP = 1, which is almost impossible). In order to resolve this ambiguity, we calculate geometric mean (GM) of zone probabilities of each path. The geometric mean

m

zPm

i i

epGM

1

ln

where |PATH|=m. We use this metric to

compare paths in terms of containing the most probable zones. For any two unique paths, PATHa and PATHb, the statements )\( ba PATHPATH and its commutative

)\( ab PATHPATH , are always TRUE, but the paths

may not be mutually exclusive, i.e., both may contain common zone(s). For this reason, we introduce a new parameter zGM to each zone (in a path) whose value is computed according to the following equation:

otherwisepGM

PATHandPATHzifpGMzGM

y

yyxymy

x

1|}{|}{})({max,..,1

The reason for using zGM as a metric is to handle the conflicting situation where a path with a high pGM may contain a zone with zGM < pGM, but the probability of X

traveling on this path is high. Additionally, if a zone is shared among multiple paths, it may have different zGM values for different paths. Whether to broadcast TREQs in zone or not is determined by a pre-established minimum threshold zGMmin. If zGMx < zGMmin, RSUs in zx are not considered for TREQ broadcast. Tracking efficiency can be further enhanced by incorporating highly probable zone IDs to the TREQs. An OBU may remain in surveillance mode and broadcast TREQs if its own trajectory contains these highly probable zones.

Localization success depends on the rate of successful and true positive observations of the target X. Let us assume, when X is in zone i∈Z, at time t∈T, X is observed by an OBU u in i with probability ρi and not observed with probability 1-ρi. Observation probability ρ depends on onboard camera’s detection probability ς and φ, probability of identification reliability of the LPIA and hence, ρ=ςφ. An OBU may make a false observation that X is in zone j (j ≠ i) at time t with probability δj and false-negative observation with probability 1-δj. Therefore, at t, the probability of u making an independent observation is,

jt

t

jt

it

it e

jjX

e

j

e

i

e

ittut XOPO

11)1()()1()()|( where

eti=1 is the event that X is observed in i at t and et

i=0 when

not observed. etj=1 is the event that X is falsely observed in j

at t and etj=0 when not-falsely observed. Consequently, the

probability of k OBUs making independent observations in i

at t is, )|()|(1

tt

k

u

uttk XOPXOP

. If P(X1) is the initial state

probability and P(Xt|Xt-1) is the state transition probability of X, the joint probability over the fixed time interval T is,

T

t

T

t

tt

k

u

uttTT XOPXXPXPOXP2 1 1

11:1,:1 )|()|()()( .

P(X1:T,O1:T) reveals two pieces of information, localization success likelihood and reliability of the sample available for future prediction. We assume that ξ is the minimum reliability threshold (to be established empirically). The sample S is only usable if P(X1:T,O1:T) > ξ . The proposed tracking system aims to maximize P(X1:T,O1:T) to increase chance of localization success.

V. EXPERIMENTS AND RESULTS

In this section, we evaluate our proposal by means of an experimental analysis. We compare the results of the conditional logit (C-L) model with the D-M model. We have chosen a part of the central-downtown area of the city of Toronto. First, we transform the 2-D map of the considered area into a graph G(V, E) as explained in Sect. III. The graph contains zones and simulated road traffic information. We have developed a tool based on Google Maps API [30] which allowed us embed zone information to the city map and obtain a graph representation of the city area. The tool was used to retrieve all the relevant data such as zone lengths and travel times. We refer to a highway as a zone of type ZA, a major road with traffic lights as ZB and a minor road or street with stop signs as ZC. Lengths of zones of type ZB and ZC are the same as in the original map (intersection-to-intersection) and are always less than 500 m. Since, the highways stretch over 500 m without any intersection or exit, the zone lengths for type ZA are limited to 500 m. We allow the target to travel for 25 minutes without any preplanned motion constrains and

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obtain an uninterrupted sample S as in Fig. 2. Traffic levels are shown using green for TA, orange for TB and red for TC. The intersections are shown using blue points. In the traveled path, type ZA zones are shown using orange overlays, ZB using purple and none for ZC. The hypothesis used here is, to minimize the chances of traveling through high traffic zones.

Figure 2. The sample trajectory after 25 minutes of movement. Traffic

levels in the traveled zones and their neighbouring zones are shown.

