Environment and Movement Model for Mobile Terminal ...

Wireless Personal Communications 24: 483–505, 2003.© 2003 Kluwer Academic Publishers. Printed in the Netherlands.

Environment and Movement Model for Mobile TerminalLocation Tracking �

M. McGUIRE, K.N. PLATANIOTIS and A.N. VENETSANOPOULOSThe Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto,10 King’s College Road, Toronto, Ontario, M5S 3G4, CanadaE-mail: {mmcguire,kostas,anv}@dsp.toronto.edu

Abstract. Mobile terminal position location, tracking and prediction are becoming important areas of researchfor advanced cellular communications. Methods for mobile terminal location are evaluated using simulations. Toobtain accurate simulation results, the simulation environment and terminal motion model must be as realisticas possible. This paper describes a simulation system for mobile terminals located within vehicles in dense urbanenvironments. These are the mobiles with the greatest need for location predictions in the environments of greatestinterest to network providers. The radio propagation model is based on well known multipath radio propagationmodels. The motion model combines an accurate kinematic model for vehicular motion with a driver decisionmodel to mimic human driving decisions. Simulated mobile terminal motion tracks are presented, showing howrealistic motions are generated.

Keywords: mobile communication, mobility, motion model.

1. Introduction

The purpose of wireless terminals is to free the user from having to be at a fixed location whilesending or receiving communications. To satisfy this desire, cellular mobile phone systemswere designed so that users could use these systems while they were in motion [1]. Thismotion during a communication session creates several difficulties in resource and networkmanagement for the network operator. Some of these issues are terminal location and pagingfor incoming calls, ensuring quality of service for users as they move from one area to anotherduring a call, and maintaining the quality of service of on-going calls while accepting newcalls. These problems will only become more difficult to solve for third generation cellularsystems since mobile calls will no longer be only voice or low bandwidth data but also highbandwidth multimedia applications such as video or high quality music. One method that isoften proposed to solve these problems is to use mobile terminal motion prediction to reserveresources for a user at locations they are likely to be occupying in the future [2, 3].

Several methods for location and tracking of mobile terminal position have been presentedin the literature [4–8]. The best way to evaluate a terminal location method is to performexperiments in the environment of interest. Unfortunately, this is expensive so the only methodto evaluate a location method is via computer simulations. The computer simulations of thenetwork environment and mobile terminal motion must be realistic or the location methodevaluation will be of extremely limited value.

This paper will describe a simulation environment for the evaluation of mobile terminallocation methods. This paper will concentrate on simulation models for mobile terminals

� Partially supported by a grant from the Nortel Institute for Telecommunications.

484 M. McGuire et al.

within road vehicles located in dense urban areas. These are the regions of greatest interest tocellular network providers for mobile terminal tracking. These areas have the largest numbersof wireless terminals users with the highest demand for high bandwidth services. The users ofmobile terminals in road vehicles are likely to obtain the greatest benefit from mobile terminallocation prediction for resource allocation.

This paper reviews the propagation model used for wireless communications concentrat-ing on the affects this propagation will have on the distance measurements used for mobileterminal location. A motion model for mobile terminals is proposed which concentrates on anaccurate kinematic model of vehicular motion combined with a model for driver decisions. Asimulation system based on the propagation and motion model is then presented.

Section 2 describes the propagation and motion models. Section 3 then describes thesimulations developed based on the models. Section 4 summarizes the results of the paper.

2. Model of Mobile Terminals in Dense Urban Areas

The Model of the mobile terminal can be split into two main parts: The propagation model andthe motion model. The propagation models describes how a radio signal transmitted from abase station changes before it is received by the mobile terminal. The motion model describesthe how the position of the mobile terminal evolves over time. These models are describedseparately below.

2.1. PROPAGATION MODEL

Radio propagation in urban environments is a complex phenomenon. An effect that is commonin cellular radio propagation is multipath propagation. During multipath propagation the radiosignals travels from the transmitter to receiver via multiple paths each with its own attenuationand transmission delay. This is shown in Figure 8. The received signal at the mobile terminal,r(t), is modeled as being

r(t) =N∑

j=1

Aj(t)s(t − τj ) + n(t), (1)

where N is the number propagation paths from the base station to the mobile terminal, and s(t)

is the signal transmitted from the base station, and n(t) represents interference and noise [9].Each propagation path has an attenuation Aj(t), and propagation delay, τj . The attenuation isgiven by

Aj(t) = l(dj )f (t), (2)

where dj is the length of propagation path j , l(dj ) is the deterministic path loss, and f (t) is arandom process representing fast fading such as Rayleigh fading [10]. The deterministic pathloss in decibels, denoted L(dj ) = 10 log10(l(dj )), has been shown to be well modeled as alogarithmic function of dj such as

L(dj ) = −10c log10(dj ) + Cj , (3)

where Cj is a constant that is a function of radio frequency, and diffraction [11]. The valueof c is determined by the environment. A value of c = 2 is used in free space while in

Environment and Movement Model for Mobile Terminal Location Tracking 485

urban environments a value of c ∈ [3, 5] matches field measurements. For the COST Walfish-Ikegami Model with antennae below roof tops, Cj = 24 dB and c = 4.5 [11].

