# Joint Probabilistic Data Association Multi Object Tracker

Joint probabilistic data association tracker

• Library:
• Sensor Fusion and Tracking Toolbox / Multi-Object Tracking Algorithms

## Description

The Joint Probabilistic Data Association Multi Object Tracker block is 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, in which multiple detections can contribute to each track. The tracker initializes, confirms, corrects, predicts (performs coasting), and deletes tracks. 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.

You can enable different JPDA tracking modes by specifying the Type of track confirmation and deletion logic and Value of k for k-best JPDA parameters.

• Setting the Type of track confirmation and deletion logic parameter 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 Value of k for k-best JPDA parameter 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.

Any new track starts in a tentative state. If enough detections are assigned to a tentative track, its status changes to confirmed. If the detection already has a known classification (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.

## Ports

### Input

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Detection list, specified as a Simulink bus containing a MATLAB structure. The structure has the form:

FieldDescriptionType
NumDetectionsNumber of detectionsInteger
DetectionsObject detectionsArray of objectDetection structures. The first NumDetections of these detections are actual detections.

The fields of detections are:

FieldDescriptionType
TimeMeasurement timeSingle or Double
MeasurementObject measurementsSingle or Double
MeasurementNoiseMeasurement noise covariance matrixSingle or Double
SensorIndexUnique ID of the sensorSingle or Double
ObjectClassIDObject classification IDSingle or Double
MeasurementParametersParameters used by initialization functions of tracking filtersSimulink Bus

See objectDetection for more detailed explanation of these fields.

Note

The object detection structure contains a Time field. The time tag of each object detection must be less than or equal to the time of the current invocation of the block. The time tag must also be greater than the update time specified in the previous invocation of the block.

Track update time, specified as a real scalar in seconds. The tracker updates all tracks to this time. The update time must always increase with each invocation of the block. The update time must be at least as large as the largest Time specified in the Detections input port.

If the port is not enabled, the simulation clock managed by Simulink determines the update time.

#### Dependencies

To enable this port, on the Port Setting tab, set Prediction time source to Input port.

Cost matrix, specified as a real-valued Nt-by-Nd matrix, where Nt is the number of existing tracks and Nd is the number of current detections.

The rows of the cost matrix correspond to the existing tracks. The columns correspond to the detections. Tracks are ordered as they appear in the list of tracks from the All Tracks output port on the previous invocation of the block.

In the first update to the tracker, or if the tracker has no previous tracks, assign the cost matrix a size of [0, Nd]. The cost must be calculated so that lower costs indicate a higher likelihood that the tracker assigns a detection to a track. To prevent certain detections from being assigned to certain tracks, use Inf.

If this port is not enabled, the filter initialized by the Filter initialization function calculates the cost matrix using the distance method.

#### Dependencies

To enable this port, on the Port Setting tab, select Enable cost matrix input.

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 enables you to add the detection probability for each track.

Tracks whose identifiers are not included in Detectable TrackIDs are considered undetectable. The track deletion logic does not count the lack of detection as a "missed detection" for track deletion purposes.

If this port is not enabled, the tracker assumes all tracks to be detectable at each invocation of the block.

#### Dependencies

To enable this port, on the Port Setting tab, select Enable detectable track IDs Input.

Track state parameters, specified as a Simulink bus containing a MATLAB structure. The structure has the form:

FieldDescription
NumParametersNumber of non-default state parameters, specified as a nonnegative integer
ParametersArray of state parameter structures

The block uses the value of the Parameters field for the StateParameters field 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]

#### Dependencies

To enable this port, in the Tracker Configuration tab, select the Update track state parameters with time parameter.

### Output

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Confirmed tracks, returned as a Simulink bus containing a MATLAB structure. The structure has the form:

FieldDescription
NumTracksNumber of tracks
TracksArray of track structures of a length set by the Maximum number of tracks parameter. Only the first NumTracks of these are actual tracks.

The fields of the track structure are shown in Track Structure.

Depending on the track logic, a track is confirmed if:

• History – A track receives at least M detections in the last N updates. M and N are specified in Confirmation threshold for the History logic.

• Integrated – The integrated probability of track existence is higher than the confirmation threshold specified in Confirmation threshold for the Integrated logic.

