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    CONTENTS

    Tracking How is Tracking done? Tracking Algorithms

    Kalman Filter The IMM Kalman Filter Monte Carlo Simulaions Basic Recursive MTT systems Joint Probabilistic Data Association Algorithms

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    Tracking radar system measures the coordinates of the target and

    provides data which may be used to determine the target path and to

    predict its future position.

    All or only a part of available radar data- range, elevation angle,azimuth angle and doppler frequency shift may be used in predicting the

    Future position.The 2 types of tracking radar are :1. Continuous tracking radar2. Track-while-scan radar

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    HOW IS TRACKING DONE??

    TRACK-WHILE-SCAN RADAR SYSTEM CONCEPT

    The track-while-scan concept illustrates how a mechanically scanned

    fan-beam search radar determines the path of a target and predicts its

    future position. The coordinates of the target obtained and presented on

    PPI display are superimposed and the target then gives rise to a fairly

    regularly spaced sequence of returns.

    The TWS radar supplies sample data on one or more targets.

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    The working principle of the tracking procedure consists of

    track initiation

    plot-track correlationtrack prediction

    track filtering

    track termination

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    TRACK INITITATION :

    An initial estimate of the kinetic state of the target can usually be

    obtained from two consecutive target returns.

    This simple procedure is not reliable if false plots are present.

    It is then necessary to use a longer string of plots and initiate as tracks

    only those sequences which are consistent with the expected behaviour

    of target.

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    PLOT TRACK CORRELATION:

    On next scan it is desired to capture the return signal from the sametarget and associate it with the track.

    In order to do this, the properties of the target are used in the

    following way.

    TRACK PREDICTION LOGICSuppose the target is moving with a uniform velocity.The position of the target on the next scan can be predicted using the

    current estimates of position and velocity.

    Allowances for errors can be achieved by deploying a search areacentred on the predicted position.The search area must be sufficiently large to reneder it highly probabl

    that the next target return will fall inside it.

    It should not be too large else it will catch more false plots.

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    TRACK TERMINATION LOGIC

    It remains to examine the eventuality of no successful correlationbetween plot and existing tracks.

    Two cases can occur : the existing tracks do not correlate with

    incoming plot or one or more tracks do not receive plots on particular sca

    In the first case, a new track could appear and the track initiation

    procedure is applied to verify the hypothesis.

    In the second case, the track is extrapolated or suppressed in the event

    of a sufficient number of consecutive plots being missing.

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    Tracking Algorithms

    The fundamental tracking algorithm has to be refined for different

    operational cases encountered in practice:

    1 single target path(straight line/maneuver) in clear environment2 single target in clutter environment

    3 two target paths in close vicinity

    4 formation of targets

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    In addition to estimating the track parameters for a single target,

    it is necessary to solve the following identification problems:

    1. recognition of the number of targets and their dynamic behavior

    (straight or maneuver)

    2.recognition of the plots provided by the useful target so as to update

    the corresponding track

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    The combination of estimation and identification problems is usually

    solved by resorting to adaptive filters and the Kalman Filter solves thepurpose. Nonlinear filters are essential for the employment of radial velocity

    measurements in modern tracking systems and example for this is the

    Extended Kalman Filter.

    The various kinds of tracking algorithms for target tracking are:

    Kalman Filter

    Extended Kalman FilterInteraction Multiple Model Kalman Filter

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    Kalman FilterThe Kalman filter is a set of mathematical equations that provides arecursive means to estimate the state of a process, in a way that

    minimizes the mean of the squared error.

    The filter supports estimations of past, present, and even future states.The Kalman filter can be thought of as operating in two distinct phase

    predict and update(correct).

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    The Kalman filter estimates a process by using a form of feedback

    control:

    the filter estimates the process state at some time and then obtainsfeedback in the form of (noisy) measurements.

    As such, the equations for the Kalman filter fall into two groups: time update equations and measurement update equations.

    The time update equations are responsible for projecting forward(in time) the current state and error covariance estimates to obtain the

    a priori estimates for the next time step. The measurement update equations are responsible for the

    feedbacki.e. for incorporating a new measurement into the a priori

    estimate to obtain an improved a posteriori estimate.The time update equations can also be thought of as predictor equations

    while the measurement update equations can be thought of as corrector

    equations.

