Environment and Movement Model for Mobile Terminal Location Tracking

Transcription

1 Wireless Personal Communications 24: , Kluwer Academic Publishers. Printed in the Netherlands. Environment and Movement Model for Mobile Terminal Location Tracking M. McGUIRE, K.N. PLATANIOTIS and A.N. VENETSANOPOULOS The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, 10 King s College Road, Toronto, Ontario, M5S 3G4, Canada {mmcguire,kostas,anv}@dsp.toronto.edu Abstract. Mobile terminal position location, tracking and prediction are becoming important areas of research for advanced cellular communications. Methods for mobile terminal location are evaluated using simulations. To obtain accurate simulation results, the simulation environment and terminal motion model must be as realistic as possible. This paper describes a simulation system for mobile terminals located within vehicles in dense urban environments. These are the mobiles with the greatest need for location predictions in the environments of greatest interest to network providers. The radio propagation model is based on well known multipath radio propagation models. The motion model combines an accurate kinematic model for vehicular motion with a driver decision model to mimic human driving decisions. Simulated mobile terminal motion tracks are presented, showing how realistic 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 while sending or receiving communications. To satisfy this desire, cellular mobile phone systems were designed so that users could use these systems while they were in motion [1]. This motion during a communication session creates several difficulties in resource and network management for the network operator. Some of these issues are terminal location and paging for incoming calls, ensuring quality of service for users as they move from one area to another during a call, and maintaining the quality of service of on-going calls while accepting new calls. These problems will only become more difficult to solve for third generation cellular systems since mobile calls will no longer be only voice or low bandwidth data but also high bandwidth multimedia applications such as video or high quality music. One method that is often proposed to solve these problems is to use mobile terminal motion prediction to reserve resources 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 presented in the literature [4 8]. The best way to evaluate a terminal location method is to perform experiments in the environment of interest. Unfortunately, this is expensive so the only method to evaluate a location method is via computer simulations. The computer simulations of the network environment and mobile terminal motion must be realistic or the location method evaluation will be of extremely limited value. This paper will describe a simulation environment for the evaluation of mobile terminal location methods. This paper will concentrate on simulation models for mobile terminals Partially supported by a grant from the Nortel Institute for Telecommunications.

2 484 M. McGuire et al. within road vehicles located in dense urban areas. These are the regions of greatest interest to cellular network providers for mobile terminal tracking. These areas have the largest numbers of wireless terminals users with the highest demand for high bandwidth services. The users of mobile terminals in road vehicles are likely to obtain the greatest benefit from mobile terminal location prediction for resource allocation. This paper reviews the propagation model used for wireless communications concentrating on the affects this propagation will have on the distance measurements used for mobile terminal location. A motion model for mobile terminals is proposed which concentrates on an accurate kinematic model of vehicular motion combined with a model for driver decisions. A simulation system based on the propagation and motion model is then presented. Section 2 describes the propagation and motion models. Section 3 then describes the simulations 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 and the motion model. The propagation models describes how a radio signal transmitted from a base station changes before it is received by the mobile terminal. The motion model describes the how the position of the mobile terminal evolves over time. These models are described separately below PROPAGATION MODEL Radio propagation in urban environments is a complex phenomenon. An effect that is common in cellular radio propagation is multipath propagation. During multipath propagation the radio signals travels from the transmitter to receiver via multiple paths each with its own attenuation and transmission delay. This is shown in Figure 8. The received signal at the mobile terminal, r(t), is modeled as being r(t) = N A j (t)s(t τ j ) + n(t), (1) j=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 A j (t), and propagation delay, τ j. The attenuation is given by A j (t) = l(d j )f (t), (2) where d j is the length of propagation path j, l(d j ) is the deterministic path loss, and f(t)is a random process representing fast fading such as Rayleigh fading [10]. The deterministic path loss in decibels, denoted L(d j ) = 10 log 10 (l(d j )), has been shown to be well modeled as a logarithmic function of d j such as L(d j ) = 10c log 10 (d j ) + C j, (3) where C j is a constant that is a function of radio frequency, and diffraction [11]. The value of c is determined by the environment. A value of c = 2 is used in free space while in

