trackerJPDA

Joint probabilistic data association tracker

Since R2019a

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.

• Setting the ClassFusionMethod property to "Bayes" to enable detection class fusion.

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?

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.

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

MaxNumEvents — Value of k for k-best JPDA

Inf (default) | positive integer

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

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 an association likelihood matrix between tracks and detections. For details, see jpadEvents.

To write your own generation function, you must use this syntax.

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

The input and output arguments of this function must be the same as the arguments in jpdaEvents.

You can use the type command to examine the details of jpdaEvents function.

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

MaxNumDetections — Maximum number of detections

Inf (default) | positive integer

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

Data Types: single | double

OOSMHandling — Handle out-of-sequence measurement (OOSM)

'Terminate' (default) | 'Neglect' | 'Retrodiction'

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

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

MaxNumOOSMSteps — Maximum number of out-of-sequence measurement steps

3 (default) | positive integer

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'.

StateParameters — Parameters of track state reference frame

struct([]) (default) | struct array

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 Name	Value
Frame	"Rectangular"
Position	[10 10 0]
Velocity	[2 -2 0]

Tunable: Yes

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 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.

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]. The object uses this property to evaluate 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 object uses the detection 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. Selecting this value enables the joint integrated data association (JIPDA) tracker.

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 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

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) :

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

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 of the same cluster from the same sensor in seconds, specified as a positive scalar. Ideally, trackerJPDA expects detections from the same cluster to have identical time stamps. However, if the time stamp differences between detections from the same cluster 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

EnableMemoryManagement — Enable memory management properties

false or 0 (default) | true or 1

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

MaxNumDetectionsPerSensor — Maximum number of detections per sensor

100 (default) | positive integer

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

MaxNumDetectionsPerCluster — Maximum number of detections per cluster

5 (default) | positive integer

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

MaxNumTracksPerCluster — Maximum number of tracks per cluster

5 (default) | positive integer

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

ClusterViolationHandling — Handling of run-time violation of cluster bounds

'Split and warn' (default) | 'Terminate' | 'Split'

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

ClassFusionMethod — Class fusion method

"None" (default) | "Bayes"

Class fusion method, specified as one of these:

• "None" — The tracker does not fuse classification information from detections. When the tracker initializes a track from a detection that has a nonzero class ID, the tracker immediately confirms the track and assigns the class ID of the detection to the track. In the subsequent updates to the track, the tracker assigns only detections with the same class ID or a class ID of 0 to the track. As a result, the track classification cannot change once the tracker establishes it.

• "Bayes" — The tracker fuses classification information from detections. When the tracker initializes a tentative track from detections, the tracker determines the class probability of the track based on the a priori class distribution and the class information of the detections. In the subsequent updates to the track, the tracker considers all possible detections for association with the track regardless of their classifications. The tracker uses the kinematic state as well as class information of the detections to calculate the detection-track association likelihoods. The tracker updates the classification of a track by using the marginal probabilities and class information of relevant detections.

Data Types: char | string

InitialClassProbabilities — Prior class probability distribution for new tracks

1 (default) | N-element vector of nonnegative scalars that sum to 1

Prior class probability distribution for new tracks, specified as an N-element vector of nonnegative scalars that sum to 1. N must be equal to the total number of classes.

For each objectDetection object that you specify through the detections input, the ObjectClassID property of the objectDetection object must be less than or equal to N.

Example: [0.2 0.8]

Data Types: single | double

ClassFusionWeight — Weight factor of class fusion

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

Weight factor of class fusion, specified as a scalar in the range [0,1]. When you set the ClassFusionMethod property to "Bayes", the tracker calculates the mixed likelihood of association between a detection m and a track t as:

$$\Lambda (m,t)={\Lambda }_k^{1-\alpha }(m,t){\Lambda }_c^{\alpha }(m,t)$$

where

• α — Weight factor of class fusion

• Λ_k — Likelihood of assigning a detection to a track based on the kinematic states

• Λ_c — Likelihood of assigning a classified detection to a track based on the class information

Using the mixed likelihoods between detections and tracks in each cluster, the tracker performs joint probabilistic data association between tracks and detections.

Tunable: Yes

Data Types: single | 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 structure contains the following field.

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

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

Field	Description
DetectionIndices	Indices of clustered detections, returned as an M-element vector.
TrackIDs	Track IDs of clustered tracks, returned as an N-element vector.
ValidationMatrix	Validation matrix of the cluster, returned as an M-by-(N+1) matrix. See the validationMatrix input of the jpadEvents function for more details.
SensorIndex	Index of the originating sensor of detections in the cluster.
TimeStamp	Mean time stamp of clustered detections.
MarginalProbabilities	Matrix of marginal posterior joint association probabilities, returned as an (M+1)-by-N matrix. In the upper M-by-N matrix, the (i,j) element represents the probability that the i-th detection (specified in the DetectionIndices field) is assigned to the j-th track (specified in the TrackIDs field). The elements in the M+1 row represents the probability that the corresponding track in the TrackIDs field is unassigned with any detection. When the TrackLogic property is 'Integrated', each returned probability value is divided by the probability of existence of the corresponding track.
Likelihood	Individual association likelihoods based on kinematic information, returned as an (M+1)-by-(N+1) matrix. See the likelihoodMatrix input of the jpadEvents function for more details.
ClassLikelihood	Individual association likelihoods based on classification information, returned as an (M+1)-by-(N+1) matrix. See the likelihoodMatrix input of the jpadEvents function for more details. The field appears when you set the ClassFusionMethod property to "Bayes".