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    Some of the examples of Kalman filter are:

    Constant Velocity Kalman Filter

    Constant Acceleration Kalman Filter Constant Turn Kalman Filter

    There can be other models of Kalman Filter also.

    For example, if the acceleration of the target changes with respect to

    time i.e. if the target has a jerk motion, then that motion can be tracked

    by a Kalman filter which considers rate of change of acceleration

    and the corresponding Transition matrix can be obtained.

    The above examples of Kalman filters have been classified based on

    their Transition matrices.

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    CV KALMAN FILTER

    The target is following a constant velocity motion with no maneuvers.

    CA KALMAN FILTER

    The target is following a maneuvering constant acceleration motion.

    CT KALMAN FILTERThe target is following a large random maneuver level constant turn

    motion.

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    THE IMM KALMAN FILTER

    The Kalman filter has some ability to adapt to maneuvers by tuning

    the Kalman filter to the most stressing maneuver expected.

    However, for targets that are not maneuvering or maneuvering at a level

    less than the most stressing maneuver, this approach results in less noisereduction than could be achieved with a Kalman filter tuned to a less

    stressing maneuver.

    The Kalman filter is designed for a relatively benign maneuver to give

    adequate noise reduction when targets are not maneuvering, and the

    maneuver detector is used to adapt the filter to maneuvers and to provide

    improved tracking performance through maneuvers.

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    The Interaction Multiple Model (IMM) is generally considered to

    provide superior tracking information compared to maneuver detectionschemes.

    For the tracking of maneuvering targets, the IMM is based on several

    possible models for the targets motion (e.g., different random

    maneuver levels) and a probabilistic (Markov) switching between thes

    models is assumed.

    During one sampling period, one of the models may describe the

    targets motion, but over another sampling period, a different modelmay be the more appropriate one.

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    Monte Carlo Simulations

    Monte Carlo methods are a class of computational algorithms that

    rely on repeated random sampling to compute their results.

    These methods are often used in simulating physical and mathematicsystems. Uses of Monte Carlo methods require large amounts of

    random numbers and this led to the development of Pseudo random

    number generators.

    Because the simulations rely on repeated computation of random orpseudo-random numbers, they are most suited to calculation by a

    computer.Monte Carlo simulation methods are especially useful for modeling

    phenomena with significant uncertainty in inputs.

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    0 20 40 60 80 100 120 140 160 1801

    1.5

    2

    2.5

    3

    3.5

    4

    4.5

    5x 10

    -3 Monte Carlo Analysis of ELEVATION

    time track in seconds

    RMS

    valueoferrorinelevation(radians)

    RMS of ERROR IN ELEV FOR PLANT NOISE=10

    RMS of ERROR IN ELEV FOR PLANT NOISE=60

    Graph depicting the monte carlo analysis for

    elevation for different plant noises for a CA filter

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    Basic Recursive MTT systems

    In many Multitarget tracking (MTT) systems, a validation region (also

    called a gate or window) is constructed around the predicted

    measurement for a track

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    . The validation region is that region about the predicted measurement

    where the actual target-originated measurement is likely to be foundwith a specified probability.

    If a measurement fall inside the validation region, it becomes a

    candidate for association to the track, otherwise it is not considered

    as an association candidate.

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    Incoming observations are first considered for the update of the

    existing tracks.

    Gating tests determine which possible observation-to-track

    pairings are reasonable. And a more refined correlation algorithm isused to determine final pairings.

    Finally, after inclusion of the new observations, tracks are predicted

    ahead to the arrival time for the next set of observations.

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    Joint Probabilistic Data Association Algorithms

    0 500 1000 1500 2000 2500 3000 3500600

    800

    1000

    1200

    1400

    1600

    1800

    2000

    x(metres)

    y(metres)

    Input to the Radar

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    JOINT PROBABILISTIC DATA ASSOCIATION FILTER (JPDA

    The JPDAF is an approach that computes the probability that each

    measurement in a tracks validation region is the correct measurement

    and that none of the validated measurements is target oriented, for a

    multitarget case.

