trackerJPDA

Joint probabilistic data association tracker

Description

The trackerJPDA System object™ is a tracker capable of processing detections of multiple targets from multiple sensors. The tracker uses joint probabilistic data association to assign detections to each track. The tracker applies a soft assignment where multiple detections can contribute to each track. The tracker initializes, confirms, corrects, predicts (performs coasting), and deletes tracks. Inputs to the tracker are detection reports generated by objectDetection, radarSensor, monostaticRadarSensor, irSensor, or sonarSensor objects. The tracker estimates the state vector and state estimate error covariance matrix for each track. Each detection is assigned to at least one track. If the detection cannot be assigned to any existing track, the tracker creates a new track.

Any new track starts in a tentative state. If enough detections are assigned to a tentative track, its status changes to confirmed (see the ConfirmationThreshold property). If the detection already has a known classification (i.e., the ObjectClassID field of the returned track is nonzero), that corresponding track is confirmed immediately. When a track is confirmed, the tracker considers the track to represent a physical object. If detections are not assigned to the track within a specifiable number of updates, the track is deleted.

To track targets using this object:

1. Create the trackerJPDA object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects? (MATLAB).

Creation

Syntax

tracker = trackerJPDA

tracker = trackerJPDA(Name,Value)

Description

tracker = trackerJPDA creates a trackerJPDA System object with default property values.

tracker = trackerJPDA(Name,Value) sets properties for the tracker using one or more name-value pairs. For example, trackerJPDA('FilterInitializationFcn',@initcvukf,'MaxNumTracks',100) creates a multi-object tracker that uses a constant-velocity, unscented Kalman filter and allows a maximum of 100 tracks. Enclose each property name in quotes.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects (MATLAB).

TrackerIndex — Unique tracker identifier

0 (default) | nonnegative integer

Unique tracker identifier, specified as a nonnegative integer. This property is used as the SourceIndex in the tracker outputs, and distinguishes tracks that come from different trackers in a multiple-tracker system. You must specify this property as a positive integer to use the track outputs as inputs to a track fuser.

Example: 1

FilterInitializationFcn — Filter initialization function

@initcvekf (default) | function handle | character vector

Filter initialization function, specified as a function handle or as a character vector containing the name of a valid filter initialization function. The tracker uses a filter initialization function when creating new tracks.

Sensor Fusion and Tracking Toolbox™ supplies many initialization functions that you can use to specify FilterInitializationFcn for a trackerJPDA object.

Initialization Function	Function Definition
initcvkf	Initialize constant-velocity linear Kalman filter.
initcakf	Initialize constant-acceleration linear Kalman filter.
initcvabf	Initialize constant-velocity alpha-beta filter
initcaabf	Initialize constant-acceleration alpha-beta filter
initcvekf	Initialize constant-velocity extended Kalman filter.
initcaekf	Initialize constant-acceleration extended Kalman filter.
initrpekf	Initialize constant-velocity range-parametrized extended Kalman filter.
initapekf	Initialize constant-velocity angle-parametrized extended Kalman filter.
initctekf	Initialize constant-turn-rate extended Kalman filter.
initcackf	Initialize constant-acceleration cubature filter.
initctckf	Initialize constant-turn-rate cubature filter.
initcvckf	Initialize constant-velocity cubature filter.
initcvukf	Initialize constant-velocity unscented Kalman filter.
initcaukf	Initialize constant-acceleration unscented Kalman filter.
initctukf	Initialize constant-turn-rate unscented Kalman filter.
initcvmscekf	Initialize constant-velocity extended Kalman filter in modified spherical coordinates.
initekfimm	Initialize tracking IMM filter.

You can also write your own initialization function using the following syntax:

filter = filterInitializationFcn(detection)

The input to this function is a detection report like those created by objectDetection. The output of this function must be a filter object: trackingKF, trackingEKF, trackingUKF, trackingCKF, trackingGSF, trackingIMM, trackingMSCEKF, or trackingABF.