The simple path loss propagation equation in (3) is fairly accurate for terminals positionedat the edge of the cells which are the positions of greatest interest to designers of handoffand resource allocation algorithms. More complex propagation models can also be used thattake into account the position and geometry of the obstacles [4], or use more exact propagationmodels for micro-cells [12]. The advantages of these models is greater accuracy of radio prop-agation simulation for terminals position closer to the base stations obtained at the expenseof more computational cost. Since these locations are off less interest, these models are notdescribed in detail here. They might be implemented in future versions of the simulator.

The measurements most often proposed for location of digital mobile terminals are theTime of Arrival (ToA) and Time Difference of Arrival (TDoA) measurements [4, 7]. Thereason for this is that modulation and multiple access schemes used in current digital networksallow for high resolution time measurements. This paper concentrates on ToA measurements.A great deal of work for third generation cellular systems proposed the use of CDMA as theradio interface [13]. In these systems, the data sequence is multiplied with a binary sequencecalled the spreading sequence or spreading code that has special autocorrelation properties.The spreading sequence, p(k) has an autocorrelation, Rpp(K) function with the properties[14]:

Rpp(K) = E[p(k)p(k + K)

] =

1 K = cN c ∈ {0, 1, 2, . . .}− 1

Notherwise

, (4)

where N is the period of the spreading sequence. The continuous time version of the auto-correlation function is shown in Figure 1 with the assumption that the spreading sequence isconverted to square pulses before the autocorrelation is evaluated.

The properties of the spreading sequence allow propagation delays in a received signal tobe measured at a receiver provided the spreading sequence is synchronized at the transmitterand receiver. The principles are shown in Figure 1. By sweeping the value of n, the variabledelay, and looking for peaks in the average output of the system, it is possible to calculatevalues for the delays N1, N2 and N3 [15].

Multipath propagation creates greater entropy in propagation measurements as a signalmeasurement gives less information about the relative positions of the receiver and transmitter.The result in the cross-correlation between received signal and the spreading sequence is extrapeaks such as those generated by N2 and N3 in Figure 1.

In a real system, this is complicated by different powers for each of the received propaga-tion paths, noise, signal interference, and modulation effects. The cross-correlation betweenthe received signal and known spreading sequence resembles Figure 2. The receiver must iden-tify the position of the first peak in the received correlation to find the propagation time. Thenoise and interference generate a time-correlated noise sequence which is added to the cross-correlation waveform at the receiver output. This makes the propagation time measurementinto an estimation problem.

The result of this estimation is the measured propagation delay, τ , given by

τ = τ + ε, (5)

where τ is the true propagation delay, and ε is a random variable modeling the effect of errorsin the estimation process.


Figure 1. Spreading sequence properties.

Figure 2. Received signal correlation with spreading sequence.

The measurement noise has been shown in many cases to be near Gaussian in density[16]. The variance of the measurement noise is a function of the signal power, interferencepower, and noise power at the receiver. Multipath propagation increases the variance of thethe measurement noise as the power of the first signal path is decreased and makes the distancemeasurement biased to a value greater than the shortest propagation path distance [17]. Thispositive bias is created by the probability that the time measurement device will incorrectlydetect one of the extra longer propagation paths as the shortest propagation path instead of thetrue shortest distance path.


Figure 3. Modes of mobile terminal mobility.

2.2. MOTION MODEL

Modes of mobile terminal mobility are shown in Figure 3. Mobile terminals are more likelyto be carried by pedestrians than to be located inside vehicles but the higher mobility ofvehicle mounted mobile terminals makes tracking their position and estimating future lo-cations a larger concern than for pedestrian carried mobiles. A mobile within a vehicle islikely to require more handoffs as it will move over a greater distance during the period of acommunication session than a pedestrian carried mobile terminal. This makes the processingrequirement for resource management of the vehicle mounted terminal higher and greaterperformance gains can be had by tracking and predicting the motion of vehicle mounted ter-minals than pedestrian terminals. The motion of mobile terminals located on trains or subwaysis also likely to be of high velocities and thus experience many handoffs, but the motion is alsohighly predictable so the tracking problem is much simpler than for mobile terminals in roadvehicles. Other modalities for mobile terminal motion will have other characteristics similarto one of those described above or are rare enough that tracking is not a concern for networkproviders. For these reasons, this paper concentrates on the motion model for mobile terminalsinside of road vehicles.

The motion of a mobile terminal is also influenced by the environment in which it islocated. On a highway, an automobile’s motion is highly predictable with the speed beingnear the speed limit while remaining in one lane for a long period of time. The randomness ismainly restricted to lane changing maneuvering and exiting behavior. Conversely, an automo-bile that is located in a parking lot has a high degree of randomness as the direction of motioncan be fairly unrestricted with a limit on speed.

A pedestrian in an urban environment will be restricted to motion on sidewalks with limitedmotion on vehicle lanes. Pedestrians can change direction in short distances while automobilesthat wish to make major direction changes must do so only at intersection locations. Pedestrianmotion in suburban and rural environments is almost unrestricted with motion across vehiclelanes being common. Bicycles have behavior that at some times is like an automobile but atother times can be like a pedestrian.

