Probability Hypothesis Density (PHD) Tracker

Multi-sensor, multi-object PHD tracker

Since R2021a

• 

×

Libraries:
Sensor Fusion and Tracking Toolbox / Multi-Object Tracking Algorithms

Description

The Probability Hypothesis Density (PHD) Tracker block creates and manages tracks of stationary and moving objects in a multi-sensor environment. The tracker uses a multi-target probability hypothesis density filter to estimate the states of point targets and extended objects. The PHD is represented by a weighted summation of probability density functions, and peaks in the PHD are extracted to represent possible targets. See Algorithms for more details.

Examples

Track Point Targets in Dense Clutter Using GM-PHD Tracker in Simulink

Radars generally receive echoes from all surfaces in the signal path. These unwanted back-scattered signals or echoes generated from physical objects are called clutter. In a densely cluttered environment, missed detections and false alarms make tracking objects a challenging task for conventional trackers such as Global Nearest-Neighbor (GNN) tracker. In such an environment a PHD tracker provides better estimation of objects as it can handle multiple detections per object per sensor without clustering them first. This example shows you how to track points targets in dense clutter using a Gaussian mixture probability hypothesis density (GM-PHD) tracker with a constant velocity model in Simulink. The example closely follows the Track Point Targets in Dense Clutter Using GM-PHD Tracker MATLAB® example.

• Since R2021a
• Open Model

Ports

Input

Detections — Detection list

Simulink^® bus containing MATLAB^® structure

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

Field	Description	Type
NumDetections	Number of detections	Integer.
Detections	Object detections	Array of object detection structures. The first NumDetections of these detections are actual detections.

The fields of Detections are:

Field	Description	Type
Time	Measurement time	single or double
Measurement	Object measurements	single or double
MeasurementNoise	Measurement noise covariance matrix	single or double
SensorIndex	Unique ID of the sensor	single or double
ObjectClassID	Object classification ID	single or double
MeasurementParameters	Parameters used by initialization functions of tracking filters	Simulink Bus
ObjectAttributes	Additional information passed to tracker	Simulink Bus

See objectDetection for more detailed explanations 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.

Prediction Time — Track update time

real scalar

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

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

Dependencies

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

Sensor Configurations — Configurations of tracking sensors

Simulink bus containing MATLAB structure

Configurations of tracking sensors, specified as a Simulink bus containing a MATLAB structure. The structure has the form:

Field	Description	Type
NumConfigurations	Number of sensor configurations	Integer.
Configurations	Sensor configurations	Array of sensor configuration structures. The first NumConfigurations of these configurations are actual configurations. The field names and definitions must correspond to names and values, respectively, of properties of the trackingSensorConfiguration object. If you use a Radar Data Generator (Radar Toolbox) block in the tracking system, you can directly specify this value by using the Configuration output of the Radar Data Generator (Radar Toolbox) block, instead.

Dependencies

To enable this port, in the Tracker tab, select the Update sensor configurations with time parameter.

State Parameters — Track state parameters

Simulink bus containing MATLAB structure

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

Field	Description
NumParameters	Number of non-default state parameters, specified as a nonnegative integer
Parameters	Array 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 Name	Value
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

Confirmed Tracks — Confirmed tracks

Simulink bus containing MATLAB structure

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

Field	Description
NumTracks	Number of tracks.
Tracks	Array 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.

Tentative Tracks — Tentative tracks

Simulink bus containing MATLAB structure

Tentative tracks, returned as a Simulink bus containing a MATLAB structure. A track is tentative before it is confirmed. The output of this port has the same form as the output of the Confirmed Tracks port.

Dependencies

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

All Tracks — Confirmed and Tentative tracks

Simulink bus containing MATLAB structure

Combined list of confirmed and tentative tracks, returned as a Simulink bus containing a MATLAB structure. The output of this port has the same form as the output of the Confirmed Tracks port.