The OOSMHandling structure contains these fields:

Field	Description
DiscardedDetections	Indices 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 related only to the out-of-sequence detections.
UnassignedDetections	Indices 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)

Specific to trackerJPDA

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

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

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

Detection Class Fusion Using trackerJPDA

Create two objectDetection objects at time $\mathit{t}$ = 0 and $\mathit{t}$ = 1, respectively. The ObjectClassID of the two detections is 1. Specify the confusion matrix for each detection.

detection0 = objectDetection(0,[0 0 0],...
    ObjectClassID=1,...
    ObjectClassParameters=struct("ConfusionMatrix",[0.6 0.2 0.2; 0.2 0.6 0.2; 0.2 0.2 0.6]));

detection1 = objectDetection(1,[0 0 0],...
    ObjectClassID=1,...
    ObjectClassParameters=struct("ConfusionMatrix",[0.5 0.3 0.2; 0.3 0.5 0.2; 0.2 0.2 0.6]));

Create a trackerJPDA object. Set the class fusion method to "Bayes" and specify the initial probability of each class as 1/3.

tracker = trackerJPDA(ClassFusionMethod="Bayes",InitialClassProbabilities=[1/3 1/3 1/3])

tracker = 
  trackerJPDA with properties:

                  TrackerIndex: 0
       FilterInitializationFcn: 'initcvekf'
                  MaxNumEvents: Inf
            EventGenerationFcn: 'jpdaEvents'
                  MaxNumTracks: 100
              MaxNumDetections: Inf
                 MaxNumSensors: 20
                 TimeTolerance: 1.0000e-05

           AssignmentThreshold: [30 Inf]
       InitializationThreshold: 0
          DetectionProbability: 0.9000
                ClutterDensity: 1.0000e-06

                  OOSMHandling: 'Terminate'

                    TrackLogic: 'History'
         ConfirmationThreshold: [2 3]
             DeletionThreshold: [5 5]
              HitMissThreshold: 0.2000

            HasCostMatrixInput: false
    HasDetectableTrackIDsInput: false
               StateParameters: [1x1 struct]

             ClassFusionMethod: 'Bayes'
     InitialClassProbabilities: [0.3333 0.3333 0.3333]
             ClassFusionWeight: 0.7000

                     NumTracks: 0
            NumConfirmedTracks: 0

        EnableMemoryManagement: false

Update the track with the first and second detections sequentially.

tracker(detection0,0);
[tracks,~,~,info] = tracker(detection1,1);

Show the maintained tracks and analysis information.

disp(tracks)

  objectTrack with properties:

                     TrackID: 1
                    BranchID: 0
                 SourceIndex: 0
                  UpdateTime: 1
                         Age: 2
                       State: [6x1 double]
             StateCovariance: [6x6 double]
             StateParameters: [1x1 struct]
               ObjectClassID: 1
    ObjectClassProbabilities: [0.7409 0.1530 0.1060]
                  TrackLogic: 'History'
             TrackLogicState: [1 1 0 0 0]
                 IsConfirmed: 1
                   IsCoasted: 0
              IsSelfReported: 1
            ObjectAttributes: [1x1 struct]

disp(info)

       OOSMDetectionIndices: [1x0 uint32]
    TrackIDsAtStepBeginning: 1
           UnassignedTracks: [1x0 uint32]
       UnassignedDetections: [1x0 uint32]
                 CostMatrix: 13.8823
                   Clusters: {[1x1 struct]}
        InitializedTrackIDs: [1x0 uint32]
            DeletedTrackIDs: [1x0 uint32]
          TrackIDsAtStepEnd: 1
            ClassCostMatrix: -0.1823

Display the cluster information.

disp(info.Clusters{:})

         DetectionIndices: 1
                 TrackIDs: 1
         ValidationMatrix: [1 1]
              SensorIndex: 1
                TimeStamp: 1
    MarginalProbabilities: [2x1 double]
               Likelihood: [2x2 double]
          ClassLikelihood: [2x2 double]

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).

Detection Class Fusion for trackerJPDA

Single Detection Class Probability Update

First, consider the class information association between one detection and one track. Assume the confusion matrix of the detection is

$$C=[c_{ij}],$$

where c_ij denotes the likelihood that the classifier outputs the classification as j if the truth class of the target is i. Here, i, j = 1,…, N, and N is the total number of possible classes.

At time k-1, the probability distribution of a track is given as

$$\mu (k-1)=\left[\begin{array}{l}{\mu }_1(k-1)\\ ⋮\\ {\mu }_N(k-1)\end{array}\right],$$

where μ_i is the probability that the classification of the track is i.

