trackerPHD
Multi-sensor, multi-object PHD tracker
Description
The trackerPHD
System object™ is a tracker capable of processing detections of multiple targets from multiple
sensors by using a multi-target probability hypothesis density (PHD) filter to estimate the
states of point targets and extended objects. 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 represented by a weighted summation (mixture) of
probability density functions, and peaks in the PHD correspond to possible targets. For an
overview of how the tracker functions, see Algorithms.
By default, the trackerPHD
can track extended objects using the ggiwphd
filter, which models
detections from an extended object as a parse points cloud. You can also use
trackerPHD
with the gmphd
filters, which tracks point targets and extended objects with designated
shapes. Inputs to the tracker are detection reports generated by objectDetection
, fusionRadarSensor
,
irSensor
, or
sonarSensor
objects. The tracker outputs all maintained tracks and their analysis information.
To track targets using this object:
Create the
trackerPHD
object and set its properties.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
Description
creates a
tracker
= trackerPHDtrackerPHD
System object with default property values.
sets properties for the tracker using one or more name-value pairs. For example,
tracker
= trackerPHD(Name,Value
)trackerPHD('MaxNumTracks',100)
creates a PHD tracker that 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
SensorConfigurations
— Configurations of tracking sensors
trackingSensorConfiguration
object | array of trackingSensorConfiguration
objects | cell array of trackingSensorConfiguration
objects | equivalent structure formats
Configuration of tracking sensors, specified as a trackingSensorConfiguration
object, an array of
trackingSensorConfiguration
objects, or a cell array of array of
trackingSensorConfiguration
objects. This property provides the
tracking sensor configuration information, such as sensor detection limits and sensor
resolution, to the tracker. Note that there are no default values for the
SensorConfigurations
property, and you must specify the
SensorConfigurations
property before using the tracker. However,
you can update the configuration by setting the
HasSensorConfigurationsInput
property to true
and specifying the configuration input, config
. If you set the
MaxDetsPerObject
property of the
trackingSensorConfiguration
object to 1, the tracker creates only one
partition, such that at most one detection can be assigned to each target.
Alternately, you can specify this property using structures with field names same as
the property names of the trackingSensorConfiguration
object.
PartitioningFcn
— Function to partition detections into detection cells
@partitionDetections
(default) | function handle | character vector
Function to partition detections into detection cells, specified as a function handle or as a character vector. When each sensor can report more than one detection per object, a partition function is required. 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
as:
type partitionDetections
Example:
@myfunction
or 'myfunction'
Data Types: function_handle
| char
BirthRate
— 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 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
trackingSensorConfiguration
used with the tracker. In general, the tracker
adds components to the density function in two ways:
Predictive birth density – density initialized by
FilterInitializationFcn
function when called with no inputs.Adaptive birth density – density initialized by
FilterInitializationFcn
function when called with detections inputs. The detections are chosen by the tracker based on their log-likelihood of association with the current estimates of the targets.
Note that the value for the BirthRate
property
represents the summation of both predictive birth density and adaptive birth density for
each time step.
Example: 0.01
Data Types: single
| double
DeathRate
— Death rate of components in the density
1e-6
(default) | positive real scalar
Death rate of components in the density, specified as a scalar. Death rate indicates the rate at which a component vanishes in the density after one time step. Death rate (Pd) relates to the survival probability (Ps) of a component between successive time steps by
where ΔT is the time step.
Example: 1e-4
Data Types: single
| double
AssignmentThreshold
— 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
ExtractionThreshold
— Threshold for initializing tentative track
0.5
(default) | real positive scalar
Threshold for initializing a tentative track, specified as a scalar. If the weight
of a component is higher than the threshold specified by the
ExtractionThreshold
property, the component is labeled as a
'Tentative'
track and given a TrackID
.