Dependencies

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

Info — Additional information for analyzing track updates

Simulink bus containing MATLAB structure

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
CorrectionOrder	The order in which sensors are used for state estimate correction, returned as a row vector of SensorIndex values. For example, [1 3 2 4].
TrackIDsAtStepBeginning	Track IDs when the step began.
DeletedTrackIDs	IDs of tracks deleted during the step.
TrackIDsAtStepEnd	Track IDs when the step ended.
SensorAnalysisInfo	Cell array of sensor analysis information.

The SensorAnalysisInfo field can include multiple sensor information reports. Each report is a structure containing these fields:

Field	Description
SensorIndex	Sensor index.
DetectionCells	Detection cells, returned as a logical matrix. Each column of the matrix denotes a detection cell. In each column, if the ith element is 1, then the ith detection belongs to the detection cell denoted by that column.
DetectionLikelihoods	The association likelihoods between components in the density function and detection cells, returned as an N-by-P matrix. N is the number of components in the density function, and P is the number of detection cells.
IsBirthCells	Indicates if the detection cells listed in DetectionCells give birth to new tracks, returned as a 1-by-P logical vector, where P is the number of detection cells.
NumPartitions	Number of partitions.
DetectionProbability	Probability of existing tracks being detected by the sensor, returned as a 1-by-N row vector, where N is the number of components in the density function.
LabelsBeforeCorrection	Labels of components in the density function before correction, return as a 1-by-Mb row vector. Mb is the number of components maintained in the tracker before correction. Each element of the vector is a TrackID. For example, [1 1 2 0 0]. Note that multiple components can share the same TrackID.
LabelsAfterCorrection	Labels of components in the density function after correction, returned as a 1-by-Ma row vector. Ma is the number of components maintained in the tracker after correction. Each element of the vector is a TrackID. For example, [1 1 1 2 2 0 0]. Note that multiple components can share the same TrackID.
WeightsBeforeCorrection	Weights of components in the density function before correction, returned as a 1-by-Mb row vector. Mb is the number of components maintained in the tracker before correction. Each element of the vector is the weight of the corresponding component in LabelsBeforeCorrection. For example, [0.1 0.5 0.7 0.3 0.2].
WeightsAfterCorrection	Weights of components in the density function after correction, returned as a 1-by-Ma row vector. Ma is the number of components maintained in the tracker after correction. Each element of the vector is the weight of the corresponding component in LabelsAfterCorrection. For example, [0.1 0.4 0.2 0.6 0.3 0.2 0.2].

Dependencies

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

Parameters

Tracker Configuration

Tracker identifier — Unique tracker identifier

0 (default) | nonnegative integer

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

Detection partition function — Function to partition detections into detection cells

partitionDetections (default) | function name

Function to partition detections into detection cells, specified as a function name. When each sensor can report more than one detection per object, you must use a partition function. The partition function reports all possible partitions of the detections from a sensor. In each partition, the detections are separated into mutually exclusive detection cells, assuming that each detection cell belongs to one extended object.

You can also specify your own detections partition function. For guidance in writing this function, you can examine the details of the default partitioning function, partitionDetections, using the type command:

type partitionDetections

Example: myfunction

Assignment threshold — Threshold of selecting detections for component initialization

25 (default) | real positive scalar

Threshold of selecting detections for component initialization, specified as a positive scalar. During correction, the tracker calculates the likelihood of association between existing tracks and detection cells. If the association likelihood (given by negative log-likelihood) of a detection cell to all existing tracks is higher than the threshold (which means the detection cell has low likelihood of association to existing tracks), the detection cell is used to initialize new components in the adaptive birth density.

Example: 18.1

Data Types: single | double

Maximum number of sensors — 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 block.

Data Types: single | double

Maximum number of tracks — Maximum number of tracks

1000 (default) | positive integer

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

Data Types: single | double

Maximum number of components — Maximum number of components

1000 (default) | positive integer

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

Data Types: single | double

Sensor configurations — Configurations of tracking sensors

struct('SensorIndex',1,'IsValidTime',true) (default) | structure | structure array

Configuration of tracking sensors, specified as a structure or an array of structures. This parameter provides the tracking sensor configuration information, such as sensor detection limits and sensor resolution, to the tracker. The allowable field names of each structure are the same as the property names of the trackingSensorConfiguration object. If you set the MaxDetsPerObject field of the structure to 1, the tracker creates only one partition, such that at most one detection can be assigned to each target.