    The multitarget case must not only consider random interference

    caused by the clutter but must also consider persistent interference,

    which arises if the measurements from a nearby target consistently

    fall in the validation regions of another target.

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    To ease the mathematical calculations we go for the

    CHEAP JPDA

    SUBOPTIMAL JPDA

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    CHEAP JPDABecause the computational complexity of the JPDAF is

    relatively high for more than two targets, so an ad hoc

    approximation of the JPDAF probability calculations,called the cheap JPDA was developed. It reduces to the

    correct expression for one target and multiple

    measurements, and to a symmetric form for the case of

    one measurement and multiple targets

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    For the case of a track with only one validated

    measurement, which has not been validated by anyother track, the cheap JDA assigns a large

    association probability a non-zero which reduces the

    probability to reflect the possibility that the

    measurement was not detected. For the case ofmultiple targets with overlapping validation regions,

    the cheap JPDA reduces the association

    probabilities, which is indicative of increased

    measurement origin uncertainty

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    SUBOPTIMAL

    Some defects have been documented in the cheap

    JPDA, for example the association probabilities for a

    given track need not sum to unity. To remove these

    defects, the Suboptimal JPDA has been developed,

    which provide more accurate calculations, while being

    just slightly more complex. The concept of partial joint

    events has been developed. A partial joint event

    considers at most one track to measurement pairings.

    That is, a partial joint event consists of two singleevents. Also, the suboptimal JPDA assumes the

    probability of detection for each track is near unity, so

    that all of the targets are detected and all of the joint

    events have the same number of measurements assignedto clutter

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    Following are the important points about thesuboptimal JPDA:

    Like the cheap JPDA, the suboptimal JPDA gives the correct

    probability for the case of one target and multiple measurements

    For the case of two targets and two measurements the suboptimal

    JPDA give the correct probability

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    There are several difficulties however in this process. For several

    closely spaced targets the weighted average updating results in the

    target tracks being attracted to one another, which results in trackbiases and track coalescence. For the case of two targets it was

    found that the target tracks coalesce midway between the targets

    when the target separation distance was less than about 1.2

    residual standard deviations, and this results in a positional bias

    error which is one half of the target separation distance. Toavoid some of the difficulties of the JPDAF the NNJPDA was

    developed

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    NEAREST NEIGHBOUR JPDA (NNJPDA)

    The above-mentioned JPDA techniques use the weighted average of allthe measurements falling inside a tracks validation region to update the

    track state.

    The NNJPDA abandons the weighted average updating of the tracks in

    favor of one-to one assignment of measurements to tracks.

    The association probabilities are used in making the one to one

    assignments.

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    There are 3 varieties of the NN JPDA algorithms :

    GNN JPDA

    CNN JPDA

    SNN JPDA

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    The cheap JPDA (CNNJPDA) is used tocompute the association probabilities but the

    suboptimal (SNNJPDA) as well as the JPDAF

    could be used to compute the association

    probabilities. The NNJPDA removed many ofthe difficulties in the average updating and I

    greatly reduced the complexity of the algorithm

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    For a given scan of data, the association probability I

    computed for each validated measurement track pair.A search is then made for the measurement-track pair

    with the largest probability, the assignment of the

    measurement to track is made, and the measurement

    and the track are removed from further consideration.

    This procedure is repeated until all the associations

    have been made.

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    Thos procedure is the same as the standard nearest

    neighbor technique; except that the associationprobabilities are used instead of the normalized

    distances and a search is made for the largest

    probabilities are used instead of the normalized

    distances. The one to one assignments could be made byformulating the problem in terms of the optimal

    assignment problem. In this case, the assignment would

    be made by maximizing the sum of the association

    probabilities for all the possible measurement-track

    pairings, subject to the maximizing the number of

    assignments or by using some suboptimal solution to

    the assignment problem

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    CONCLUSION

    Different types of filters are used for the purpose of Tracking inThe RADARS for the purpose of estimating and smoothing the

    Next location of the target.

    Hence, a RADAR can follow a target within certain limits.

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    REFERENCES

    1.Merill I.Skolnik, Radar Handbook

    2.www.ieee.org

    3.www.drdo.org4.Simon Haykin,Kalman filtering and Neural Network

    5.A V Balakrishnan,Kalman Filtering Theory

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