Example: 0.45
Data Types: single
| double
ConfirmationThreshold
— Threshold for track confirmation
0.8
(default) | real positive scalar
Threshold for track confirmation, specified as a scalar. In a
trackerPHD
object, a track can have multiple components sharing the
same TrackID
. If the weight summation of a tentative track's
components is higher than the threshold specified by the
ConfirmationThreshold
property, the track's status is marked as
'Confirmed'
.
Example: 0.85
Data Types: single
| double
DeletionThreshold
— Threshold for component deletion
1e-3
(default) | real positive scalar
Threshold for component deletion, specified as a scalar. In the PHD tracker, if the
weight of a component is lower than the value specified by the
DeletionThreshold
property, the component is deleted.
Example: 0.01
Data Types: single
| double
MergingThreshold
— Threshold for components merging
25
(default) | real positive scalar
Threshold for components merging, specified as a real positive scalar. In the PHD
tracker, if the Kullback-Leibler distance between components with the same
TrackID
is smaller than the value specified by the
MergingThreshold
property, 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 LabelingThresholds
property, the
merged weight is truncated to the first threshold. Note that components with
TrackID
equal to 0
can also be merged with each
other.
Example: 30
Data Types: single
| double
LabelingThresholds
— 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 the
LabelingThresholds
property, 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 to 0. When this occurs, it essentially means that some components may represent other objects. This treatment keeps the possibility for these unreserved components to be extracted again in the future.
Data Types: single
| double
HasSensorConfigurationsInput
— Enable updating sensor configurations with time
false
(default) | true
Enable updating sensor configurations with time, specified as
false
or true
. Set this property to
true
if you want the configurations of the sensor updated with
time. Also, when this property is set to true
, the tracker must be
called with the configuration input, config
, as shown in the usage
syntax.
Data Types: logical
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
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: 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: 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.
Data Types: single
| double
MaxNumTracks
— 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
MaxNumComponents
— Maximum number of components
1000
(default) | positive integer
Maximum number of components that the tracker can maintain, specified as a positive integer.
Note
The tracker always uses this property to set the maximum number of components
that the tracker can maintain and ignores the MaxNumComponents
property set in the tracking filter object (ggiwphd
or gmphd
), which you specify through
the SensorConfigurations property.
Data Types: single
| double
Usage
To process detections and update tracks, call the tracker with arguments, as if it were a function (described here).
Note
You must specify the SensorConfigurations
property before using the
tracker.
Syntax
Description
returns a list of confirmed tracks that are updated from a list of detections,
confirmedTracks
= tracker(detections
,time
)detections
, at the update time, time
.
Confirmed tracks are corrected and predicted to the update time.
also specifies a sensor configuration input, confirmedTracks
= tracker(detections
,config
,time
)config
. Use this syntax
when the configurations of sensors are changing with time. To enable this syntax, set the
HasSensorConfigurationsInput
property to
true
.
[
also returns a list of tentative tracks, confirmedTracks
,tentativeTracks
,allTracks
] = tracker(___)tentativeTracks
, and a list
of all tracks, allTracks
. You can use this output syntax with any of
the previous input syntaxes.
[
also returns the analysis information, confirmedTracks
,tentativeTracks
,allTracks
,analysisInformation
] = tracker(___)analysisInformation
, which can
be used for track analysis. You can use this output syntax with any of the previous input
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
config
— Sensor configurations
array of structures | cell array of structures | cell array of trackingSensorConfiguration
objects
Sensor configurations, specified as an array of structures, a cell array of
structures, or a cell array of trackingSensorConfiguration
objects. If you specify the value using an
array of structures or a cell array of structures, you must include
SensorIndex
as a field for each structure. Other fields are
optional, but each field in a structure must have the same name as one of the
properties of the trackingSensorConfiguration
object. Note that
you only need to specify sensor configurations that need to be updated. For example,
if you only want to update the IsValidTime
property of the fifth
sensor, specify config
as
struct('SensorIndex',5,'IsValidTime',false)
.