You can update the configuration through the Sensor configurations input port by selecting the Update sensor configurations with time parameter.

Update sensor configurations with time — Update sensor configurations with time

off (default) | on

Select this parameter to enable the input port for tracking sensor configurations through the Sensor Configurations input port.

Track state parameters — Parameters of track state reference frame

structure | structure array

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 Name	Value
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

Update track state parameters with time — Update track state parameters with time

off (default) | on

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

Simulate using — Type of simulation to run

Interpreted Execution (default) | Code Generation

Select the type of simulation to run from these options:

• Interpreted execution — Simulate the model using the MATLAB interpreter. This option shortens startup time. In the 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.

Track Management

Birth rate of new targets — Birth rate of new targets in the density

1e-3 (default) | positive real scalar

Birth rate of new targets in the density, specified as a positive real scalar. Birth rate indicates the expected number of targets added in the density per unit time. The birth density is created by using the FilterInitializationFcn of the sensor configuration used with the tracker. In general, the tracker adds components to the density function in two ways:

1. Predictive birth density — This density is initialized by the FilterInitializationFcn function when called with no inputs.

2. Adaptive birth density — This density is initialized by the FilterInitializationFcn function when called with detection inputs. The tracker chooses detections based on their log-likelihood of association with the current estimates of the targets.

The value for the Birth rate of new targets parameter represents the summation of both predictive birth density and adaptive birth density for each time step.

Example: 0.01

Data Types: single | double

Death rate of components — Death rate of components in the density

1e-6 (default) | positive real scalar

Death rate of components in the density, specified as a positive real scalar. Death rate indicates the rate at which a component vanishes in the density after one time step. This equation illustrates how death rate (P_d) relates to the survival probability (P_s) of a component between successive time steps:

$$P_{\text{s}}={\left(1-P_d\right)}^{\Delta T}$$

where ΔT is the time step.

Example: 1e-4

Data Types: single | double

Threshold for initializing tentative tracks — Threshold for initializing tentative track

0.5 (default) | positive real scalar

Threshold for initializing a tentative track, specified as a positive real scalar. If the weight of a component is higher than the threshold, the component is labeled as a 'Tentative' track and given a TrackID.

Example: 0.45

Data Types: single | double

Threshold for track confirmation — Threshold for track confirmation

0.8 (default) | positive real scalar

Threshold for track confirmation, specified as a positive real scalar. In a PHD tracker, a track can have multiple components sharing the same TrackID. If the weight summation of the components of a tentative track is higher than the confirmation threshold, the track status is marked as 'Confirmed'.

Example: 0.85

Data Types: single | double

Threshold for track deletion — Threshold for component deletion

1e-3 (default) | positive real scalar

Threshold for component deletion, specified as a positive real scalar. In the PHD tracker, if the weight of a component is lower than the deletion threshold, the component is deleted.

Example: 0.01

Data Types: single | double

Threshold for components merging — Threshold for components merging

25 (default) | positive real scalar

Threshold for components merging, specified as a positive real scalar. In the PHD tracker, if the Kullback-Leibler distance between components with the same TrackID is smaller than the merging threshold, then these components are merged into one component. The merged weight of the new component is equal to the summation of the weights of the pre-merged components. Moreover, if the merged weight is higher than the first threshold specified in the Thresholds for label management parameter, the merged weight is truncated to the first threshold. Note that components with a TrackID of 0 can also be merged with each other.

Example: 30

Data Types: single | double

Thresholds for label management — Thresholds for label management

[1.1 1 0.8] (default) | 1-by-3 vector of positive values

Labeling thresholds, specified as a 1-by-3 vector of decreasing positive values, [C₁, C₂, C₃]. Based on this parameter, the tracker manages components in the density using these rules:

1. The weight of any component that is higher than the first threshold C₁ is reduced to C₁.

2. For all components with the same TrackID, if the largest weight among these components is greater than C₂, then the component with the largest weight is preserved to retain the TrackID, while all other components are deleted.