For guidance in writing this function, use the type command to examine the details of built-in MATLAB^® functions. For example:

type initcvekf

Note

trackerJPDA does not accept all filter initialization functions in Sensor Fusion and Tracking Toolbox. The full list of filter initialization functions available in Sensor Fusion and Tracking Toolbox are given in the Initialization section of Estimation Filters.

Data Types: function_handle | char

EventGenerationFcn — Feasible joint events generation function

@jpdaEvents (default) | function handle | character vector

Feasible joint events generation function, specified as a function handle or as a character vector containing the name of a feasible joint events generation function. A generation function generates feasible joint event matrices from admissible events (usually given by a validation matrix) of a tracking scenario. A validation matrix is a binary matrix listing all possible detections-to-track associations. For details, see jpadEvents.

You can also write your own generation function. The function must have the following syntax:

FJE = myfunction(ValidationMatrix)

The input and out of this function must exactly follow the formats used in jpdaEvents. For guidance in writing this function, use the type command to examine the details of jpdaEvents:

type jpdaEvents

Example: @myfunction or 'myfunction'

Data Types: function_handle | char

MaxNumTracks — Maximum number of tracks

100 (default) | positive integer

Maximum number of tracks that the tracker can maintain, specified as a positive integer.

Data Types: single | double

MaxNumSensors — Maximum number of sensors

20 (default) | positive integer

Maximum number of sensors that can be connected to the tracker, specified as a positive integer. MaxNumSensors must be greater than or equal to the largest value of SensorIndex found in all the detections used to update the tracker. SensorIndex is a property of an objectDetection object. The MaxNumSensors property determines how many sets of ObjectAttributes each track can have.

Data Types: single | double

StateParameters — Parameters of the track state reference frame

struct([]) (default) | struct | struct array

Parameters of the track state reference frame, specified as a struct or a struct array. Use this property to define the track state reference frame and how to transform the track from the tracker (called source) coordinate system to the fuser coordinate system.

This property is tunable.

Data Types: struct

AssignmentThreshold — Detection assignment threshold

30*[1 Inf] (default) | positive scalar | 1-by-2 vector of positive values

Detection assignment threshold (or gating threshold), specified as a positive scalar or 1-by-2 vector of [C₁,C₂], where C₁ ≤ C₂. If specified as a scalar, the specified value, val, is expanded to [val, Inf].

Initially, the tracker executes a coarse estimation for the normalized distance between all the tracks and detections. The tracker only calculates the accurate normalized distance for the combinations whose coarse normalized distance is less than C₂. Also, the tracker can only assign a detection to a track if the accurate normalized distance between them is less than C₁. See the distance function used with tracking filters (such as trackingCKF and trackingEKF) for explanation of the distance calculation.

Tips:

• Increase the value of C₂ if there are track and detection combinations that should be calculated for assignment but are not. Decrease this value if cost calculation takes too much time.

• Increase the value of C₁ if there are detections that should be assigned to tracks but are not. Decrease this value if there are detections that are assigned to tracks they should not be assigned to (too far away).

DetectionProbability — Probability of detection

0.9 (default) | scalar in the range [0,1]

Probability of detection, specified as a scalar in the range [0,1]. This property is used in calculations of the marginal posterior probabilities of association and the probability of track existence when initializing and updating a track.

Example: 0.85

Data Types: single | double

InitializationThreshold — Threshold to initialize a track

0 (default) | scalar in the range [0,1]

The probability threshold to initialize a new track, specified as a scalar in the range [0,1]. If the probabilities of associating a detection with any of the existing tracks are all smaller than InitializationThreshold, the detection will be used to initialize a new track. This allows detections that are within the validation gate of a track but have an association probability lower than the initialization threshold to spawn a new track.

Example: 0.1

Data Types: single | double

TrackLogic — Track confirmation and deletion logic type

'History' (default) | 'Integrated'

Confirmation and deletion logic type, specified as:

• 'History' – Track confirmation and deletion is based on the number of times the track has been assigned to a detection in the latest tracker updates.

• 'Integrated' – Track confirmation and deletion is based on the probability of track existence, which is integrated in the assignment function.

