# 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, fusionRadarSensor, 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.

You can enable different JPDA tracking modes by specifying the TrackLogic and MaxNumEvents properties.

• Setting the TrackLogic property to 'Integrated' to enable the joint integrated data association (JIPDA) tracker, in which track confirmation and deletion is based on the probability of track existence.

• Setting the MaxNumEvents property to a finite integer to enable the k-best joint integrated data association (k-best JPDA) tracker, which generates a maximum of k events per cluster.

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.

## Creation

### Description

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

example

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

expand all

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.

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

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 FunctionFunction Definition
initcvkfInitialize constant-velocity linear Kalman filter.
initcakfInitialize constant-acceleration linear Kalman filter.
initcvabfInitialize constant-velocity alpha-beta filter
initcaabfInitialize constant-acceleration alpha-beta filter
initcvekfInitialize constant-velocity extended Kalman filter.
initcaekfInitialize constant-acceleration extended Kalman filter.
initrpekfInitialize constant-velocity range-parametrized extended Kalman filter.
initapekfInitialize constant-velocity angle-parametrized extended Kalman filter.
initctekf Initialize constant-turn-rate extended Kalman filter.
initcackfInitialize constant-acceleration cubature filter.
initctckfInitialize constant-turn-rate cubature filter.
initcvckfInitialize constant-velocity cubature filter.
initcvukfInitialize constant-velocity unscented Kalman filter.
initcaukf Initialize constant-acceleration unscented Kalman filter.
initctukfInitialize constant-turn-rate unscented Kalman filter.
initcvmscekfInitialize constant-velocity extended Kalman filter in modified spherical coordinates.
initekfimmInitialize 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

Value of k for k-best JPDA, specified as a positive integer. This property defines the maximum number of feasible joint events for the track and detection association of each cluster. Setting this property to a finite value enables you to run a k-best JPDA tracker, which generates a maximum of k events per cluster.

Data Types: single | double

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 or a likelihood matrix) of a scenario. For details, see jpadEvents.

You can also write your own generation function.

• If the MaxNumEvents property is set to Inf, 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.

• If the MaxNumEvents property is set to a finite value, the function must have the following syntax:

[FJE,FJEProbs] = myfunction(likelihoodMatrix,k)
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

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

Data Types: single | double

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

Maximum number of detections that the tracker can take as inputs, specified as a positive integer.

Data Types: single | double

Handling of out-of-sequence measurement (OOSM), specified as 'Terminate', 'Neglect', or 'Retrodiction'. Each detection has an associated timestamp, td, and the tracker has its own timestamp, tt, which is updated in each call to the tracker. The tracker considers a measurement as an OOSM if td < tt.

When you specify this property as:

• 'Terminate' — The tracker stops running when it encounters an out-of-sequence measurement.

• 'Neglect' — The tracker neglects any out-of-sequence measurements and continues to run.

• 'Retrodiction' — The tracker uses a retrodiction algorithm to update the tracker by either neglecting the OOSMs, updating existing tracks, or creating new tracks using the OOSM. You must specify a filter initialization function that returns a trackingKF, trackingEKF, or trackingIMM object in the FilterInitializationFcn property.

If you specify this property as 'Retrodiction', the tracker follows these steps to handle the OOSMs:

• If the OOSM timestamp is beyond the oldest correction timestamp (specified by the MaxNumOOSMSteps property) maintained by the tracker, the tracker discards the OOSMs.

• If the OOSM timestamp is within the oldest correction timestamp maintained by the tracker, the tracker first retrodicts all the existing tracks to the time of the OOSMs. Then, the tracker applies the joint probability data association algorithm to try to associate the OOSMs to the retrodicted tracks.

• If the tracker successfully associates the OOSM to at least one of the retrodicted tracks, then the tracker updates the associated, retrodicted tracks using the OOSMs by applying the retro-correction algorithm to obtain current, corrected tracks.

• If the tracker cannot associate an OOSM to any retrodicted track, then the tracker creates a new track based on the OOSM and predicts the track to the current time.

For more details on JPDA-based retrodiction, see JPDA-Based Retrodiction and Retro-Correction.To simulate out-of-sequence detections, use objectDetectionDelay.

Note

• When you select 'Retrodiction', you cannot use the costMatrix input.

• The benefits of using retrodiction decreases as the number of targets that move in close proximity increases.

• The tracker requires all input detections that share the same SensorIndex have their Time differences bounded by the TimeTolerance property. Therefore, when you set the OOSMHandling property to 'Neglect', you must make sure that the out-of-sequence detections have timestamps strictly less than the previous timestamp when running the tracker.

Tunable: Yes

Maximum number of out-of-sequence measurement (OOSM) steps, specified as a positive integer.

Increasing the value of this property requires more memory, but enables you to call the tracker with OOSMs that have a larger lag relative to the last timestamp. However, as the lag increases, the impact of the OOSM on the current state of the track diminishes. The recommended value for this property is 3.

#### Dependencies

To enable this argument, set the OOSMHandling property to 'Retrodiction'.

Parameters of the track state reference frame, specified as a structure or a structure array. The tracker passes its StateParameters property values to the StateParameters property of the generated tracks. You can use these parameters to define the reference frame in which the track is reported or other desirable attributes of the generated tracks.

For example, you can use the following structure to define a rectangular reference frame whose origin position is at [10 10 0] meters and whose origin velocity is [2 -2 0] meters per second with respect to the scenario frame.