3. For all components with the same TrackID, if the ratio of the largest weight to the weight summation of all these components is greater than C₃, then the component with the largest weight is preserved to retain the TrackID, while all other components are deleted.

4. If neither condition 2 nor condition 3 is satisfied, then the component with the largest weight retains the TrackID, while the labels of all other components are set to 0. When this occurs, it means that some components may represent other objects. This process retains the possibility for these unreserved components to be extracted again in the future.

Port Setting

Prediction time source — Source of prediction time

Auto (default) | Input port

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.

Enable tentative tracks output — Enable output port for tentative tracks

off (default) | on

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

Enable all tracks output — Enable output port for all tracks

off (default) | on

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

Enable information output — Enable output port for analysis information

off (default) | on

Select this parameter to enable the output of analysis information through the Info output port.

Source of output bus name — Source of output track bus name

Auto (default) | Property

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 output info bus name — Source of output information bus name

Auto (default) | Property

Source of the output information bus name, specified as:

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

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

Dependencies

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

Algorithms

Tracker Logic Flow

The PHD tracker adopts an iterated-corrector approach to update the probability hypothesis density by processing detection information from multiple sensors sequentially. The workflow of the tracker follows these steps:

1. The tracker sorts sensors according to their detection reporting time and determines the order of correction accordingly.

2. The tracker considers two separate densities: current density and birth density. The current density is the density of targets propagated from the previous time step. The birth density is the density of targets expected to be born in the current time step.

3. For each sensor:

   1. The tracker predicts the current density to sensor time-stamp using the survival probability calculated from the death rate and the elapsed time from the last prediction.

   2. The tracker adds new components to the birth density using the FilterInitializationFcn with no inputs. This corresponds to the predictive birth density.

   3. The tracker creates partitions of the detections from the current sensor using the detection partitioning function. Each partition is a possible segmentation of detections into detection cells for each object. If the sensor configuration structure specifies the MaxNumDetsPerObject as 1, the tracker generates only one partition, in which each detection is a standalone cell.

   4. Each detection cell is evaluated against the current density, and a log-likelihood value is computed for each detection cell.

   5. Using the log-likelihood values, the tracker calculates the probability of each partition.

   6. The tracker corrects the current density using each detection cell.

   7. For detection cells with high negative log-likelihood (greater than the assignment threshold), the tracker adds new components to the birth density using the FilterInitializationFcn parameter. This corresponds to the adaptive birth density.

4. After correcting the current density with each sensor, the tracker adds the birth density to the current density. The tracker makes sure that the number of possible targets in the birth density is equal to BirthRate × dT, where dT is the time step.

5. The current density is then predicted to the current update time.

Probability Hypothesis Density

Probability hypothesis density (PHD) is a function defined over the state-space of the tracking system, and its value at a state is defined as the expected number of targets per unit state-space volume. The PHD is usually approximated by a mixture of components, and each component corresponds to an estimate of the state. The commonly used approximations of PHD are Gaussian mixture, SMC mixture, GGIW mixture, and GIW mixture.

To understand PHD, take the Gaussian mixture as an example. The Gaussian mixture can be represented by

$$D(x)={\displaystyle \sum _{i=1}^M{w}_{i}N(x|m_i,P_i)}$$

where M is the total number of components, N(x|m_i,P_i) is a normal distribution with mean m_i and covariance P_i, and w_i is the weight of the ith component. The weight w_i denotes the number, which can be fractional, of targets represented by the ith component. Integration of D(x) over a state-space region results in the expected number of targets in that region. Integrating D(x) over the whole state space results in the total expected number of targets (∑ w_i), since the integration of a normal distribution over the whole state space is 1. The x-coordinates of the peaks (local maximums) of D(x) represent the most likely states of targets.