Tip
If you have a fusionRadarSensor
sensor object in the tracking system, you can directly
use the configuration structure output of the sensor object as this input.
Dependencies
To enable this argument, set the
HasSensorConfigurationsInput
property to
true
.
Output Arguments
confirmedTracks
— Confirmed tracks
structure | array of structures
Confirmed tracks updated to the current time, returned as a structure or an array
of structures. Each structure corresponds to a track. A track is confirmed if the
weight summation of its components is above the threshold specified by the
ConfirmationThreshold
property. If a track is confirmed, the
IsConfirmed
field of the structure is true
.
The fields of the confirmed tracks structure are defined in Track Structure.
Data Types: struct
tentativeTracks
— Tentative tracks
structure | array of structures
Tentative tracks, returned as a structure or an array of structures. Each
structure corresponds to a track. A track is tentative if the weight summation of its
components is above the threshold specified by the
ExtractionThreshold
property, but below the threshold specified
by the ConfirmationThreshold
property. In that case, the
IsConfirmed
field of the structure is false
.
The fields of the structure are defined in Track Structure.
Data Types: struct
allTracks
— All tracks
structure | array of structures
All tracks, returned as a structure or an array of structures. Each structure corresponds to a track. The set of all tracks consists of confirmed and tentative tracks. The fields of the structure are defined in Track Structure.
Data Types: struct
analysisInformation
— Additional information for analyzing track updates
structure
Additional information for analyzing track updates, returned as a structure. The fields of this structure are:
Field | Description |
CorrectionOrder | The order in which sensors are used for state estimate correction,
returned as a row vector of |
TrackIDsAtStepBeginning | Track IDs when 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:
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, specified 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 given 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 given in
|
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 trackerPHD
predictTracksToTime | Predict track state |
deleteTrack | Delete existing track |
initializeTrack | Initialize new track |
sensorIndices | List of sensor indices |
exportToSimulink | Export tracker or track fuser to Simulink model |
getPHDFilter | Get copy of PHD filter |
generateCode | Generate code for tracker object and object functions |
Examples
Track Two Objects Using trackerPHD
Set up the sensor configuration, create a PHD tracker, and feed the tracker with detections.
% Create sensor configuration. Specify clutter density of the sensor and % set the IsValidTime property to true. configuration = trackingSensorConfiguration(1); configuration.ClutterDensity = 1e-7; configuration.IsValidTime = true; % Create a PHD tracker. tracker = trackerPHD('SensorConfigurations',configuration); % Create detections near points [5;-5;0] and [-5;5;0] at t=0, and % update the tracker with these detections. detections = cell(20,1); for i = 1:10 detections{i} = objectDetection(0,[5;-5;0] + 0.2*randn(3,1)); end for j = 11:20 detections{j} = objectDetection(0,[-5;5;0] + 0.2*randn(3,1)); end tracker(detections,0);
Update the tracker again after 0.1 seconds by assuming that targets move at a constant velocity of [1;2;0] unit per second.
dT = 0.1; for i = 1:20 detections{i}.Time = detections{i}.Time + dT; detections{i}.Measurement = detections{i}.Measurement + [1;2;0]*dT; end [confTracks,tentTracks,allTracks] = tracker(detections,dT);
Visualize detections and confirmed tracks.
% Obtain measurements from detections. d = [detections{:}]; measurements = [d.Measurement]; % Extract positions of confirmed tracking using getTrackPositions function. % Note that we used the default sensor configuration % FilterInitializationFcn, initcvggiwphd, which uses a constant velocity % model and defines the states as [x;vx;y;vy;z;vy]. positionSelector = [1 0 0 0 0 0;0 0 1 0 0 0;0 0 0 0 1 0]; positions = getTrackPositions(confTracks,positionSelector); figure() plot(measurements(1,:),measurements(2,:),'x','MarkerSize',5,'MarkerEdgeColor','b'); hold on; plot(positions(1,1),positions(1,2),'v','MarkerSize',5,'MarkerEdgeColor','r' ); hold on; plot(positions(2,1),positions(2,2),'^','MarkerSize',5,'MarkerEdgeColor','r' ); legend('Detections','Track 1','Track 2') xlabel('x') ylabel('y')
Track Vehicle in Tracking Scenario Using trackerPHD
Create a tracking scenario and specify its StopTime
and UpdateRate
properties.