3 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, C j = 24 db and c = 4.5 [11]. The simple path loss propagation equation in (3) is fairly accurate for terminals positioned at the edge of the cells which are the positions of greatest interest to designers of handoff and resource allocation algorithms. More complex propagation models can also be used that take into account the position and geometry of the obstacles [4], or use more exact propagation models for micro-cells [12]. The advantages of these models is greater accuracy of radio propagation simulation for terminals position closer to the base stations obtained at the expense of more computational cost. Since these locations are off less interest, these models are not described 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 the Time of Arrival (ToA) and Time Difference of Arrival (TDoA) measurements [4, 7]. The reason for this is that modulation and multiple access schemes used in current digital networks allow 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 the radio interface [13]. In these systems, the data sequence is multiplied with a binary sequence called the spreading sequence or spreading code that has special autocorrelation properties. The spreading sequence, p(k) has an autocorrelation, R pp (K) function with the properties [14]: R pp (K) = E [ p(k)p(k + K) ] 1 K = cn c {0, 1, 2,...} = 1 N otherwise, (4) where N is the period of the spreading sequence. The continuous time version of the autocorrelation function is shown in Figure 1 with the assumption that the spreading sequence is converted to square pulses before the autocorrelation is evaluated. The properties of the spreading sequence allow propagation delays in a received signal to be measured at a receiver provided the spreading sequence is synchronized at the transmitter and receiver. The principles are shown in Figure 1. By sweeping the value of n, the variable delay, and looking for peaks in the average output of the system, it is possible to calculate values for the delays N 1, N 2 and N 3 [15]. Multipath propagation creates greater entropy in propagation measurements as a signal measurement 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 extra peaks such as those generated by N 2 and N 3 in Figure 1. In a real system, this is complicated by different powers for each of the received propagation paths, noise, signal interference, and modulation effects. The cross-correlation between the received signal and known spreading sequence resembles Figure 2. The receiver must identify the position of the first peak in the received correlation to find the propagation time. The noise and interference generate a time-correlated noise sequence which is added to the crosscorrelation waveform at the receiver output. This makes the propagation time measurement into an estimation problem. The result of this estimation is the measured propagation delay, ˆτ, givenby ˆτ = τ + ɛ, (5) where τ is the true propagation delay, and ɛ is a random variable modeling the effect of errors in the estimation process.

4 486 M. McGuire et al. 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, interference power, and noise power at the receiver. Multipath propagation increases the variance of the the measurement noise as the power of the first signal path is decreased and makes the distance measurement biased to a value greater than the shortest propagation path distance [17]. This positive bias is created by the probability that the time measurement device will incorrectly detect one of the extra longer propagation paths as the shortest propagation path instead of the true shortest distance path.

5 Environment and Movement Model for Mobile Terminal Location Tracking 487 Figure 3. Modes of mobile terminal mobility MOTION MODEL Modes of mobile terminal mobility are shown in Figure 3. Mobile terminals are more likely to be carried by pedestrians than to be located inside vehicles but the higher mobility of vehicle mounted mobile terminals makes tracking their position and estimating future locations a larger concern than for pedestrian carried mobiles. A mobile within a vehicle is likely to require more handoffs as it will move over a greater distance during the period of a communication session than a pedestrian carried mobile terminal. This makes the processing requirement for resource management of the vehicle mounted terminal higher and greater performance gains can be had by tracking and predicting the motion of vehicle mounted terminals than pedestrian terminals. The motion of mobile terminals located on trains or subways is also likely to be of high velocities and thus experience many handoffs, but the motion is also highly predictable so the tracking problem is much simpler than for mobile terminals in road vehicles. Other modalities for mobile terminal motion will have other characteristics similar to one of those described above or are rare enough that tracking is not a concern for network providers. For these reasons, this paper concentrates on the motion model for mobile terminals inside of road vehicles. The motion of a mobile terminal is also influenced by the environment in which it is located. On a highway, an automobile s motion is highly predictable with the speed being near the speed limit while remaining in one lane for a long period of time. The randomness is mainly restricted to lane changing maneuvering and exiting behavior. Conversely, an automobile that is located in a parking lot has a high degree of randomness as the direction of motion can be fairly unrestricted with a limit on speed. A pedestrian in an urban environment will be restricted to motion on sidewalks with limited motion on vehicle lanes. Pedestrians can change direction in short distances while automobiles that wish to make major direction changes must do so only at intersection locations. Pedestrian motion in suburban and rural environments is almost unrestricted with motion across vehicle lanes being common. Bicycles have behavior that at some times is like an automobile but at other times can be like a pedestrian. The description of the motion for mobile terminals will be subdivided into description of the kinematics of vehicular motion, and a description of the driver decision model. The kinematics of vehicular motion are the physical laws which affect the motion of vehicles. The drivers decision model describes the process by which drivers decide how to control their vehicles.