The description of the motion for mobile terminals will be subdivided into descriptionof the kinematics of vehicular motion, and a description of the driver decision model. Thekinematics of vehicular motion are the physical laws which affect the motion of vehicles. Thedrivers decision model describes the process by which drivers decide how to control theirvehicles.


Figure 4. Vehicle model.

2.2.1. Kinematics of Vehicle MotionSeveral complex models have been developed to model the kinematics of road vehicle motion[18, 19]. Most of the parameters generated by this models are not required for a motionsimulator with the accuracy we need for mobility modeling.

A vehicle can be modeled as shown in Figure 4. During street driving on flat ground, thevehicle usually only accelerates in directions nearly parallel to the major vehicle axis, in thedirection of the wheels. If the driver wishes to change the direction of motion of the vehicle,the steering mechanism changes the direction of the wheels and the vehicle will then changeorientation toward that direction.

A vehicle is subject to several friction and drag forces. The most important of these is theroad friction. This is what allows the car to accelerate since it is road friction that allows theengine of the vehicle to apply force in the direction of acceleration. Without road friction ortraction the vehicle could not accelerate and the direction of the vehicle could not be changed.

Two major forces resist the motion of the vehicle. These are rolling resistance, and airresistance [20]. Rolling resistance is generated by slip between the vehicles’ wheels and thedriving surface and friction inside of the vehicle. Air resistance is generated by the force of theair around the vehicle against its motion. Both of these increase with the vehicle’s speed. Theresult of these forces is that if the vehicle is subject to constant driving force, the accelerationof the vehicle will decrease as the velocity increases.

Other forces include the affect of non-flat driving surfaces such as roads up hills or rampswhich is referred to as grade resistance. The vehicle in these conditions will experience a forcein the direction down the slope of the surface. The magnitude of the force is a function of thesteepness of the grade of the surface. For tracking purposes, grade can be helpful as it is adeterministic function of location. This creates a mapping between vehicle acceleration andvehicle position. The model in this paper will concentrate on cases of flat driving surfaces.The addition of non-flat grade to the simulation is the subject of further research.

2.2.2. Driver Decision ModelA driver’s decision on what action to take at each point in a journey is determined by thelocation of the destination as well as other factors such as traffic conditions. The usual pat-tern of driving for a vehicle in North American cities is to drive along side roads from theinitial point to higher capacity roads, move on the large capacity roads such as freeways andhighways to the general area of the destination, and then take smaller capacity streets to the


Figure 5. Intersection diagram.

final destination. The driver’s decisions at each intersection during a journey are obviously notindependent.

As a driver approaches an intersection their selected route will determine what lane theywill use, the probability that they will brake, and which direction they will move away fromthe intersection. If they are going to turn, they will have to brake in order to make the cornersafely. If they have decided that they are going to go straight through an intersection, they willonly stop if a traffic control signal forces them to, or if there is some form of traffic blockage.

Vehicles remain in the center of their respective lanes with only small variations unlesspassing or turning. A standard North American intersection layout is shown in Figure 5.Turning usually only take place in the central area of the intersection. Turning takes placeoutside of intersections when the vehicle has reached its final destination and the vehicle isturned into a parking area.

3. Simulation Motion Model

The simulation model consists of three parts: the kinematic model, the decision model, and thepropagation model. The kinematic model will determine the mobile terminal’s acceleration,velocity, and position in response to control inputs. The decision model will mimic the driver’sdecisions as to lane selection, and whether to turn or brake at an intersection. The propagationmodel generates the simulated measurements from the mobile terminal’s location state. Therelationships between the different simulation models are summarized in Figure 6.

The simulated environment is a simple Manhattan model that has been used in the mobileterminal location literature to evaluate radio location performance [4]. The layout of the envi-ronment is shown in Figure 7. The positive y direction will be said to be North, making thepositive x direction East. The city blocks are 300 meters long, and the streets are 20 meterswide. Base stations are located in the intersection at every second block. This environmentand base station layout is typical of dense urban areas.

The next three section will describe the Propagation Model, the Kinematic Model, and theDecision Model.


Figure 6. Simulation models interaction.

Figure 7. Simulation environment layout.

3.1. PROPAGATION MODEL

The propagation time for a signal to travel from a base station to the mobile terminal ismeasured. Because radio wave propagation speed in the atmosphere is near the speed of lightin vacuum, c, a time measurement, τ , can be easily translated to a distance measurement, d,via

d = τ · c. (6)


Figure 8. Multipath propagation.

The measurement noise in the simulation model is modeled as being Gaussian. The distancemeasurement for a base station is given by

Zj = dj + vj , (7)

where j denotes the base station, Zj is the measurement of base station j , dj is the propagationdistance from base station j to the mobile terminal and vj is a random variable representingmeasurement noise for base station j .

The propagation between the mobile terminal and base station is called Line of Sight(LOS) when the straight line propagation path between the mobile terminal and base station isunobstructed. The propagation distance will be the true distance between the mobile terminaland base station.