scenario = trackingScenario; scenario.StopTime = Inf; scenario.UpdateRate = 0;
Add a tower platform in the scenario and specify its dimensions.
Tower = platform(scenario,'ClassID',3); Tower.Dimensions = struct( ... 'Length',10, ... 'Width',10, ... 'Height',60, ... 'OriginOffset',[0 0 30]);
Add a car platform in the scenario. Specify its dimensions and trajectory.
Car = platform(scenario,'ClassID',2); Car.Dimensions = struct( ... 'Length',4.7, ... 'Width',1.8, ... 'Height',1.4, ... 'OriginOffset',[-0.6 0 0.7]); Car.Trajectory = waypointTrajectory( ... [0 -15 -0.23;0.3 -29.5 -0.23; 0.3 -42 -0.39;0.3 -56.5 -0.23; ... -0.3 -78.2 -0.23;4.4 -96.4 -0.23], ... [0; 1.4 ; 2.7; 4.1; 6.3; 8.2], ... 'Course',[-88; -89; -89; -92; -84; -71], ... 'GroundSpeed',[10; 10; 10; 10; 10; 10], ... 'ClimbRate',[0; 0; 0; 0; 0; 0], ... 'AutoPitch',true, ... 'AutoBank',true);
Create a non-scanning radar, specify its properties, and mount the sensor on the tower.
NoScanning = fusionRadarSensor('SensorIndex',1, ... 'UpdateRate',10, ... 'MountingAngles',[-90 0 0], ... 'FieldOfView',[20 10], ... 'ScanMode','No scanning', ... 'HasINS',true, ... 'DetectionCoordinates','Scenario', ... 'TargetReportFormat','Detections', ... 'HasElevation',true); Tower.Sensors = NoScanning;
Create a theater plot to visualize sensor coverage, tracks, and detections.
tp = theaterPlot('XLim',[-58 58],'YLim',[-104 12],'ZLim',[-109 8]); set(tp.Parent,'YDir','reverse','ZDir','reverse'); view(tp.Parent,-37.5,30); % Platform plotter for the car. platp = platformPlotter(tp,'DisplayName','Targets','MarkerFaceColor','k'); % Detection plotter for sensor detections. detp = detectionPlotter(tp,'DisplayName','Detections','MarkerSize',6, ... 'MarkerFaceColor',[0.85 0.325 0.098],'MarkerEdgeColor','k','History',10000); % Coverage plotter for sensor. covp = coveragePlotter(tp,'DisplayName','Sensor Coverage'); % Track plotter for tracks. tPlotter = trackPlotter(tp,'DisplayName','Tracks');
Extract the sensor configuration of the sensor and use it to specify a PHD tracker.
sensorConfig = trackingSensorConfiguration(scenario.Platforms{1}.Sensors{1}, ... 'SensorTransformFcn',@cvmeas,'FilterInitializationFcn',@initcvggiwphd); tracker = trackerPHD('SensorConfigurations',sensorConfig, ... 'PartitioningFcn',@(x)partitionDetections(x,1,4.7),... 'AssignmentThreshold',20,'ExtractionThreshold',0.8,... 'ConfirmationThreshold',1.5,'MergingThreshold',20,... 'DeletionThreshold',2e-1,'BirthRate',1e-3,... 'HasSensorConfigurationsInput',true);
Simulate the scenario, generate detections, and use the detections to track the car. Update the theater plot during simulation.