ConfirmationThreshold — Threshold for track confirmation

scalar | 1-by-2 vector

Threshold for track confirmation, specified as a scalar or a 1-by-2 vector. The threshold depends on the type of track confirmation and deletion logic you set with the TrackLogic property:

• 'History' – Specify the confirmation threshold as 1-by-2 vector [M N]. A track is confirmed if it recorded at least M hits in the last N updates. The trackerJPDA registers a hit on a track’s history logic according to the HitMissThrehold. The default value is [2 3].

• 'Integrated' – Specify the confirmation threshold as a scalar. A track is confirmed if its probability of existence is greater than or equal to the confirmation threshold. The default value is 0.95.

Data Types: single | double

DeletionThreshold — Threshold for track deletion

scalar | real-valued 1-by-2 vector

Threshold for track deletion, specified as a scalar or a real-valued 1-by-2 vector. The threshold depends on the type of track confirmation and deletion logic you set with the TrackLogic property:

• 'History' – Specify the confirmation threshold as [P R]. A track is deleted if it recorded at least P misses in the last R updates. The trackerJPDA will register a miss on a track’s history logic according to the HitMissThrehold property. The default value is [5,5].

• 'Integrated' – Specify the deletion threshold as a scalar. A track is deleted if its probability of existence drops below the threshold. The default value is 0.1.

Example: 0.2 or [5,6]

Data Types: single | double

HitMissThreshold — Threshold for registering hit or miss

0.2 (default) | scalar in the range [0,1]

Threshold for registering a hit or miss, specified as a scalar in the range [0,1]. The track history logic will register a miss and the track will be coasted if the sum of the marginal probabilities of assignments is below the HitMissThreshold. Otherwise, the track history logic will register a hit.

Example: 0.3

Dependencies

To enable this argument, set the TrackLogic property to 'History'.

Data Types: single | double

ClutterDensity — Spatial density of clutter measurements

1e-6 (default) | positive scalar

Spatial density of clutter measurements, specified as a positive scalar. The clutter density describes the expected number of false positive detections per unit volume. It is used as the parameter of a Poisson clutter model. When TrackLogic is set to 'Integrated', ClutterDensity is also used in calculating the initial probability of track existence.

Example: 1e-5

Data Types: single | double

NewTargetDensity — Spatial density of new targets

1e-5 (default) | positive scalar

Spatial density of new targets, specified as a positive scalar. The new target density describes the expected number of new tracks per unit volume in the measurement space. It is used in calculating the probability of track existence during track initialization.

Example: 1e-3

Dependencies

To enable this argument, set the TrackLogic property to 'Integrated'.

Data Types: single | double

DeathRate — Time rate of target deaths

0.01 (default) | scalar in the range [0,1]

Time rate of target deaths, specified as a scalar in the range [0,1]. DeathRate describes the probability with which true targets disappear. It is related to the propagation of the probability of track existence (PTE) :

where δt is the time interval since the previous update time t.

Dependencies

To enable this argument, set the TrackLogic property to 'Integrated'.

Data Types: single | double

InitialExistenceProbability — Initial probability of track existence

0.9 (default) | scalar in the range [0,1]

This property is read-only.

Initial probability of track existence, specified as a scalar in the range [0,1] and calculated as InitialExistenceProbability = NewTargetDensity*DetectionProbability/(ClutterDensity + NewTargetDensity*DetectionProbability).

Dependencies

To enable this property, set the TrackLogic property to 'Integrated'. When the TrackLogic property is set to 'History', this property is not available.

Data Types: single | double

HasCostMatrixInput — Enable cost matrix input

false (default) | true

Enable a cost matrix, specified as false or true. If true, you can provide an assignment cost matrix as an input argument when calling the object.

Data Types: logical

HasDetectableTrackIDsInput — Enable input of detectable track IDs

false (default) | true

Enable the input of detectable track IDs at each object update, specified as false or true. Set this property to true if you want to provide a list of detectable track IDs. This list informs the tracker of all tracks that the sensors are expected to detect and, optionally, the probability of detection for each track.

Data Types: logical

NumTracks — Number of tracks maintained by tracker

nonnegative integer

This property is read-only.

Number of tracks maintained by the tracker, returned as a nonnegative integer.

