Probability Hypothesis Density (PHD) Tracker
![](block_phd.png)
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.
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
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 |
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
|
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 |
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 |
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
|
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
|
Dependencies
To enable this port, in the Port Setting tab, select Enable information output.
Parameters
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 theInterpreted 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.
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:
Predictive birth density — This density is initialized by the
FilterInitializationFcn
function when called with no inputs.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 (Pd) relates to the survival probability (Ps) of a component between successive time steps:
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 an 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:
The weight of any component that is higher than the first threshold C1 is reduced to C1.
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 theTrackID
, while all other components are deleted.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 theTrackID
, while all other components are deleted.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 to0
. 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.
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:
The tracker sorts sensors according to their detection reporting time and determines the order of correction accordingly.
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.
For each sensor:
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.
The tracker adds new components to the birth density using the
FilterInitializationFcn
with no inputs. This corresponds to the predictive birth density.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
as1
, the tracker generates only one partition, in which each detection is a standalone cell.Each detection cell is evaluated against the current density, and a log-likelihood value is computed for each detection cell.
Using the log-likelihood values, the tracker calculates the probability of each partition.
The tracker corrects the current density using each detection cell.
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.
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.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
where M is the total number of components, N(x|mi,Pi) is a normal distribution with mean mi and covariance Pi, and wi is the weight of the ith component. The weight wi 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 (∑ wi), 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
|
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 |
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 theNumTracks
field of the track outputs is returned as adouble
variable. If the detection inputs are specified insingle
precision, then theNumTracks
field of the track outputs is returned as auint32
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
andMaxNumDetsPerObject
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 R2021aR2023a: Simulink buses do not show in workspace
As of R2023a, the Simulink buses created by this block no longer show in MATLAB workspace.
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