6 488 M. McGuire et al. Figure 4. Vehicle model Kinematics of Vehicle Motion Several 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 motion simulator with the accuracy we need for mobility modeling. A vehicle can be modeled as shown in Figure 4. During street driving on flat ground, the vehicle usually only accelerates in directions nearly parallel to the major vehicle axis, in the direction 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 change orientation toward that direction. A vehicle is subject to several friction and drag forces. The most important of these is the road friction. This is what allows the car to accelerate since it is road friction that allows the engine of the vehicle to apply force in the direction of acceleration. Without road friction or traction 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 air resistance [20]. Rolling resistance is generated by slip between the vehicles wheels and the driving surface and friction inside of the vehicle. Air resistance is generated by the force of the air around the vehicle against its motion. Both of these increase with the vehicle s speed. The result of these forces is that if the vehicle is subject to constant driving force, the acceleration of the vehicle will decrease as the velocity increases. Other forces include the affect of non-flat driving surfaces such as roads up hills or ramps which is referred to as grade resistance. The vehicle in these conditions will experience a force in the direction down the slope of the surface. The magnitude of the force is a function of the steepness of the grade of the surface. For tracking purposes, grade can be helpful as it is a deterministic function of location. This creates a mapping between vehicle acceleration and vehicle 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 Driver Decision Model A driver s decision on what action to take at each point in a journey is determined by the location of the destination as well as other factors such as traffic conditions. The usual pattern of driving for a vehicle in North American cities is to drive along side roads from the initial point to higher capacity roads, move on the large capacity roads such as freeways and highways to the general area of the destination, and then take smaller capacity streets to the

7 Environment and Movement Model for Mobile Terminal Location Tracking 489 Figure 5. Intersection diagram. final destination. The driver s decisions at each intersection during a journey are obviously not independent. As a driver approaches an intersection their selected route will determine what lane they will use, the probability that they will brake, and which direction they will move away from the intersection. If they are going to turn, they will have to brake in order to make the corner safely. If they have decided that they are going to go straight through an intersection, they will only 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 unless passing 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 place outside of intersections when the vehicle has reached its final destination and the vehicle is turned into a parking area. 3. Simulation Motion Model The simulation model consists of three parts: the kinematic model, the decision model, and the propagation 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 s decisions as to lane selection, and whether to turn or brake at an intersection. The propagation model generates the simulated measurements from the mobile terminal s location state. The relationships between the different simulation models are summarized in Figure 6. The simulated environment is a simple Manhattan model that has been used in the mobile terminal location literature to evaluate radio location performance [4]. The layout of the environment is shown in Figure 7. The positive y direction will be said to be North, making the positive x direction East. The city blocks are 300 meters long, and the streets are 20 meters wide. Base stations are located in the intersection at every second block. This environment and base station layout is typical of dense urban areas. The next three section will describe the Propagation Model, the Kinematic Model, and the Decision Model.

8 490 M. McGuire et al. Figure 6. Simulation models interaction. Figure 7. Simulation environment layout PROPAGATION MODEL The propagation time for a signal to travel from a base station to the mobile terminal is measured. Because radio wave propagation speed in the atmosphere is near the speed of light in vacuum, c, a time measurement, ˆτ, can be easily translated to a distance measurement, ˆd, via ˆd =ˆτ c. (6)

9 Environment and Movement Model for Mobile Terminal Location Tracking 491 Figure 8. Multipath propagation. The measurement noise in the simulation model is modeled as being Gaussian. The distance measurement for a base station is given by Z j = d j + v j, (7) where j denotes the base station, Z j is the measurement of base station j, d j is the propagation distance from base station j to the mobile terminal and v j is a random variable representing measurement 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 is unobstructed. The propagation distance will be the true distance between the mobile terminal and base station. In the Non Line of Sight (NLOS) case, the shortest distance propagation path between the mobile terminal and base station is blocked by some geographical feature or a building. The propagation distance in this case is always greater than the true distance between the mobile terminal and base station. For the Manhattan model used in the simulations it is assumed that during NLOS propagation, the signal diffracts around corners and the shortest propagation path length is the distance from the base station to the corner plus the distance from the corner to mobile terminal. This is represented by d j = d c + d r in Figure 9. The measurement noise is Gaussian with a mean of 16.0 meters and a standard deviation, σ d, of 16 meters. The parameters of the noise density are taken from [4], which simulated the propagation time measurements for ToA location in this environment. Multipath propagation was 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 the propagation 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

10 492 M. McGuire et al. Figure 9. Manhattan propagation environment. the mobile terminal to be able to measure the propagation delay, or they would have reassigned the mobile terminal s channel for use by another mobile terminal of greater proximity to them [21] KINEMATIC MODEL The kinematic model describes how the mobile terminal s position and velocity evolve over time in response to driver input and random noise. The simplest kinematic motion models do not incorporate process noise. The mobile terminal motion is thus a deterministic function of the control inputs. The control input is either the mobile terminal velocity or its acceleration [22 26]. These models are used to analyze group behavior of mobiles such as handoff rates and mean sojourn times in cells. They are not selected to provide accurate representations of a single mobile terminal s behavior. The addition of random process noise to the mobile terminal motion model makes the mobile terminal motion random given the control input. The velocity and accelerations can vary between control input changes. The process noise models factors such as noise in the control system of the vehicle, variations between drivers, and random road conditions. There are several state space models with random process noise proposed in the literature for mobile terminal motion modeled as Brownian Motion [5], velocity modeled as Brownian Motion [27], and motion modeled as Fractional Brownian Motion [28]. None of the models were based on characteristics of vehicle s motion but instead were primarily selected for computational simplicity. This resulted in some of the models having characteristics disparate from actual vehicular motion. For example, the velocity modeled as Brownian Motion model has 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 finite variance at all locations in the simulation environment. As well, vehicle acceleration is dependent on the vehicle s current speed. The greater a vehicles velocity in a given direction, the less acceleration it will be capable of in that direction as resistance increases [29]. A linear