In the Non Line of Sight (NLOS) case, the shortest distance propagation path between themobile terminal and base station is blocked by some geographical feature or a building. Thepropagation distance in this case is always greater than the true distance between the mobileterminal and base station. For the Manhattan model used in the simulations it is assumed thatduring NLOS propagation, the signal diffracts around corners and the shortest propagationpath length is the distance from the base station to the corner plus the distance from the cornerto mobile terminal. This is represented by dj = dc + dr in Figure 9.

The measurement noise is Gaussian with a mean of 16.0 meters and a standard deviation,σd , of 16 meters. The parameters of the noise density are taken from [4], which simulated thepropagation time measurements for ToA location in this environment. Multipath propagationwas based on the COST 207 urban power delay profile.

It is assumed that only the five closest base stations to the mobile terminal can measure thepropagation delay. This constraint results from signal loss and channel reuse considerations.Base stations other than the closest five would either not receive a strong enough signal from


Figure 9. Manhattan propagation environment.

the mobile terminal to be able to measure the propagation delay, or they would have reassignedthe mobile terminal’s channel for use by another mobile terminal of greater proximity to them[21].

3.2. KINEMATIC MODEL

The kinematic model describes how the mobile terminal’s position and velocity evolve overtime in response to driver input and random noise.

The simplest kinematic motion models do not incorporate process noise. The mobile ter-minal motion is thus a deterministic function of the control inputs. The control input is eitherthe mobile terminal velocity or its acceleration [22–26]. These models are used to analyzegroup behavior of mobiles such as handoff rates and mean sojourn times in cells. They are notselected to provide accurate representations of a single mobile terminal’s behavior.

The addition of random process noise to the mobile terminal motion model makes themobile terminal motion random given the control input. The velocity and accelerations canvary between control input changes. The process noise models factors such as noise in thecontrol system of the vehicle, variations between drivers, and random road conditions.

There are several state space models with random process noise proposed in the literaturefor mobile terminal motion modeled as Brownian Motion [5], velocity modeled as BrownianMotion [27], and motion modeled as Fractional Brownian Motion [28]. None of the modelswere based on characteristics of vehicle’s motion but instead were primarily selected forcomputational simplicity. This resulted in some of the models having characteristics disparatefrom actual vehicular motion. For example, the velocity modeled as Brownian Motion modelhas the characteristic that the variance of velocity tends to infinity as t → ∞.

We propose a model based on vehicle motion characteristics. Vehicle velocity has a finitevariance at all locations in the simulation environment. As well, vehicle acceleration is depen-dent on the vehicle’s current speed. The greater a vehicles velocity in a given direction, theless acceleration it will be capable of in that direction as resistance increases [29]. A linear


drag term, α, is introduced into the kinematic model to model this. A random motion modelwhich matches this observation is based on a modified form of the Langevin equation [30].Mobile terminal motion in one dimension is given by

x(t) = −αx(t) + w(t) + u(t), (8)

where x(t) is mobile position, x(t) is mobile velocity, x(t) is mobile acceleration, u(t) is adeterministic function representing driver control, and w(t) is a process noise.

3.2.1. Speed ControlThe control input, u(t), is the drivers input into the system which controls the direction thevehicle is moving, in which direction it will accelerate, and so on. The value of u(t) directlyinfluences the mean speed of the vehicle in control input direction.

If u(t) = 0 then the mobile position will wander around x(t) = 0 with E[x(t)] =E[x(t)] = E[w(t)] = 0. A positive value of u(t) will bias the mobile terminal motion inthe positive direction, limt→∞ E[x(t)] = u(t)/α if u(t) is constant. A negative value ofu(t) has the opposite effect. The driver of the vehicle will select u(t) based on the vehi-cles present location, the speed limit, and the final desired destination. The process noise,w(t), is a white Gaussian process, E[w(t)] = 0, and Var[w(t)] = σ 2. The variance ofthe velocity given the control input is determined by the variance of the process noise,limt→∞ Var(x(t)) = Var(w(t))/(2α). Observations of real vehicle speeds by vehicular trafficengineers have shown that the distribution of vehicle speed at a fixed locations can be modeledas Gaussian [29]. The maximum mean acceleration of the vehicle is u(t) m/s2 which is attainedwhen x(t) = 0 m/s.

We assume that the mean velocity will be 54 km/h or about 15.0 m/s, standard velocities fordowntown North American streets. The maximum mean acceleration during standard drivingfor a standard passenger automobile is 2.5 m/s2 [20]. To match these performance values, weset α = 1

6 and the standard control input, u(t) = 2.5. We used a value of σ 2 = 13 to give a

standard deviation of 1 m/s (3.6 km/h) in the velocity.

3.2.2. Direction ControlIn reality, the mobile position is a two dimensional vector. The elevation of a vehicle is usuallya deterministic function of its (x, y) location with rare exceptions such as multi-deck bridgesor elevated highways so it is not included in this model. A four state space model is used forthe location state of the vehicle. The state vector is given by:

x(k) =

px(k)

vx(k)

py(k)

vy(k)

, (9)

where (px(k), py(k)) are the the location coordinates of the mobile at sampling time k, and(vx(k), vy(k)) are the velocities of the mobile terminal in the x and y directions at samplingtime k.