Data Types: single | double

NumConfirmedTracks — Number of confirmed tracks

nonnegative integer

This property is read-only.

Number of confirmed tracks, returned as a nonnegative integer. If the IsConfirmed field of an output track structure is true, the track is confirmed.

Data Types: single | double

TimeTolerance — Absolute time tolerance between detections

1e-5 (default) | positive scalar

Absolute time tolerance between detections for the same sensor, specified as a positive scalar. Ideally, trackerJPDA expects detections from a sensor to have identical time stamps. However, if the time stamps differences between detections of a sensor are within the margin specified by TimeTolerance, these detections will be used to update the track estimate based on the average time of these detections.

Data Types: double

Usage

To process detections and update tracks, call the tracker with arguments, as if it were a function (described here).

Syntax

confirmedTracks = tracker(detections,time)

confirmedTracks = tracker(detections,time,costMatrix)

confirmedTracks = tracker(___,detectableTrackIDs)

[confirmedTracks,tentativeTracks,allTracks] = tracker(___)

[confirmedTracks,tentativeTracks,allTracks,analysisInformation] = tracker(___)

Description

confirmedTracks = tracker(detections,time) returns a list of confirmed tracks that are updated from a list of detections at the update time. Confirmed tracks are corrected and predicted to the update time, time.

confirmedTracks = tracker(detections,time,costMatrix) also specifies a cost matrix.

To enable this syntax, set the HasCostMatrixInput property to true.

confirmedTracks = tracker(___,detectableTrackIDs) also specifies a list of expected detectable tracks given by detectableTrackIDs. This argument can be used with any of the previous input syntaxes.

To enable this syntax, set the HasDetectableTrackIDsInput property to true.

[confirmedTracks,tentativeTracks,allTracks] = tracker(___) also returns a list of tentative tracks and a list of all tracks. You can use any of the input arguments in the previous syntaxes.

[confirmedTracks,tentativeTracks,allTracks,analysisInformation] = tracker(___) also returns analysis information that can be used for track analysis. You can use any of the input arguments in the previous syntaxes.

Input Arguments

detections — Detection list

cell array of objectDetection objects

Detection list, specified as a cell array of objectDetection objects. The Time property value of each objectDetection object must be less than or equal to the current update time, time, and greater than the previous time value used to update the tracker. Also, the Time differences between different objectDetection objects in the cell array do not need to be equal.

time — Time of update

scalar

Time of update, specified as a scalar. The tracker updates all tracks to this time. Units are in seconds.

time must be greater than or equal to the largest Time property value of the objectDetection objects in the input detections list. time must increase in value with each update to the tracker.

Data Types: single | double

costMatrix — Cost matrix

real-valued M-by-N matrix

Cost matrix, specified as a real-valued M-by-N matrix, where M is the number of existing tracks in the previous update, and N is the number of current detections. The cost matrix rows must be in the same order as the list of tracks, and the columns must be in the same order as the list of detections. Obtain the correct order of the list of tracks from the third output argument, allTracks, when the tracker is updated.

At the first update of the tracker or when the tracker has no previous tracks, specify the cost matrix to be empty with a size of [0,numDetections]. Note that the cost must be given so that lower costs indicate a higher likelihood of assigning a detection to a track. To prevent certain detections from being assigned to certain tracks, you can set the appropriate cost matrix entry to Inf.

Dependencies

To enable this argument, set the HasCostMatrixInput property to true.

Data Types: double | single

detectableTrackIDs — Detectable track IDs

real-valued M-by-1 vector | real-valued M-by-2 matrix

Detectable track IDs, specified as a real-valued M-by-1 vector or M-by-2 matrix. Detectable tracks are tracks that the sensors expect to detect. The first column of the matrix contains a list of track IDs that the sensors report as detectable. The optional second column allows you to add the detection probability for each track.

Tracks whose identifiers are not included in detectableTrackIDs are considered undetectable. In this case, the track deletion logic does not count the lack of detection for that track as a missed detection for track deletion purposes.

Dependencies

To enable this input argument, set the detectableTrackIDs property to true.