If the tracker associates the detection to the track at time k, then the updated value of μ_i using Bayes' theorem is

$${\mu }_i(k)=\frac{c_{ij}{\mu }_i(k-1)}{{\displaystyle \sum _{l=1}^N{c}_{lj}{\mu }_l(k-1)}}.$$

Write this equation in a vector form for all possible classifications as

$$\mu (k)=\frac{c_j\otimes \mu (k-1)}{c_j^T\mu (k-1)}.$$

where c_j is the j-th column of the confusion matrix and ⊗ represents element-wise multiplication. This equation represents the updated class probability of a track if the track is associated with the detection of classification j.

Mixed Association Likelihood in Cluster

The tracker performs gating and clustering by using only the kinematic information between detections and tracks as explained in the Tracker Logic Flow section. After that, in each cluster, the tracker calculates the mixed likelihood of association between a detection m and a track t as:

$$\Lambda (m,t)={\Lambda }_k^{1-\alpha }(m,t){\Lambda }_c^{\alpha }(m,t)$$

where

• α — Weight factor of class likelihood

• Λ_k — Likelihood of assigning a detection to a track based on the kinematic states

• Λ_c — Likelihood of assigning a classified detection to a track based on the class information

In the equation, Λ_c takes one of these three forms based on the value of m and t.

• m > 0 and t > 0 — A hypothesis that the measurement is associated with a track in the tracker. In this case,

  $${\Lambda }_k(m,t)=c_j^T\mu (k-1),$$

  where c_j is the j-th column in the confusion matrix that detection m corresponds to, and μ(k-1) is the class probability vector of the track in the previous step.

• m > 0 and t = 0 — A hypothesis that the measurement is not associated with any track in the tracker. In this case,

  $${\Lambda }_k(m,t)=c_j^T{\mu }^0,$$

  where c_j is the j-th column in the confusion matrix that detection m corresponds to, and μ⁰ is the a priori class distribution vector of tracks.

• m = 0 and t > 0 — A hypothesis that the track is not associated with any measurement in the tracker. In this case,

  $${\Lambda }_k(m,t)=1.$$

Using the mixed likelihoods of association between detections and tracks in a cluster, the tracker generates all the feasible events and then calculates the marginal probability of assigning each detection to each track in the cluster.

Update Track Class Probability

Suppose the marginal probabilities of M detections assigned to a track in the cluster are (β₀, β₁, …, β_M), where β₀ is the marginal probability that no measurements is associated with the track. Then the tracker updates the class probability of the track as

$${\mu }_k=\left({\displaystyle \sum _{m=1}^M{\beta }_m\frac{c_{j(m)}\otimes \mu (k-1)}{c_{j(m)}^T\mu (k-1)}}\right)+{\beta }_0\mu (k-1),$$

where c_j(m) is the class probability vector of detection m, ⊗ represents element-wise multiplication, μ(k-1) is the class probability vector of the track in the k-1 step, and μ(k) is the class probability vector of the track in the k step.

The tracker updates the class properties of tracks cluster by cluster.

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 T_j, then the (i, j+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.

[3] Bar-Shalom, Y., et al. “Tracking with Classification-Aided Multiframe Data Association.” IEEE Transactions on Aerospace and Electronic Systems, vol. 41, no. 3, July 2005, pp. 868–78.

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.

• The tracker supports strict single-precision code generation with these restrictions:

  • You must specify the MaxNumEvents property as a finite positive integer.

  • You must specify the filter initialization function to return a trackingEKF, trackingUKF, trackingCKF, or trackingIMM object configured with single-precision.

  For details, see Generate Code with Strict Single-Precision and Non-Dynamic Memory Allocation.

• The tracker supports non-dynamic memory allocation code generation with these restrictions:

  • You must specify the MaxNumEvents property as a finite positive integer.

  • You must specify the filter initialization function to return a trackingEKF, trackingUKF, trackingCKF, or trackingIMM object.

  • You must specify the MaxNumDetections property as a finite integer.

  • You cannot specify the ClassFuionMethod property as "Bayes".

  For details, see Generate Code with Strict Single-Precision and Non-Dynamic Memory Allocation.

  After enabling non-dynamic memory allocation code generation, consider using these properties to set bounds on the local variables in the tracker:

  • EnableMemeryManagement

  • MaxNumDetectionsPerSensor

  • MaxNumDetectionsPerCluster

  • MaxNumTracksPerCluster

  • ClusterViolationHandling

Version History

Introduced in R2019a

R2023a: Fuse detection classification information

Using the trackerJPDA System object, you can fuse detection classification information by specifying the ClassFusionMethod property of the object as "Bayes". With this specification, the tracker uses the detection classification information to assign tracks based on the Bayesian Product Class Fusion algorithm.

Additionally, you can use these two properties to adjust the class fusion algorithm:

• InitialClassProbabilities — A priori class probability of new tracks.

• ClassFusionWeight — The weight of class fusion likelihood in the mixed likelihood.