Tentative tracks, returned as a Simulink bus containing a MATLAB structure. A track is tentative before it is confirmed.

The fields of the track structure are shown in Track Structure.

#### Dependencies

To enable this port, on the Port Setting tab, select Enable tentative tracks output.

Combined list of confirmed and tentative tracks, returned as a Simulink bus containing a MATLAB structure.

The fields of the track structure are shown in Track Structure.

#### Dependencies

To enable this port, on the Port Setting tab, select Enable all tracks output.

Additional information for analyzing track updates, returned as a Simulink bus containing a MATLAB structure.

This table shows the fields of the info structure:

 Field Description OOSMDetectionIndices Indices of out-of-sequence measurements at the current step of the tracker TrackIDsAtStepBeginning Track IDs when step began. CostMatrix Cost matrix for assignment. Clusters Cell array of cluster reports. See Feasible Joint Events for more details. 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 Enable memory management parameters as 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 Enable memory management parameters as on. OOSMHandling Analysis information for out-of-sequence measurements handling, returned as a structure. The structure has this field only when the Out-of-sequence measurement handling parameter is specified as Retordiction.

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 Feasible Joint Events 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 Maximum number of OOSM steps parameter.
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.

#### Dependencies

To enable this port, on the Port Setting tab, select Enable information output.

## Parameters

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Tracker Management

Specify the unique tracker identifier as a nonnegative integer. This parameter is passed 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-To-Track Fuser block.

Example: 1

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

Sensor Fusion and Tracking Toolbox™ supplies many initialization functions:

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 this 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

The block 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.

Value of k for k-best JPDA, specified as a positive integer. This parameter 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.

Feasible joint events generation function name, specified as 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 Value of k for k-best JPDA parameter 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 Value of k for k-best JPDA parameter 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

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

Maximum number of sensors that the block can process, specified as a positive integer. This value should be greater than or equal to the highest SensorIndex value input at the Detections input port.

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

Out-of-sequence measurements handling, specified as Terminate, Neglect, or Retrodiction. Each detection has an associated timestamp, td, and the tracker block has it own timestamp, tt, which is updated in each invocation. The tracker block considers a measurement as an OOSM if td < tt.

When you specify the parameter as:

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

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

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

If you specify this parameter as Retrodiction, the tracker follows these steps to handle the OOSM:

• If the OOSM timestamp is beyond the oldest correction timestamp (specified by the Maximum number of OOSM steps parameter) maintained in the tracker, the tracker discards the OOSMs.

• If the OOSM timestamp is within the oldest correction timestamp 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 retrodicted track, then the tracker updates the 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 Cost Matrix 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 Absolute tolerance between time stamps of detections parameter. Therefore, when you set the Out-of-sequence measurements handling parameter to Neglect, you must make sure that the out-of-sequence detections have timestamps strictly less than the previous timestamp when running the tracker.

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

Increasing the value of this parameter requires more memory but allows you to call the tracker block with OOSMs that have a larger lag relative to the last timestamp when the block was updated. Also, as the lag increases, the impact of the OOSM on the current state of the track diminishes. The recommended value of this parameter is 3.

#### Dependencies

To enable this parameter, set the Out-of-sequence measurements handling parameter to Retrodiction.

Specify the parameters of the track state reference frame as a structure or a structure array. The block passes the value of this parameter to the StateParameters field 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]

You can update the track state parameters through the State Parameters input port by selecting the Update track state parameters with time parameter.

Data Types: struct

Select this parameter to enable the input port for track state parameters through the State Parameters input port.

Select this parameter to enable memory management in the tracker. Once selected, you can use these four parameters in the Memory Management tab to specify bounds for certain variable-sized arrays in the tracker as well as determine how the tracker handles cluster size violations:

• Maximum number of detections per sensor

• Maximum number of detections per cluster

• Maximum number of tracks per cluster

• Handle run-time violation of cluster size

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

• Interpreted execution — Simulate the model using the MATLAB interpreter. This option shortens startup time. In Interpreted execution mode, you can debug the source code of the block.

• Code generation — Simulate the model using generated C code. The first time you run a simulation, Simulink generates C code for the block. The C code is reused for subsequent simulations as long as the model does not change. This option requires additional startup time.

Assignment

Threshold for assigning detections to tracks (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 the distance function used with tracking filters (such as trackingCKF and trackingEKF) for explanation of the distance calculation.