Data Types: single | double

Output Arguments

confirmedTracks — Confirmed tracks

array of objectTrack objects | array of structures

Confirmed tracks, returned as an array of objectTrack objects in MATLAB, and returned as an array of structures in code generation. In code generation, the field names of the returned structure are same with the property names of objectTrack.

A track is confirmed if it satisfies the confirmation threshold specified in the ConfirmationThreshold property. In that case, the IsConfirmed property of the object or field of the structure is true.

Data Types: struct | object

tentativeTracks — Tentative tracks

array of objectTrack objects | array of structures

Tentative tracks, returned as an array of objectTrack objects in MATLAB, and returned as an array of structures in code generation. In code generation, the field names of the returned structure are same with the property names of objectTrack.

A track is tentative if it does not satisfy the confirmation threshold specified in the ConfirmationThreshold property. In that case, the IsConfirmed property of the object or field of the structure is false.

Data Types: struct | object

allTracks — All tracks

array of objectTrack objects | array of structures

All tracks, returned as an array of objectTrack objects in MATLAB, and returned as an array of structures in code generation. In code generation, the field names of the returned structure are same with the property names of objectTrack. All tracks consists of confirmed and tentative tracks.

Data Types: struct | object

analysisInformation — Additional information for analyzing track updates

structure

Additional information for analyzing track updates, returned as a structure. The fields of this structure are:

Field	Description
TrackIDsAtStepBeginning	Track IDs when step began.
CostMatrix	Cost matrix for assignment.
Clusters	Cell array of cluster reports.
InitiatedTrackIDs	IDs of tracks initiated during the step.
DeletedTrackIDs	IDs of tracks deleted during the step.
TrackIDsAtStepEnd	Track IDs when the step ended.

The Clusters field can include multiple cluster reports. Each cluster report is a structure containing:

Field	Description
DetectionIndices	Indices of clustered detections.
TrackIDs	Track IDs of clustered tracks.
ValidationMatrix	Validation matrix of the cluster. See jpadEvents for more details.
SensorIndex	Index of the originating sensor of the clustered detections.
TimeStamp	Mean time stamp of clustered detections.
MarginalProbabilities	Matrix of marginal posterior joint association probabilities.

Data Types: struct

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Specific to trackerJPDA

predictTracksToTime	Predict track state
getTrackFilterProperties	Obtain track filter properties
setTrackFilterProperties	Set track filter properties

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
isLocked	Determine if System object is in use
clone	Create duplicate System object
reset	Reset internal states of System object

Examples

Track Two Objects Using trackerJPDA

Construct a trackerJPDA object with a default constant velocity Extended Kalman Filter and 'History' track logic. Set AssignmentThreshold to 100 to allow tracks to be jointly associated.

tracker = trackerJPDA('TrackLogic','History', 'AssignmentThreshold',100,...
    'ConfirmationThreshold', [4 5], ...
    'DeletionThreshold', [10 10]);

Specify the true initial positions and velocities of the two objects.

pos_true = [0 0 ; 40 -40 ; 0 0];
V_true = 5*[cosd(-30) cosd(30)  ; sind(-30) sind(30) ;0 0];

Create a theater plot to visualize tracks and detections.

tp = theaterPlot('XLimits',[-1 150],'YLimits',[-50 50]);
trackP = trackPlotter(tp,'DisplayName','Tracks','MarkerFaceColor','g','HistoryDepth',0);
detectionP = detectionPlotter(tp,'DisplayName','Detections','MarkerFaceColor','r');

To obtain the position and velocity, create position and velocity selectors.

positionSelector = [1 0 0 0 0 0; 0 0 1 0 0 0; 0 0 0 0 0 0]; % [x, y, 0]
velocitySelector = [0 1 0 0 0 0; 0 0 0 1 0 0; 0 0 0 0 0 0 ]; % [vx, vy, 0]

Update the tracker with detections, display cost and marginal probability of association information, and visualize tracks with detections.

dt = 0.2;
for time = 0:dt:30
    % Update the true positions of objects.
    pos_true = pos_true + V_true*dt;
    