11 Environment and Movement Model for Mobile Terminal Location Tracking 493 drag term, α, is introduced into the kinematic model to model this. A random motion model which matches this observation is based on a modified form of the Langevin equation [30]. Mobile terminal motion in one dimension is given by ẍ(t) = αẋ(t) + w(t) + u(t), (8) where x(t) is mobile position, ẋ(t) is mobile velocity, ẍ(t) is mobile acceleration, u(t) is a deterministic function representing driver control, and w(t) is a process noise Speed Control The control input, u(t), is the drivers input into the system which controls the direction the vehicle is moving, in which direction it will accelerate, and so on. The value of u(t) directly influences 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[ẋ(t)] =E[w(t)] =0. A positive value of u(t) will bias the mobile terminal motion in the positive direction, lim t E[ẋ(t)] = u(t)/α if u(t) is constant. A negative value of u(t) has the opposite effect. The driver of the vehicle will select u(t) based on the vehicles 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 of the velocity given the control input is determined by the variance of the process noise, lim t Var(ẋ(t)) = Var(w(t))/(2α). Observations of real vehicle speeds by vehicular traffic engineers have shown that the distribution of vehicle speed at a fixed locations can be modeled as Gaussian [29]. The maximum mean acceleration of the vehicle is u(t) m/s 2 which is attained when ẋ(t) = 0m/s. We assume that the mean velocity will be 54 km/h or about 15.0 m/s, standard velocities for downtown North American streets. The maximum mean acceleration during standard driving for a standard passenger automobile is 2.5 m/s 2 [20]. To match these performance values, we set α = 1 6 and the standard control input, u(t) = 2.5. We used a value of σ 2 = 1 to give a 3 standard deviation of 1 m/s (3.6 km/h) in the velocity Direction Control In reality, the mobile position is a two dimensional vector. The elevation of a vehicle is usually a deterministic function of its (x, y) location with rare exceptions such as multi-deck bridges or elevated highways so it is not included in this model. A four state space model is used for the location state of the vehicle. The state vector is given by: x(k) = p x (k) v x (k) p y (k) v y (k), (9) where (p x (k), p y (k)) are the the location coordinates of the mobile at sampling time k, and (v x (k), v y (k)) are the velocities of the mobile terminal in the x and y directions at sampling time k.

12 494 M. McGuire et al. The continuous time two-dimensional model is ẋ(t) = Ax(t) + B{w(t) + u(t)} = 0 α x(t) α {[ ] [ ]} wx (t) ux (t) +. w y (t) u y (t) The terms w x (t) and w y (t) represent zero mean white Gaussian noise processes with variances of E [ w x (0) 2] = E [ w y (0) 2] = σ 2 which are the process noise terms for the continuous time dynamic model. The deterministic inputs, representing driver control input in the x and y directions are given by u x (t) and u y (t). These inputs determine the direction that the mobile terminal will move.ifforallvaluesoft T f, u x (t) = u x (T f ) and u y (t) = u y (T f ),then {[ ]} lim E vx (t) = 1 [ ] ux (t) t v y (t) α u y (t) Thus, u x (t) and u y (t) determine the final direction of motion. If the control inputs change, the mobile terminal motion will smoothly change to the new direction of motion as the drag term forces the velocity functions to remain continuous. The asymptotic covariance of the velocity vector, using the results from Section 3.2.1, can be easily found to be lim t E {[ vx (t) v y (t) ] [v x (t) v y (t)] } = [ σ 2 2α 0 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 the dynamic model can be obtained from the continuous time model [31]. We make the simplifying assumption that the inputs (u x (t), u y (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. The error introduced by this mismatch between the modeling assumptions and real model will be negligible provided the sampling period is small compared to the time constant of the continuous system, α 1. The sampling period is set at T = 0.5 seconds which is less than the time constant of the system of 1/α = 6.0 seconds which justifies the assumption made to discretize the continuous state space model. The resulting discrete time dynamic model is given by [ ] ux (k) x(k + 1) = x(k) + Ɣ + W(k), (11) u y (k) where (1 exp( αt )) α 0 exp( αt ) 0 0 = (1 exp( αt )) α exp( αt ), ]. (10)