The continuous time two-dimensional model is

x(t) = Ax(t) + B{w(t) + u(t)}

=

0 1 0 00 −α 0 00 0 0 10 0 0 −α

x(t) +

0 01 00 00 1

{[wx(t)

wy(t)

]+

[ux(t)

uy(t)

]}.

(10)

The terms wx(t) and wy(t) represent zero mean white Gaussian noise processes with variancesof E

[wx(0)2

] = E[wy(0)2

] = σ 2 which are the process noise terms for the continuous timedynamic model.

The deterministic inputs, representing driver control input in the x and y directions aregiven by ux(t) and uy(t). These inputs determine the direction that the mobile terminal willmove. If for all values of t ≥ Tf , ux(t) = ux(Tf ) and uy(t) = uy(Tf ), then

limt→∞ E

{[vx(t)

vy(t)

]}= 1

α

[ux(t)

uy(t)

]Thus, ux(t) and uy(t) determine the final direction of motion. If the control inputs change, themobile terminal motion will smoothly change to the new direction of motion as the drag termforces the velocity functions to remain continuous.

The asymptotic covariance of the velocity vector, using the results from Section 3.2.1, canbe easily found to be

limt→∞ E

{[vx(t)

vy(t)

][vx(t) vy(t)]

}=

[σ 2

2α0

0 σ 2

2α

].

3.3. DISCRETE TIME KINEMATIC MODEL

In practice, we can only sample measurements of the state of the system at discrete times.We will assume that the state is sampled at a frequency of 1/T . A discrete version of thedynamic model can be obtained from the continuous time model [31]. We make the simpli-fying assumption that the inputs (ux(t), uy(t)) change only at the sample times. Obviously,in the field the inputs can change at any time instant not just at the sampling instants. Theerror introduced by this mismatch between the modeling assumptions and real model willbe negligible provided the sampling period is small compared to the time constant of thecontinuous system, α−1. The sampling period is set at T = 0.5 seconds which is less thanthe time constant of the system of 1/α = 6.0 seconds which justifies the assumption madeto discretize the continuous state space model. The resulting discrete time dynamic model isgiven by

x(k + 1) = �x(k) + �

[ux(k)

uy(k)

]+ W(k), (11)

where

� =

1 (1−exp(−αT ))

α0 0

0 exp(−αT ) 0 0

0 0 1 (1−exp(−αT ))

α

0 0 0 exp(−αT )

,


� =

exp(−αT )−1+αT

α2 01−exp(−αT )

α0

0 exp(−αT )−1+αT

α2

0 1−exp(−αT )

α

,

and

Q = E

[∫ T

0exp(At1)Bw(t1)dt1

∫ T

0exp(At2)Bw(t2)dt2

]

= E[W(k)W(k)T ] =

r11 r12 0 0

r12 r22 0 0

0 0 r11 r12

0 0 r12 r22

.

The components of the process noise covariance Q are given by

r11 = σ 2(2αT − 3 + 4 exp(−αT ) − exp(−2αT ))

2α3,

r12 = σ 2(1 − exp(−αT ))2

2α2, and

r22 = σ 2(1 − exp(−2αT ))

2α.

For handoff measurements, mobile terminals make measurements of the signal for thebase stations they are using for primary communications but also of the signal from otherbase stations. It is likely to be these measurements that will be extended for mobile terminallocation purposes. Therefore, the sampling period was set to the approximate the time betweenmeasurements in support of the handoff algorithm in GSM. Other networks standards, e.g. IS-95, have different sampling intervals for handoff but the handoff sampling periods are of thesame order of magnitude so the results are still valid.

3.4. DECISION MODEL

The decision model generates the control inputs into the kinematic model that will deter-mine future mobile terminal position based on the mobile terminal’s current location, and thesimulated street layout.

Several types of decision models have been proposed in the mobility modeling literature.The simplest models only change the control inputs on the boundaries of cells and do notconsider street layout [23, 24]. More complex motion models have been proposed that allowthe control inputs to change at any time [22, 25, 26]. The control inputs are kept constantover time periods with random lengths sampled from an exponential distribution. The modelin [22] models realistic direction changing behavior for vehicles. Before a vehicle makes amajor direction change, it must slow down or come to a stop. Again, street layout is notconsidered in these models. Simple models that consider street layout have been described inthe literature as well [11]. These models assume that vehicles can change their velocity anddirections instantaneously. Realistic vehicle braking and turning behavior are not considered.


Table 1. Setting for moving north onstreet (street centered at x = 0 meters).

Control input Value

ux(k) β (px(k) − 5)

uy(k) 2.5

The models allow for simple simulation and analysis of the behavior of groups of mobileterminals but are not designed to provide realistic behavior for a single mobile terminal.

Modeling human driver decision patterns accurately is difficult for computer simulations.The solution proposed in this paper is to use a model for driver behavior that has higherentropy than actual driver behavior. This means that mobile terminal position state at a sampleinterval k gives less information about the mobile terminal position state at interval k+N withN > 0 in the simulation motion than for true vehicular motion. The simulated motion is harderto track than the motion that would be generated by human drivers since past measurementsof mobile terminal position give less information about the present mobile terminal locationthan for motions generated by human decisions.