• 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 the 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.

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 is 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

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.

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 Type of track confirmation and deletion logic is set to 'Integrated', this parameter is also used in calculating the initial probability of track existence.

Track Logic

Confirmation and deletion logic type, selected 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.

Track confirmation threshold for history logic, specified as a real-valued 1-by-2 vector of positive integers [M N]. A track is confirmed if it receives at least M detections in the last N updates.

#### Dependencies

To enable this parameter, set Type of track confirmation and deletion logic to 'History'.

Track deletion threshold for history logic, specified as a real-valued 1-by-2 vector of positive integers, [P Q]. If, in P of the last Q tracker updates, a confirmed track is not assigned to any detection that has a likelihood greater than the Threshold for registering 'hit' or 'miss' parameter, then that track is deleted.

#### Dependencies

To enable this parameter, set Type of track confirmation and deletion logic to 'History'.

Threshold for registering a 'hit' or 'miss', specified as a scalar in the range [0, 1]. The track history logic registers 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 registers a 'hit'.

#### Dependencies

To enable this parameter, set Type of track confirmation and deletion logic to 'History'.

Track confirmation threshold for integrated logic, specified as a real-valued positive scalar. A track is confirmed if its probability of existence is greater than or equal to the confirmation threshold.

#### Dependencies

To enable this parameter, set Type of track confirmation and deletion logic to 'Integrated'.

Track deletion threshold for integrated logic, specified as a positive scalar. A track is deleted if its probability of existence drops below this threshold.

#### Dependencies

To enable this parameter, set Type of track confirmation and deletion logic to 'Integrated'.

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.

#### Dependencies

To enable this parameter, set Type of track confirmation and deletion logic to 'Integrated'.

Time rate of true target deaths, specified as a scalar in the range [0, 1]. This parameter 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 DeathRate is the time rate of true target deaths, and δt is the time interval since the previous update time t.

#### Dependencies

To enable this parameter, set Type of track confirmation and deletion logic to 'Integrated'.

Port Setting

Source for prediction time, specified as Input port or Auto. Select Input port to input an update time by using the Prediction Time input port. Otherwise, the simulation clock managed by Simulink determines the update time.

Select this check box to enable the input of a cost matrix by using the Cost Matrix input port.

Select this check box to enable the Detectable track IDs input port.

Select this check box to enable the output of tentative tracks through the Tentative Tracks output port.

Select this check box to enable the output of all the tracks through the All Tracks output port.

Select this check box to enable the output port for analysis information through the Info output port.

Source of the output track bus name, specified as:

• Auto — The block automatically creates an output track bus name.

• Property — Specify the output track bus name by using the Specify an output bus name parameter.

Source of the output info bus name, specified as one of these options:

• Auto — The block automatically creates an output info bus name.

• Property — Specify the output info bus name by using the Specify an output bus name parameter.

Memory Management

Specify the maximum number of detections per sensor as a positive integer. This parameter determines the maximum number of detections that each sensor can pass to the tracker during one call of the tracker.

Set this parameter 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 parameter, select Enable Memory Management in the Tracker Management tab.

Specify the maximum number of detections per cluster during the run-time of the tracker as a positive integer.

Setting this parameter 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 this parameter, the tracker reacts based on the Handle run-time violation of cluster size parameter.

#### Dependencies

To enable this parameter, select Enable Memory Management in the Tracker Management tab.

Specify the maximum number of tracks per cluster during the run-time of the tracker as a positive integer.

Setting this parameter 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 tracks in a cluster exceeds this parameter, the tracker reacts based on the Handle run-time violation of cluster size parameter.

#### Dependencies

To enable this parameter, select Enable Memory Management in the Tracker Management tab.

Specify the handling of run-time violation of cluster size as one of these options:

• Teminate — The tracker reports an error if any of the cluster bounds specified in the Maximum number of detections per cluster and Maximum number of tracks per cluster parameters is violated during run-time.

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

• Split — The tracker splits the size-violating cluster into smaller clusters by using a suboptimal approach and does not report any 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 Threshold for assigning detections to tracks parameter.

#### Dependencies

To enable this parameter, select Enable Memory Management in the Tracker Management tab.

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## Version History

Introduced in R2019b