13 Ɣ = Environment and Movement Model for Mobile Terminal Location Tracking α exp( αt ) 1+αT 0, exp( αt ) 1+αT α exp( αt ) 0 α 2 1 exp( αt ) α and [ T T ] Q = E exp(at 1 )Bw(t 1 )dt 1 exp(at 2 )Bw(t 2 )dt r 11 r = E[W(k)W(k) T r 12 r ]= 0 0 r 11 r r 12 r 22 The components of the process noise covariance Q are given by r 11 = σ 2 (2αT 3 + 4exp( αt ) exp( 2αT )), 2α 3 r 12 = σ 2 (1 exp( αt )) 2, and 2α 2 r 22 = σ 2 (1 exp( 2αT )). 2α For handoff measurements, mobile terminals make measurements of the signal for the base stations they are using for primary communications but also of the signal from other base stations. It is likely to be these measurements that will be extended for mobile terminal location purposes. Therefore, the sampling period was set to the approximate the time between measurements 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 the same order of magnitude so the results are still valid DECISION MODEL The decision model generates the control inputs into the kinematic model that will determine future mobile terminal position based on the mobile terminal s current location, and the simulated 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 not consider street layout [23, 24]. More complex motion models have been proposed that allow the control inputs to change at any time [22, 25, 26]. The control inputs are kept constant over time periods with random lengths sampled from an exponential distribution. The model in [22] models realistic direction changing behavior for vehicles. Before a vehicle makes a major direction change, it must slow down or come to a stop. Again, street layout is not considered in these models. Simple models that consider street layout have been described in the literature as well [11]. These models assume that vehicles can change their velocity and directions instantaneously. Realistic vehicle braking and turning behavior are not considered.

14 496 M. McGuire et al. Table 1. Setting for moving north on street (street centered at x = 0 meters). Control input Value u x (k) β (p x (k) 5) u y (k) 2.5 The models allow for simple simulation and analysis of the behavior of groups of mobile terminals 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 higher entropy than actual driver behavior. This means that mobile terminal position state at a sample interval k gives less information about the mobile terminal position state at interval k +N with N>0 in the simulation motion than for true vehicular motion. The simulated motion is harder to track than the motion that would be generated by human drivers since past measurements of mobile terminal position give less information about the present mobile terminal location than for motions generated by human decisions. The simulated driver in the model described below makes decisions at every intersection independently of the previous intersection decision. Thus the tracking algorithm cannot use any form of long term behavior model to improve performance. The tracking algorithms performance for mobiles with motion controlled by human drivers is likely to be superior than for mobiles with the control logic described below. The performance of a tracking algorithm on motion 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 of a long term behavior model to the simulator is the subject of on-going research Simple Motion without Turns This decision model describes the control behavior when the mobile is located away from intersections or when the mobile terminal is traveling down a highway. The allowed direction of all motion is in one of two directions up or down the street. Motion is restricted by the lane the mobile terminal is in. The control inputs are categorized as u (k) which is the control input in the direction parallel to the street direction, and u (k) which is perpendicular to the street direction. For example, if the street is parallel to the Y-axis then u y (k) = u (k) and u x (k) = u (k). The control input u (k) is used to control the speed along the street. The control input u (k) is used 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 along the street. This will result, as described in Section 3.2, to a mean velocity of 15.0 m/s in that direction 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 whose middle is located at x = 5 m, the control inputs will be set as shown in Table 1. For the simulations described in this paper, β = 1 4.

15 Environment and Movement Model for Mobile Terminal Location Tracking 497 Figure 10. State transition diagram for motion simulator Motion with Turns In the real world, a driver of a vehicle has a specific destination in mind and the general decisions made at intersections concerning turn direction and speed selection are known in advance. These decisions will be modified by a large number of factors such as traffic conditions and weather. For simulation purposes, we use a simplified decision logic system to model driver decision behavior. The driver s decision at each intersection is independent of the decision made at any other intersection during the mobile s journey. A simple finite state machine is used to control mobile decisions. The simulated driver is in one of four states: Normal, Braking, Turning, and Transit. The state transition diagram is shown in Figure 10. Normal state. The mobile starts in the Normal state. In this state, the control inputs are selected as described in Section The mobile will, after an initial period of acceleration, move at the mean velocity of 15.0 m/s down the street while staying in the proper lane. The control inputs for the main direction of travel will be set as shown in Table 2. The position of the center of the next intersection in the decided direction of travel is calculated. If the mobile is within B meters of the next intersection, the mobile decides if it will turn at the next intersection. The probability of turning is given by the constant P turn. If the mobile is within B meters of the next intersection and turning it will transition to the Braking state in the next sampling interval. If the mobile is within B meters of the