For example, the following figure illustrates a PHD function given by D(x) = N(x|−4,2) + 0.5N(x|3,0.4) + 0.5N(x|4,0.4). The weight summation of these components is 2, which means that two targets probably exist. From the peaks of D(x), the possible positions of these targets are at x = −4, x = 3, and x = 4. Notice that the last two components are very close to each other, which means that these two components can possibly be attributed to one object.

Track Structure

The fields of the track structure are:

Field	Definition
SourceIndex	Unique source index used to distinguish tracking sources in a multiple tracker environment.
TrackID	Unique track identifier used to distinguish multiple tracks.
BranchID	Unique track branch identifier used to distinguish multiple track branches.
UpdateTime	Time at which the track is updated. Units are in seconds.
Age	Number of times the track survived.
State	Value of the state vector at the update time.
StateCovariance	Uncertainty covariance matrix.
TrackLogic	Confirmation and deletion logic type, returned as 'History' or 'Score'.
TrackLogicState	The current state of the track logic type. Based on the logic type TrackLogic, the logic state is returned as: 'History' — A 1-by-K logical array, where K is the number of latest track logical states recorded. In the array, 1 denotes hit and 0 denote miss. 'Score' — A 1-by-2 array of real scalars, [cs ms]. cs is the current score and ms is the maximum score.
IsConfirmed	Confirmation status. This field is true if the track is confirmed to be a real target.
IsCoasted	Coasting status. This field is true if the track is updated without a new detection.
IsSelfReported	Indicate if the track is reported by the tracker. This field is used in a track fusion environment. It is returned as true by default.
ObjectClassID	Integer value representing the object classification. The value 0 represents an unknown classification. Nonzero classifications apply only to confirmed tracks.
ObjectAttributes	Additional information of the track.

References

[1] Granstorm, K., C. Lundquiest, and O. Orguner. " Extended target tracking using a Gaussian-mixture PHD filter." IEEE Transactions on Aerospace and Electronic Systems. Vol. 48, Number 4, 2012, pp. 3268-3286.

[2] Granstorm, K., and O. Orguner." A PHD filter for tracking multiple extended targets using random matrices." IEEE Transactions on Signal Processing. Vol. 60, Number 11, 2012, pp. 5657-5671.

[3] Granstorm, K., and A. Natale, P. Braca, G. Ludeno, and F. Serafino."Gamma Gaussian inverse Wishart probability hypothesis density for extended target tracking using X-band marine radar data." IEEE Transactions on Geoscience and Remote Sensing. Vol. 53, Number 12, 2015, pp. 6617-6631.

[4] Panta, Kusha, et al. “Data Association and Track Management for the Gaussian Mixture Probability Hypothesis Density Filter.” IEEE Transactions on Aerospace and Electronic Systems, vol. 45, no. 3, July 2009, pp. 1003–16.

[5] Ristic, B., et al. “Adaptive Target Birth Intensity for PHD and CPHD Filters.” IEEE Transactions on Aerospace and Electronic Systems, vol. 48, no. 2, 2012, pp. 1656–68.

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

• In code generation, if the detection inputs are specified in double precision, then the NumTracks field of the track outputs is returned as a double variable. If the detection inputs are specified in single precision, then the NumTracks field of the track outputs is returned as a uint32 variable.

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

  • You must specify the filter initialization function as single-precision in each tracking sensor configuration structure.

  • The filter specified in each tracking sensor configuration structure must use motion and measurement models that support single-precision.

  For details on strict single-precision code generation, 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 MaxNumDetections and MaxNumDetsPerObject fields in each tracking sensor configuration structure as finite integers.

  • You must specify the Maximum number of components parameter as a finite integer.

  • You must specify the Maximum number of tracks parameter as a finite integer.

  For details on non-dynamic memory allocation code generation, see Generate Code with Strict Single-Precision and Non-Dynamic Memory Allocation.

Version History

Introduced in R2021a

R2023a: Simulink buses do not show in workspace

As of R2023a, the Simulink buses created by this block no longer show in MATLAB workspace.