Figure 3. Comparision of the PFH selection probabilities of DIR.

Figure 4. Comparision of the PFH selection probabilities of TYP.

We would like to verify if the model maximizes the PFH

selection probabilities that best describe the hypothesis. Figs.

3, 4 and 5 compare the PFH selection probabilities of DIR,

TRF and TYP respectively. We observe that the PFHs differ

across the two models. In Fig. 3, the D-M model gives

DIR:E the highest probability while in the C-M model, it has

the second lowest probability. This is due to the fact that in

addition to being selected, despite being present in the

choice sets, DIR:E was avoided a considerable number of

times In Fig. 4, according to the D-M model, TYP:B has the

highest probability but has the lowest probability according

the C-L model. Similar reasoning applies to TYP:B in Fig. 3.

TRF demonstrates similar outcomes in both models (Fig. 5).

TRF:A has the highest selection probability by. We observe

that the results are consistent with the original hypothesis.

Figure 5. Comparision of the PFH selection probabilities of TRF.

Figure 6. Updating of the modes of the posterior distribution of the

conditional logit parameter for TRF when 2 =1.

Figs. 6 and 7 show updating of the modes of the

posterior distribution of the conditional logit parameter

where 2 =1 and 100 respectively. Due to space limitations

we only present results for TRF. Here, the prior mode is

=(0, 0, 0). The mean of a Gaussian distribution is also the

mode of the distribution; hence, the mode of the posterior is

an approximation of the mean of the posterior. The results

show that when 2 =100, the prior contributes less to the

estimates.

Figure 7. Updating of the modes of the posterior distribution of the

conditional logit parameter for TRF when 2 =100.

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The latest know zone zj of the target is z27 (or the

intersection n39) (Fig. 2). The getPathsByTime(zj=z27, P=7

minutes) function returns a very large set of future paths for

the considered city area. For our analysis, we consider six

different paths, indexed P1 to P6 (Fig. 8). The stripchart in

Fig. 9 compares path probability of the six future paths. The

probabilities are presented on a log scale. Comparing the

means (red dots) on a log scale is equivalent to comparing

the geometric means on the linear scales of the probabilities.

P4 and P5 have the highest means while P2 have the lowest.

RSUs belonging to the zones that fall below the minimum

threshold are not be considered for TREQ broadcast. Zones

z49, z60, z61 and z62 are shared among the paths P4, P5 and P6

and hence, are assigned the highest mean value which is the

one of P5.

Figure 8. Six possible future paths from z27 rechable in 7 minutes. Traffic

levels are mapped to average velocity according to the zone type. For

example, for the zone type ZB, if traffc level is TC,then average velocity is

considered to be 30 kph.

VI. CONCLUSION

We have presented a technique for tracking an on the run vehicle in a metropolitan VANET. First, we have described the VANET and message-passing infrastructures. We have proposed an efficient way of managing location information in the VANET setting. Instead of presuming any motion model, we have utilized a probabilistic technique that classifies the target’s movement patterns, which in turn aid future trajectory prediction. The objective is to scope the search to limit the number of OBUs and RSUs involved in the tracking operation, thus, minimizing the number of tracking messages. In our previous work, we proposed a Dirichlet-multinomial model under the Bayesian framework. We have identified limitations of this model and presented newly identified cues towards improving the model. To this end, we have proposed a conditional logit based movement estimation model. The model uses a Bayesian nonparametric computational technique with a Gaussain prior on the parameters of the conditional logit system. We have evaluated the new model by means of an experimental analysis, using a real city map and compared the results with that of the D-M model. The results show successful identification of features that dominate the target’s movement behavior.

The next step in this ongoing research would be developing a simulation environment for the addressed

problem. Considering additional feature descriptions of the target will also enhance the detection and identification procedures, e.g., color, type of vehicle and make. There are research opportunities regarding forwarding of collected tracking data to RSUs and should be thoroughly investigated in the context of the addressed problem. The proposed movement modeling technique and probabilistic trajectory prediction algorithm can be adapted for other problem scenarios such as, control of autonomous vehicles, mobile robotics, persons tracking, road traffic modeling, adaptive content delivery network and emergency vehicle notification in VANETs.

Figure 9. Log probabilites of six future paths showing mean values (red

dots).

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