16 498 M. McGuire et al. next intersection and not turning it will change to the Transit state in the next sampling interval. If the mobile terminal is farther than B meters from the intersection then the mobile remains in the Normal state. The distance B is set to 40 meters. This distance was selected based on data on vehicle braking distances in typical urban environments [20]. In other environments this parameters would be set based on the mean speed in the environment and road conditions. This information is also used by those designing road systems. The network operator needing this 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 stop just inside of the intersection region. The control input in the main direction of travel will be set to zero. The control input in the direction perpendicular to the main direction of travel 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 is calculated: α new = v d, (12) where v is the velocity is the selected direction of travel and d is the distance to the intersection entry point. The drag coefficient, α is set to value in the interval [ 1 6, 5.0] nearest to α new. This interval represents the drag coefficients that the vehicle s brakes can generate. When the mobile terminal enters the intersection, the control state transitions to the Turn state in the next sampling interval. Turning state. In the Turn state the mobile will move the mobile terminal turn the mobile into 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 and sets the direction of travel to 6 the new direction. The new direction for the mobile is 50% likely to be either of the perpendicular cardinal directions to mobile s current direction of travel. When the mobile terminal leaves the intersection, it will change to the Normal state in the next sampling period. The lane holding logic is set for the new direction of travel to move the mobile terminal into the new lane. Transit state. When the mobile terminal is in the Transit state, control inputs will be set as in the Normal state. When the mobile terminal is in the Transit state it will set control inputs as in the Normal state according to Table 2. When the mobile leaves the intersection, it will transit to the Normal state in the next sampling period. The value of P turn was set to the value of 2. The result of this choice is that when a mobile 3 approaches an intersection it has an equal probability of going straight, turning left, or turning right. This is the maximum entropy case when the mobile is restricted from going back the direction it came Initial Conditions We choose initial conditions in a manner that replicates the random motion state of a mobile terminal that has just been switched on. To simplify the simulation, we always assume the mobile terminal starts in the central cell with the base station located at coordinates (0, 0).

17 Environment and Movement Model for Mobile Terminal Location Tracking 499 Table 2. Inputs for mobile terminal directions. Direction Control input North u y (k) = 2.5 South u y (k) = 2.5 East u x (k) = 2.5 West u x (k) = 2.5 Table 3. Initial state of mobile terminal. Initial direction p x (0) v x (0) p y (0) v y (0) u x (0) u y (0) North L 0 P S South L 0 P S East P S L West P S L This is not an unrealistic assumption, as when a mobile terminal initiates a call it quickly identifies the base station that it is closest to. The location and velocity state parameters are uniformly distributed within the space of possible values. This is the distribution of maximum entropy 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 range of ( D,D) where D is the block length (300 meters in Figure 9). An initial speed, S, is sampled from a uniform distribution with a range of [0, 15.0]. A lane position value, L, is sampled from a uniform distribution with a range of [0, 10]. From these random values the initial state of the mobile terminal position is generated as shown 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 1 6 a Lane control β 1 4 Braking distance B 40 m Turning probability P turn 2 3 Maximum mean acceleration max(u(t)) 2.5 m/s 2 Block length D 300 m Street width W 20 m a α value when not breaking.

18 500 M. McGuire et al. Figure 11. Example of motion generated by simulation SIMULATION RESULTS An example of a motion track generated by the simulation model is shown in Figure 11, where the dotted lines indicate the edges of the streets. The starting position of the mobile terminal is near (0, 300). The velocity during the simulated motion is shown in Figure 12. The mobile terminal shows the proper braking behavior before turning at intersections. As well the mobile position and velocity are continuous curves. The braking and acceleration of the mobile terminal result in smooth transitions in the mobile terminal velocity and position. The drag in the 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 same location and make identical turn decisions will not follow exactly the same path. This is closer to actual motion behavior than a deterministic decision to path mapping. The drag in the kinematic model creates the exponential velocity behavior which is seen about every twenty seconds in the velocity plot in Figure 12. These patterns are created when the mobile terminal accelerates after making a turn at an intersection. Without this drag, the mobile terminal s velocity would make large jumps after a direction change creating inaccurate behavior in intersections. A motion model without drag would result in the simulated mobile terminals spending less time in the area around the intersections than they would in an actual network. As can be seen in Figure 7, intersections are on the edges of cells so proper simulated behavior around these points is critical to proper evaluation of handoff and resource allocation algorithms. The motion model presented in this paper will allow for more accurate assessment of wireless network resource management schemes.