    % Create detections of the two objects with noise.
    detection(1) = objectDetection(time,pos_true(:,1)+1*randn(3,1));
    detection(2) = objectDetection(time,pos_true(:,2)+1*randn(3,1));
    
    % Step the tracker through time with the detections.
    [confirmed,tentative,alltracks,info] = tracker(detection,time);
    
    % Extract position, velocity and label info.
    [pos,cov] = getTrackPositions(confirmed,positionSelector);
    vel = getTrackVelocities(confirmed,velocitySelector);
    meas = cat(2,detection.Measurement);
    measCov = cat(3,detection.MeasurementNoise);
    
    % Update the plot if there are any tracks.
    if numel(confirmed)>0
        labels = arrayfun(@(x)num2str([x.TrackID]),confirmed,'UniformOutput',false);
        trackP.plotTrack(pos,vel,cov,labels);
    end
    detectionP.plotDetection(meas',measCov);
    drawnow;
    
    % Display the cost and marginal probability of distribution every eight
    % seconds.
    if time>0 && mod(time,8) == 0
        disp(['At time t = ' num2str(time) ' seconds,']);
        disp('The cost of assignment was: ')
        disp(info.CostMatrix);
        disp(['Number of clusters: ' num2str(numel(info.Clusters))]);
        if numel(info.Clusters) == 1
            
            disp('The two tracks were in the same cluster.')
            disp('Marginal probabilities of association:')
            disp(info.Clusters{1}.MarginalProbabilities)
        end
        disp('-----------------------------')
    end
end

At time t = 8 seconds,
The cost of assignment was: 
   1.0e+03 *

    0.0020    1.1523
    1.2277    0.0053

Number of clusters: 2
-----------------------------

At time t = 16 seconds,
The cost of assignment was: 
    1.3968    4.5123
    2.0747    1.9558

Number of clusters: 1
The two tracks were in the same cluster.
Marginal probabilities of association:
    0.8344    0.1656
    0.1656    0.8344
    0.0000    0.0000

-----------------------------

At time t = 24 seconds,
The cost of assignment was: 
   1.0e+03 *

    0.0018    1.2962
    1.2664    0.0013

Number of clusters: 2
-----------------------------

Algorithms

Tracker Logic Flow

When a JPDA tracker processes detections, track creation and management follow these steps.

1. The tracker divides detections into multiple groups by originating sensor.

2. For each sensor:

   1. The tracker calculates the distances from detections to existing tracks and forms a costMatrix.

   2. The tracker creates a validation matrix based on the assignment threshold (or gate threshold) of the existing tracks. A validation matrix is a binary matrix listing all possible detections-to-track associations. For details, see Feasible Joint Events.

   3. Tracks and detections are then separated into clusters. A cluster can contain one track or multiple tracks if these tracks share common detections within their validation gates. A validation gate is a spatial boundary, in which the predicted detection of the track has a high likelihood to fall. For details, see Feasible Joint Events.

3. Update all clusters following the order of the mean detection time stamp within the cluster. For each cluster, the tracker:

   1. Generates all feasible joint events. For details, see jpdaEvents.

   2. Calculates the posterior probability of each joint event.

   3. Calculates the marginal probability of each individual detection-track pair in the cluster.

   4. Reports weak detections. Weak detections are the detections that are within the validation gate of at least one track, but have probability association to all tracks less than the IntitializationThreshold.

   5. Updates tracks in the cluster using correctjpda.

4. Unassigned detections (these are not in any cluster) and weak detections spawn new tracks.

5. The tracker checks all tracks for deletion. Tracks are deleted based on the number of scans without association using 'History' logic or based on their probability of existence using'Integrated' track logic.

6. All tracks are predicted to the latest time value (either the time input if provided, or the latest mean cluster time stamp).

Feasible Joint Events

In the typical workflow for a tracking system, the tracker needs to determine if a detection can be associated with any of the existing tracks. If the tracker only maintains one track, the assignment can be done by evaluating the validation gate around the predicted measurement and deciding if the measurement falls within the validation gate. In the measurement space, the validation gate is a spatial boundary, such as a 2-D ellipse or a 3-D ellipsoid, centered at the predicted measurement. The validation gate is defined using the probability information (state estimation and covariance, for example) of the existing track, such that the correct or ideal detections have high likelihood (97% probability, for example) of falling within this validation gate.