while advance(scenario) && ishghandle(tp.Parent) % Generate sensor data. [dets,configs,sensorConfigPIDs] = detect(scenario); % Read sensor data. allDets = [dets{:}]; if ~isempty(allDets) % Extract measurement positions. meas = cat(2,allDets.Measurement)'; % Extract measurement noise. measCov = cat(3,allDets.MeasurementNoise); else meas = zeros(0,3); measCov = zeros(3,3,0); end % Obtain true positions. truePoses = platformPoses(scenario); truePosition = vertcat(truePoses(:).Position); % Update tracker with the detections and sensor configuration. [cTracks,tTracks,allTracks] = tracker(dets,configs,scenario.SimulationTime); % Update the theater plot. plotPlatform(platp,truePosition); plotDetection(detp,meas,measCov); plotCoverage(covp,coverageConfig(scenario)); % Update the track plotter. Extract track positions. positionSelector = [1 0 0 0 0 0; 0 0 1 0 0 0; 0 0 0 0 1 0]; positions = getTrackPositions(cTracks,positionSelector); % Label and plot the tracks. if ~isempty(cTracks) labels = cell(numel(cTracks),1); for i =1:numel(cTracks) labels{i} = {['T',num2str(cTracks(i).TrackID)]}; end plotTrack(tPlotter,positions,labels); end drawnow end
More About
Track Structure
Track information is returned as an array of structures having the following fields:
Field | Description |
TrackID | Unique integer that identifies the track. |
SouceIndex | Unique identifier of the tracker in a multiple tracker environment. The
|
UpdateTime | The time the track was updated. |
Age | Number of times the track survived. |
State | Value of state vector at the update time. |
StateCovariance | Uncertainty covariance matrix. |
Extent | Spatial extent estimate of the tracked object, returned as a
d-by-d matrix, where d
is the dimension of the object. This field is only returned when the tracking
filter is specified as a |
MeasurementRate | Expected number of detections from the tracked object. This field is only
returned when the tracking filter is specified as a |
IsConfirmed | True if the track is assumed to be of a real target. |
IsCoasted |
|
ObjectClassID |
|
StateParamaters | Parameters about the track state reference frame specified in the
|
IsSelfReported | Indicate if the track is reported by the tracker. This field is used in a
track fusion environment. It is returned as |
Algorithms
Tracker Logic Flow
trackerPHD
adopts an iterated-corrector approach to update the
probability hypothesis density by processing detection information from multiple sensors
sequentially. The workflow of trackerPHD
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
DeathRate
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 function specified by the
PartitioningFcn
property. Each partition is a possible segmentation of detections into detection cells for each object. If theSensorConfiguration
specifies theMaxNumDetsPerObject
as 1, the tracker generates only 1 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
AssignmentThreshold
), the tracker adds new components to the birth density usingFilterInitializationFcn
. 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 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.
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 MATLAB® Coder™.
Usage notes and limitations:
See System Objects in MATLAB Code Generation (MATLAB Coder).
All the detections must have properties with the same sizes and types.
The tracker supports strict single-precision code generation with these restrictions:
You must specify the filter initialization function as single-precision in each
trackingSensorConfiguration
object.The filter specified in each
trackingSensorConfiguration
object 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
properties in eachtrackingSensorConfiguration
object as finite integers.You must specify the
MaxNumComponents
property as a finite integer.You must specify the
MaxNumTracks
property 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 R2019aR2024a: Generate code automatically
You can generate C/C++ code automatically by using the generateCode
object function.
R2022b: Specify maximum of components in tracker
You can specify the maximum number of PHD components maintained in the
trackerPHD
System object using the new
MaxNumComponents
property. Also, the tracker ignores the
MaxNumComponents
property set in the tracking filter object (ggiwphd
or gmphd
), which you specify through the SensorConfigurations property.
See Also
Functions
Objects
Objects
Blocks
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