19 Environment and Movement Model for Mobile Terminal Location Tracking 501 Figure 12. Mobile velocity generated by simulation. 4. Conclusions This paper described models for propagation time measurements and mobile terminal motion for several different modes of mobile terminal mobility. A model describing mobile terminal mobility in dense urban environments was derived from the observations of vehicular traffic engineers. The model for propagation time measurements was based on the methods used for measuring propagation time in CDMA wireless networks. The effects of multipath propagation and signal noise and interference were described. The forces which affect mobile terminal motion were described. The decision process which a driver uses while controlling their vehicle was briefly discussed. A Manhattan simulation environment with exhibits both LOS and NLOS propagation effects was described. This simulated environments has propagation phenomenon common in the crowded urban environments of interest to network providers. A simulation model for mobile terminal vehicular motion in urban environments was developed based on a realistic kinematic model of road vehicle motion combined with an artificial decision making process. Since the computer simulation cannot incorporate the long term decision making ability of a human driver, the decision process was designed so that it would create motions with higher entropy than the motion tracks of true vehicles. In this way, the simulated mobile terminal motions would be harder to track than the motions of true vehicles. A motion track generated by this simulation model was generated. This motion track has the desired properties of true vehicular motion. The simulator was designed so the motion is accurate 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 making process into the simulation model. This would allow this simulation model to be used

20 502 M. McGuire et al. 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 prediction algorithms. The kinematic model can be used to develop a recursive tracking algorithm. References 1. F.H. Blecher, Advanced Mobile Phone Service, IEEE Transactions on Vehicular Technology, Vol. VT-29, No. 2, pp , L. Jorguseski, E. Fledderus, J. Farserotu and R. Prasad, Radio Resource Allocation in Third-generation Mobile Communication Systems, IEEE Communications Magazine, Vol. 39, No. 2, pp , G.S. Kuo, P.C. Ko and M.L. Kuo, A Probabilistic Resource Estimation and Semi-reservation Scheme for Flow-oriented Multimedia Wireless Networks, IEEE Communications Magazine, Vol. 39, No. 2, pp , J.J. Caffery, Jr. and G.L. Stüber, Subscriber Location in COMA Cellular Networks, IEEE Transactions on Vehicular Technology, Vol. 47, No. 2, pp , M. Hellebrandt and R. Mathar, Location Tracking of Mobiles in Cellular Radio Networks, IEEE Transactions on Vehicular Technology, Vol. 48, No. 5, pp , Z. Salcic, GSM Mobile Station Location Using Reference Stations and Artificial Neural Networks, Wireless Personal Communications, Vol. 19, pp , I. Jami, M. Ali and R.F. Ormondroyd, Comparison of Methods of Locating and Tracking Cellular Mobiles, in IEE Colloquium on Novel Methods of Location and Tracking of Cellular Mobiles and Their System Applications, 1999, pp. 1/1 1/6. 8. R.R. Collman, Evaluation of Methods for Determining the Mobile Traffic Distribution in Cellular Radio Networks, IEEE Transactions on Vehicular Technology, Vol. 50, No. 6, pp , J.D. Parsons, The Mobile Radio Propagation Channel, Pentech Press, W.C.Y Lee, Mobile Communications Engineering, McGraw-Hill, Toronto, second edition, ETSI, Universal Mobile Telecommunications Systems (UMTS); Selection Procedures for the Choice of Radio Transmission Technologies of the UMTS (UMTS Version 3.2.0), Technical Report, European Telecommunications Standards Institute, S. Ichitsubo, T. Furono, T. Taga and R. Kawasaki, Multipath Propagation Model for Line-of-sight Street Microcells in Urban Area, IEEE Transactions on Vehicular Technology, Vol. 49, No. 2, pp , E. Dahlman, B. Gudmundson, M. Nilsson and J. Sköld, UMTS/IMT-2000 Based on Wideband CDMA, IEEE Communications Magazine, Vol. 36, No. 9, pp , S. Haykin, Digital Communications, John Wiley & Sons, Inc., Toronto, Ontario, Canada, A.J.Viterbi,CDMA : Principles of Spread Spectrum Communication, Addison-Wesley Publishing Company, Don Mills, Ontario, H.S.H Gombachika and O.K. Tonguz, Influence of Multipath Fading and Mobile Unit Velocity on the Performance of PN Tracking in CDMA Systems, in IEEE Vehicular Technology Conference, May 1997, pp R.D.J. Van Nee, Spread-spectrum Code and Carrier Synchronization Errors Caused by Multipath and Interference, IEEE Transactions on Aerospace and Electronic Systems, Vol. 29, No. 4, pp , S. Takezono, H. Minamoto and K. Tao, Two-dimensional Motion of Four-wheel Vehicles, Vehicle System Dynamics, Vol. 32, pp , C.-F. Lin, A.G. Ulsoy and D.J. LeBlanc, Vehicle Dynamics and External Disturbance Estimation for Vehicle Path Predicition, IEEE Transactions on Control Systems Technology, Vol. 8, No. 3, pp , W.D. Glauz and D.W. Harwood, Chapter 3: Vehicles, in J.L. Pline (ed.), Traffic Engineering Handbook, Institution of Transportation Engineers, Washington, D.C., 5th edition, M.D. Yacoub, Foundations of Mobile Radio Engineering, CRC Press, Inc., Boca Raton, Florida, C. Bettstetter, Smooth is Better than Sharp: A Random Mobility Model for Simulation of Wireless Networks, in ACM International Workshop on Modelling, Analysis, and Simulation of Wireless and Mobile Systems, Rome, Italy, July 2001, pp B. Jabbari, Y. Zhou and F. Hillier, Simple Random Walk Models for Wireless Terminal Movements, in Vehicular Technology Conference, Houston, Texas, May 1999, pp