The simulated driver in the model described below makes decisions at every intersectionindependently of the previous intersection decision. Thus the tracking algorithm cannot useany form of long term behavior model to improve performance. The tracking algorithms per-formance for mobiles with motion controlled by human drivers is likely to be superior than formobiles with the control logic described below. The performance of a tracking algorithm onmotion generated by the simulator will be worse than on motion generated by a human driver.This makes this model useful for generating bounds on tracking performance. The addition ofa long term behavior model to the simulator is the subject of on-going research.

3.4.1. Simple Motion without TurnsThis decision model describes the control behavior when the mobile is located away fromintersections or when the mobile terminal is traveling down a highway. The allowed directionof all motion is in one of two directions up or down the street. Motion is restricted by the lanethe mobile terminal is in.

The control inputs are categorized as u‖(k) which is the control input in the directionparallel to the street direction, and u⊥(k) which is perpendicular to the street direction. Forexample, if the street is parallel to the Y-axis then uy(k) = u‖(k) and ux(k) = u⊥(k). Thecontrol input u‖(k) is used to control the speed along the street. The control input u⊥(k) isused to keep the mobile terminal within the proper lane.

A deterministic constant input of u‖(k) = 2.5 is applied in the direction of motion alongthe street. This will result, as described in Section 3.2, to a mean velocity of 15.0 m/s in thatdirection after a period of initial acceleration. The other control input will be set to u⊥(k) =β(p⊥(k) − c) where β is a control constant and c is the location of the center of the lane.

For example, if the mobile terminal is to heading in the positive y direction in a lane whosemiddle is located at x = 5 m, the control inputs will be set as shown in Table 1. For thesimulations described in this paper, β = − 1

4 .


Figure 10. State transition diagram for motion simulator.

3.4.2. Motion with TurnsIn the real world, a driver of a vehicle has a specific destination in mind and the generaldecisions made at intersections concerning turn direction and speed selection are knownin advance. These decisions will be modified by a large number of factors such as trafficconditions and weather.

For simulation purposes, we use a simplified decision logic system to model driver decisionbehavior. The driver’s decision at each intersection is independent of the decision made at anyother intersection during the mobile’s journey.

A simple finite state machine is used to control mobile decisions. The simulated driver isin one of four states: Normal, Braking, Turning, and Transit. The state transition diagram isshown in Figure 10.

Normal state. The mobile starts in the Normal state. In this state, the control inputs areselected as described in Section 3.4.1. The mobile will, after an initial period of ac-celeration, move at the mean velocity of 15.0 m/s down the street while staying in theproper lane. The control inputs for the main direction of travel will be set as shown inTable 2.

The position of the center of the next intersection in the decided direction of travel iscalculated. If the mobile is within B meters of the next intersection, the mobile decidesif it will turn at the next intersection. The probability of turning is given by the constantPturn. If the mobile is within B meters of the next intersection and turning it will transitionto the Braking state in the next sampling interval. If the mobile is within B meters of the


next intersection and not turning it will change to the Transit state in the next samplinginterval. If the mobile terminal is farther than B meters from the intersection then themobile remains in the Normal state.

The distance B is set to 40 meters. This distance was selected based on data on vehiclebraking distances in typical urban environments [20]. In other environments this parame-ters would be set based on the mean speed in the environment and road conditions. Thisinformation is also used by those designing road systems. The network operator needingthis information could obtain it from the traffic control authorities for the area of interest.

Braking state. In the Braking state, the mobile’s motion will be reduced so that it will stopjust inside of the intersection region. The control input in the main direction of travel willbe set to zero. The control input in the direction perpendicular to the main direction oftravel will still be set to hold the proper lane, just as in the Normal state.

The drag needed to bring the mobile to a stop just after entering the intersection iscalculated:

αnew = v

d, (12)

where v is the velocity is the selected direction of travel and d is the distance to theintersection entry point. The drag coefficient, α is set to value in the interval [ 1

6 , 5.0]nearest to αnew. This interval represents the drag coefficients that the vehicle’s brakes cangenerate. When the mobile terminal enters the intersection, the control state transitionsto the Turn state in the next sampling interval.

Turning state. In the Turn state the mobile will move the mobile terminal turn the mobileinto the proper lane for its new direction of travel. Upon first entering the Turn state,the mobile resets the drag coefficient, α back to 1

6 and sets the direction of travel tothe new direction. The new direction for the mobile is 50% likely to be either of theperpendicular cardinal directions to mobile’s current direction of travel. When the mobileterminal leaves the intersection, it will change to the Normal state in the next samplingperiod. The lane holding logic is set for the new direction of travel to move the mobileterminal into the new lane.

Transit state. When the mobile terminal is in the Transit state, control inputs will be set as inthe Normal state. When the mobile terminal is in the Transit state it will set control inputsas in the Normal state according to Table 2. When the mobile leaves the intersection, itwill transit to the Normal state in the next sampling period.

The value of Pturn was set to the value of 23 . The result of this choice is that when a mobile

approaches an intersection it has an equal probability of going straight, turning left, or turningright. This is the maximum entropy case when the mobile is restricted from going back thedirection it came.

3.4.3. Initial ConditionsWe choose initial conditions in a manner that replicates the random motion state of a mobileterminal that has just been switched on. To simplify the simulation, we always assume themobile terminal starts in the central cell with the base station located at coordinates (0, 0).