Field NameValue
Frame"Rectangular"
Position[10 10 0]
Velocity[2 -2 0]

Tunable: Yes

Data Types: struct

Detection assignment threshold (or gating threshold), specified as a positive scalar or 1-by-2 vector of [C1,C2], where C1C2. 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 Algorithms for an explanation of the normalized distance.

• 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).

Note

If the value of C2 is finite, the state transition function and measurement function, specified in the tracking filter used in the tracker, must be able to take an M-by-N matrix of states as input and output N predicted states and N measurements, respectively. M is the size of the state. N, the number of states, is an arbitrary nonnegative integer.

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

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

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. Selecting this value enables the joint integrated data association (JIPDA) tracker.

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

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 deletion threshold as [P R]. If, in P of the last R tracker updates, a confirmed track is not assigned to any detection that has a likelihood greater than the HitMissThreshold property, then that track is deleted. 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

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

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

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

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) :

$PTE\left(t+\delta t\right)={\left(1-DeathRate\right)}^{\delta t}PTE\left(t\right)$

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

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

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

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

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

Data Types: single | double

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

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

Enable memory management properties, specified as a logical 1 (true) or false (0). Setting this property to true enables you to use these four properties to specify bounds for certain variable-sized arrays in the tracker, as well as determine how the tracker handles cluster-size violations:

• MaxNumDetectionsPerSensor

• MaxNumDetectionsPerCluster

• MaxNumTracksPerCluster

• ClusterViolationHandling

Specifying bounds for variable-sized arrays enables you to manage the memory footprint of the tracker in the generated C/C++ code.

Data Types: logical

Maximum number of detections per sensor, specified as a positive integer. This property determines the maximum number of detections that each sensor can pass to the tracker during each call of the tracker.

Set this property to a finite value if you want the tracker to establish efficient bounds on local variables for C/C++ code generation. Set this property to Inf if you do not want to bound the maximum number of detections per sensor.

#### Dependencies

To enable this property, set the EnableMemoryManagement property to true.

Data Types: single | double

Maximum number of detections per cluster during the run-time of the tracker, specified as a positive integer.

Setting this property to a finite value allows the tracker to bound cluster sizes and reduces the memory footprint of the tracker in generated C/C++ code. Set this property to Inf if you do not want to bound the maximum number of detections per cluster.

If, during run-time, the number of detections in a cluster exceeds the specified MaxNumDetectionsPerCluster, the tracker reacts based on the ClusterViolationHandling property.

#### Dependencies

To enable this property, set the EnableMemoryManagement property to true.

Data Types: single | double

Maximum number of tracks per cluster during the run-time of the tracker, specified as a positive integer.

Setting this property to a finite value enables the tracker to bound cluster sizes and reduces the memory footprint of the tracker in generated C/C++ code. Set this property to Inf if you do not want to bound the maximum number of tracks per cluster.

If, during run-time, the number of tracks in a cluster exceeds the specified MaxNumTracksPerCluster, the tracker reacts based on the ClusterViolationHandling property.

#### Dependencies

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

Data Types: single | double

Handling of run-time violation of cluster bounds, specified as:

• 'Teminate' — The tracker reports an error if, during run-time, any cluster violates the cluster bounds specified in the MaxNumDetectionsPerCluster and MaxNumTracksPerCluster properties.

• 'Split and warn' — The tracker splits the size-violating cluster into smaller clusters using a suboptimal approach. The tracker also reports a warning to indicate the violation.

• 'Split' — The tracker splits the size-violating cluster into smaller clusters by using a suboptimal approach. The tracker does not report a warning.

In the suboptimal approach, the tracker separates out detections or tacks that have the smallest likelihood of association to other tracks or detections until the cluster bounds are satisfied. These separated-out detections or tracks can form one or many new clusters depends on their association likelihoods with each other and the AssignmentThreshold property.

#### Dependencies

To enable this property, set the EnableMemoryManagement property to true.

Data Types: char | string

## Usage

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

### 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

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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 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

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

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

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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

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

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

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

 Field Description OOSMDetectionIndices Indices of out-of-sequence measurements at the current step of the tracker TrackIDsAtStepBeginning Track IDs when step began. CostMatrix Cost of kinematic assignment matrix, in which the (i, j) element denotes the cost of assigning track i to detection j. UnassignedTracks IDs of unassigned tracks. UnassignedDetections Indices of unassigned detections in the detections input. 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. MaxNumDetectionsPerCluster The maximum number of detections in all the clusters generated during the step. The structure has this field only when you set the EnableMemoryManagement property to 'on'. MaxNumTracksPerCluster The maximum number of tracks in all the clusters generated during the step. The structure has this field only when you set the EnableMemoryManagement property to 'on'. OOSMHandling Analysis information for out-of-sequence measurements handling, returned as a structure. The structure returns this field only when the OOSMHandling property of the tracker is specified as 'Retrodiction'.

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.

The OOSMHandling structure contains these fields:

FieldDescription
DiscardedDetectionsIndices of discarded out-of-sequence detections. An OOSM is discarded if it is not covered by the saved state history specified by the MaxNumOOSMSteps property.
CostMatrix

Cost of assignment matrix for the out-of-sequence detections.

Clusters

Clusters that are only related to the out-of-sequence detections.

UnassignedDetectionsIndices of unassigned out-of-sequence detections. The tracker creates new tracks for unassigned out-of-sequence detections.

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)

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 predictTracksToTime Predict track state getTrackFilterProperties Obtain track filter properties setTrackFilterProperties Set track filter properties initializeTrack Initialize new track confirmTrack Confirm tentative track deleteTrack Delete existing track exportToSimulink Export tracker or track fuser to Simulink model
 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

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

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## 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.

## Version History

Introduced in R2019a