However, if a tracker maintains multiple tracks, the data association process becomes more complicated, because one detection can fall within the validation gates of multiple tracks. For example, in the following figure, tracks T₁ and T₂ are actively maintained in the tracker, and each of them has its own validation gate. Since the detection D₂ is in the intersection of the validation gates of both T₁ and T₂, the two tracks (T₁ and T₂) are connected and form a cluster. A cluster is a set of connected tracks and their associated detections.

To represent the association relationship in a cluster, the validation matrix is commonly used. Each row of the validation matrix corresponds to a detection while each column corresponds to a track. To account for the eventuality of each detection being clutter, a first column is added and usually referred to as "Track 0" or T₀. If detection D_i is inside the validation gate of track D_j, then the (j, i+1) entry of the validation matrix is 1. Otherwise, it is zero. For the cluster shown in the figure, the validation matrix Ω is

$$\Omega =\left[\begin{array}{ccc}1& 1& 0\\ 1& 1& 1\\ 1& 0& 1\end{array}\right]$$

Note that all the elements in the first column of Ω are 1, because any detection can be clutter or false alarm. One important step in the logic of joint probabilistic data association (JPDA) is to obtain all the feasible independent joint events in a cluster. Two assumptions for the feasible joint events are:

• A detection cannot be emitted by more than one track.

• A track cannot be detected more than once by the sensor during a single scan.

Based on these two assumptions, feasible joint events (FJEs) can be formulated. Each FJE is mapped to an FJE matrix Ω_p from the initial validation matrix Ω. For example, with the validation matrix Ω, eight FJE matrices can be obtained:

$$\begin{array}{l}{\Omega }_1=\left[\begin{array}{ccc}1& 0& 0\\ 1& 0& 0\\ 1& 0& 0\end{array}\right],{\Omega }_2=\left[\begin{array}{ccc}0& 1& 0\\ 1& 0& 0\\ 1& 0& 0\end{array}\right],{\Omega }_3=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 1& 0& 0\end{array}\right],{\Omega }_4=\left[\begin{array}{ccc}1& 0& 0\\ 0& 0& 1\\ 1& 0& 0\end{array}\right]\\ {\Omega }_5=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 1& 0& 0\end{array}\right],{\Omega }_6=\left[\begin{array}{ccc}1& 0& 0\\ 1& 0& 0\\ 0& 0& 1\end{array}\right],{\Omega }_7=\left[\begin{array}{ccc}0& 1& 0\\ 1& 0& 0\\ 0& 0& 1\end{array}\right],{\Omega }_8=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]\end{array}$$

As a direct consequence of the two assumptions, the Ω_p matrices have exactly one "1" value per row. Also, except for the first column which maps to clutter, there can be at most one "1" per column. When the number of connected tracks grows in a cluster, the number of FJE increases rapidly. The jpdaEvents function uses an efficient depth-first search algorithm to generate all the feasible joint event matrices.

References

[1] Fortmann, T., Y. Bar-Shalom, and M. Scheffe. "Sonar Tracking of Multiple Targets Using Joint Probabilistic Data Association." IEEE Journal of Ocean Engineering. Vol. 8, Number 3, 1983, pp. 173-184.

[2] Musicki, D., and R. Evans. "Joint Integrated Probabilistic Data Association: JIPDA." IEEE transactions on Aerospace and Electronic Systems . Vol. 40, Number 3, 2004, pp 1093-1099.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• See System Objects in MATLAB Code Generation (MATLAB Coder).

• All the detections used with a multi-object tracker must have properties with the same sizes and types.

• If you use the ObjectAttributes field within an objectDetection object, you must specify this field as a cell containing a structure. The structure for all detections must have the same fields, and the values in these fields must always have the same size and type. The form of the structure cannot change during simulation.

• If ObjectAttributes are contained in the detection, the SensorIndex value of the detection cannot be greater than 10.

• The first update to the multi-object tracker must contain at least one detection.