21 Environment and Movement Model for Mobile Terminal Location Tracking K.-S. Kim, M.-H. Cho and K.-R. Cho, A Simple Analytic Approach for the Cell Sojourn Time in the Gaussian Distributed Mobile Velocity, IEICE Transactions on Communications, Vol. E83-B, No. 5, pp , H. Xie and D.J. Goodman, Mobility Models and Biased Sampling Problem, in International Conference on Universal Personal Communications, Ottawa, Ontario, October 1999, pp M.M. Zonoozi and P. Dassanayake, A Novel Method for Tracing Mobile Users in a Cellular Mobile Communication System, Wireless Personal Communications, Vol. 4, pp , T. Liu, P. Bahl and I. Chlamtac, Mobility Modeling, Location Tracking, and Trajectory Prediction in Wireless ATM Networks, IEEE Journal on Selected Areas in Communications, Vol. 16, No. 6, pp , E. Aleman-Llanes, D. Munoz-Rodriguez and C. Molina, PCS Subscribers Mobility Modelling Using Fractional Brownian Motion (FBM), European Transactions on Communication, Vol. 11, No. 2, pp , C.F Daganzo, Fundamentals of Transportation and Traffic Operations, Elsevier Science Inc., London, U.K., A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, Addison-Wesley Publishing Company, Don Mills, Ontario, second edition, K. Ogata, Discrete-Time Control Systems, Prentice Hall, Englewood Cliffs, N.J., Michael McGuire is presently a Ph.D. candidate in the Department of Electrical and Computer Engineering at the University of Toronto. He obtained a B.Eng. in Computer Engineering, and a M.A.Sc. from the University of Victoria in 1995 and 1997 respectively. His research interests are estimation and control algorithms for wireless cellular networks. Konstantinos N. Plataniotis received the B. Engineering degree in Computer Engineering from 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 Florida Institute of Technology (Florida Tech), Melbourne, Florida in 1992 and 1994 respectively. He

22 504 M. McGuire et al. was a Research Associate with the Computer Technology Institute (C.T.I), Patras, Greece from 1989 to 1991 and a Postdoctoral Fellow at the Digital Signal & Image Processing Laboratory, Department of Electrical and Computer Engineering University of Toronto, from 1995 to From August 1997 to June 1999 he was an Assistant Professor with the School of Computer Science at Ryerson Polytechnic University. While at Ryerson Prof. Plataniotis served as a lecturer in 12 courses to industry and Continuing Education programs. Since 1999 he has been with the University of Toronto as an Assistant Professor at the Department of Electrical & Computer Engineering where he researches and teaches adaptive systems and multimedia signal processing. He co-authored, with A.N. Venetsanopoulos, a book on Color Image Processing & Applications, Springer Verlag, May 2000, ISBN , he is a contributor to three books, and he has published more than 100 papers in refereed journals and conference proceedings on the areas of adaptive systems, signal and image processing, and communication systems and stochastic estimation. Prof. Plataniotis is a member of the IEEE 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 systems statistical 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 Technical University of Athens (NTU), Greece, in 1965, and the M.S., M.Phil., and Ph.D. degrees in Electrical Engineering from Yale University in 1966, 1968 and 1969 respectively. He joined the Department of Electrical and Computer Engineering of the University of Toronto in September 1968 as a Lecturer and he was promoted to Assistant Professor in 1970, Associate Professor in 1973, and Professor in Since July 1997, he has been Associate Chair: Graduate Studies of the Department of Electrical and Computer Engineering and was Acting Chair during the spring term of In 1999 a Chair in Multimedia was established in the ECE Department, made possible by a donation of $ 1.25M from Bell Canada, matched by $ 1.0M of university funds. Prof. A.N. Venetsanopoulos assumed the position as Inaugural Chairholder in July 1999 and two additional Assistant Professor positions became available in the same area. Prof. A.N. Venetsanopoulos has served as Chair of the Communications Group and Associate Chair of the Department of Electrical Engineering and Associate Chair: Graduate Studies for the Department of Electrical and Computer Engineering. He was on research leave at Imperial College of Science and Technology, the National Technical University of Athens, the Swiss Federal Institute of Technology, the University of Florence and the Federal University of Rio de Janeiro, and has also served as Adjunct Professor