Table 2. Inputs for mobile terminaldirections.

Direction Control input

North uy(k) = 2.5

South uy(k) = −2.5

East ux(k) = 2.5

West ux(k) = −2.5

Table 3. Initial state of mobile terminal.

Initial direction px(0) vx(0) py(0) vy(0) ux(0) uy(0)

North L 0 P S 0 2.5

South –L 0 P –S 0 –2.5

East P S –L 0 2.5 0

West P –S L 0 –2.5 0

This is not an unrealistic assumption, as when a mobile terminal initiates a call it quicklyidentifies the base station that it is closest to. The location and velocity state parameters areuniformly distributed within the space of possible values. This is the distribution of maximumentropy when no other information is known about the mobile terminal’s state.

First the direction of the mobile terminal motion is selected from the possible set of {North,South, East, West}. A position value, P , is sampled from a uniform distribution with a rangeof (−D,D) where D is the block length (300 meters in Figure 9). An initial speed, S, issampled from a uniform distribution with a range of [0, 15.0]. A lane position value, L, issampled from a uniform distribution with a range of [0, 10].

From these random values the initial state of the mobile terminal position is generated asshown in Table 3 based on North American lane use.

All the motion model parameters as summarized in Table 4.

Table 4. Motion simulation parameters.

Parameter Symbol Value

Drag α 16

a

Lane control β − 14

Braking distance B 40 m

Turning probability Pturn23

Maximum mean acceleration max(u(t)) 2.5 m/s2

Block length D 300 m

Street width W 20 m

a α value when not breaking.


Figure 11. Example of motion generated by simulation.

3.5. SIMULATION RESULTS

An example of a motion track generated by the simulation model is shown in Figure 11, wherethe dotted lines indicate the edges of the streets. The starting position of the mobile terminal isnear (0, −300). The velocity during the simulated motion is shown in Figure 12. The mobileterminal shows the proper braking behavior before turning at intersections. As well the mo-bile position and velocity are continuous curves. The braking and acceleration of the mobileterminal result in smooth transitions in the mobile terminal velocity and position. The drag inthe kinematic model ensures that the velocity and position tracks remain continuous.

The random process noise adds variation to the motion. Two mobiles that start at the samelocation and make identical turn decisions will not follow exactly the same path. This is closerto actual motion behavior than a deterministic decision to path mapping.

The drag in the kinematic model creates the exponential velocity behavior which is seenabout every twenty seconds in the velocity plot in Figure 12. These patterns are created whenthe mobile terminal accelerates after making a turn at an intersection. Without this drag, themobile terminal’s velocity would make large jumps after a direction change creating inac-curate behavior in intersections. A motion model without drag would result in the simulatedmobile terminals spending less time in the area around the intersections than they would in anactual network. As can be seen in Figure 7, intersections are on the edges of cells so propersimulated behavior around these points is critical to proper evaluation of handoff and resourceallocation algorithms. The motion model presented in this paper will allow for more accurateassessment of wireless network resource management schemes.


Figure 12. Mobile velocity generated by simulation.

4. Conclusions

This paper described models for propagation time measurements and mobile terminal motionfor several different modes of mobile terminal mobility. A model describing mobile terminalmobility in dense urban environments was derived from the observations of vehicular trafficengineers.

The model for propagation time measurements was based on the methods used for measur-ing propagation time in CDMA wireless networks. The effects of multipath propagation andsignal noise and interference were described. The forces which affect mobile terminal motionwere described. The decision process which a driver uses while controlling their vehicle wasbriefly discussed.

A Manhattan simulation environment with exhibits both LOS and NLOS propagation ef-fects was described. This simulated environments has propagation phenomenon common inthe crowded urban environments of interest to network providers.

A simulation model for mobile terminal vehicular motion in urban environments wasdeveloped based on a realistic kinematic model of road vehicle motion combined with anartificial decision making process. Since the computer simulation cannot incorporate the longterm decision making ability of a human driver, the decision process was designed so thatit would create motions with higher entropy than the motion tracks of true vehicles. In thisway, the simulated mobile terminal motions would be harder to track than the motions of truevehicles.

A motion track generated by this simulation model was generated. This motion track hasthe desired properties of true vehicular motion. The simulator was designed so the motion isaccurate on the edges of cells so that radio resource algorithms can be properly evaluated.

Directions for future research include the development of a long range decision mak-ing process into the simulation model. This would allow this simulation model to be used


to realistically evaluate resource reservation and hand off algorithms in wireless networks.This simulation model can also be used to evaluate mobile motion tracking and predictionalgorithms. The kinematic model can be used to develop a recursive tracking algorithm.

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Michael McGuire is presently a Ph.D. candidate in the Department of Electrical andComputer Engineering at the University of Toronto. He obtained a B.Eng. in Computer En-gineering, and a M.A.Sc. from the University of Victoria in 1995 and 1997 respectively. Hisresearch interests are estimation and control algorithms for wireless cellular networks.

Konstantinos N. Plataniotis received the B. Engineering degree in Computer Engineeringfrom the Department of Computer Engineering and Informatics, University of Patras, Patras,Greece in 1988 and the M.S. and Ph.D. degrees in Electrical Engineering from the FloridaInstitute of Technology (Florida Tech), Melbourne, Florida in 1992 and 1994 respectively. He


was a Research Associate with the Computer Technology Institute (C.T.I), Patras, Greecefrom 1989 to 1991 and a Postdoctoral Fellow at the Digital Signal & Image ProcessingLaboratory, Department of Electrical and Computer Engineering University of Toronto, from1995 to 1997. From August 1997 to June 1999 he was an Assistant Professor with the Schoolof Computer Science at Ryerson Polytechnic University. While at Ryerson Prof. Plataniotisserved as a lecturer in 12 courses to industry and Continuing Education programs. Since 1999he has been with the University of Toronto as an Assistant Professor at the Department ofElectrical & Computer Engineering where he researches and teaches adaptive systems andmultimedia signal processing. He co-authored, with A.N. Venetsanopoulos, a book on “ColorImage Processing & Applications”, Springer Verlag, May 2000, ISBN 3-540-66953-1, he isa contributor to three books, and he has published more than 100 papers in refereed journalsand conference proceedings on the areas of adaptive systems, signal and image processing,and communication systems and stochastic estimation. Prof. Plataniotis is a member of theIEEE Technical Committee on Neural Networks for Signal processing, and the Technical Co-Chair of the Canadian Conference on Electrical and Computer Engineering, CCECE 2001,May 13–16, 2001, Toronto, Ontario. His current research interests include: adaptive systemsstatistical pattern recognition, multimedia data processing, statistical communication systems,and stochastic estimation and control.

A.N. Venetsanopolous received the Diploma in Engineering degree from the National Tech-nical University of Athens (NTU), Greece, in 1965, and the M.S., M.Phil., and Ph.D. degreesin Electrical Engineering from Yale University in 1966, 1968 and 1969 respectively. He joinedthe Department of Electrical and Computer Engineering of the University of Toronto in Sep-tember 1968 as a Lecturer and he was promoted to Assistant Professor in 1970, AssociateProfessor in 1973, and Professor in 1981. Since July 1997, he has been Associate Chair:Graduate Studies of the Department of Electrical and Computer Engineering and was ActingChair during the spring term of 1998–1999. In 1999 a Chair in Multimedia was establishedin the ECE Department, made possible by a donation of $ 1.25M from Bell Canada, matchedby $ 1.0M of university funds. Prof. A.N. Venetsanopoulos assumed the position as InauguralChairholder in July 1999 and two additional Assistant Professor positions became availablein the same area. Prof. A.N. Venetsanopoulos has served as Chair of the CommunicationsGroup and Associate Chair of the Department of Electrical Engineering and Associate Chair:Graduate Studies for the Department of Electrical and Computer Engineering. He was onresearch leave at Imperial College of Science and Technology, the National Technical Uni-versity of Athens, the Swiss Federal Institute of Technology, the University of Florenceand the Federal University of Rio de Janeiro, and has also served as Adjunct Professor


at Concordia University. He has served as lecturer in 138 short courses to industry andcontinuing education programs and as Consultant to numerous organizations; he is a con-tributor to twenty nine (29) books, a co-author of Nonlinear Filters in Image Processing:Principles Applications (ISBN-0-7923-9049-0), and Artificial Neural Networks: LearningAlgorithms, Performance Evaluation and Applications (ISBN-0-7923-9297-3), Fuzzy Rea-soning in Information Decision and Control systems (ISBN-0-7293-2643-1) and Color ImageProcessing and Applications (ISBN-3-540-66953-1), and has published over 680 papers inrefereed journals and conference proceedings on digital signal and image processing anddigital communications. Prof. Venetsanopoulos has served as Chair on numerous boards,councils and technical conference committees of the Institute of Electrical and ElectronicEngineers (IEEE), such as the Toronto Section (1977–1979) and the IEEE Central CanadaCouncil (1980–1982); he was President of the Canadian Society for Electrical Engineeringand Vice President of the Engineering Institute of Canada (EIC) (1983–1986). He was a GuestEditor or Associate Editor for several IEEE journals and the Editor of the Canadian ElectricalEngineering Journal (1981-1983). He is a member of the IEEE Communications, Circuitsand Systems, Computer, and Signal Processing Societies of IEEE, as well as a member ofSigma Xi, the Technical Chamber of Greece, the European Association of Signal Processing,the Association of Professional Engineers of Ontario (APEO) and Greece. He was elected asa Fellow of the IEEE “for contributions to digital signal and image processing”, he is alsoa Fellow of the EIC, and was awarded an Honorary Doctorate from the National TechnicalUniversity of Athens, in October 1994. In October 1996 he was awarded the “Excellencein Innovation Award” of the Information Technology Research Centre of Ontario and RoyalBank of Canada, “for innovative work in color image processing and its industrial applica-tions”. In November 2000 he became Recipient of the “Millennium Medal of IEEE”. In April2001 he became a Fellow of the Canadian Academy of Engineering. Between July 2001 andJune 2006 he will be the Dean of the Faculty of Applied Science and Engineering of theUniversity of Toronto.

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