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Joint probabilistic data association tracker
The trackerJPDA
System
object™ is a tracker capable of processing detections of multiple targets from multiple
sensors. The tracker uses Joint probabilistic data association to assign detections to each
track. The tracker applies a soft assignment where multiple detections can contribute to each
track. The tracker initializes, confirms, corrects, predicts (performs coasting), and deletes
tracks. Inputs to the tracker are detection reports generated by objectDetection
, radarSensor
,
monostaticRadarSensor
, irSensor
, or
sonarSensor
objects. The tracker estimates the state vector and state estimate error covariance matrix for
each track. Each detection is assigned to at least one track. If the detection cannot be
assigned to any existing track, the tracker creates a new track.
Any new track starts in a tentative state. If enough detections are
assigned to a tentative track, its status changes to confirmed (see the
ConfirmationThreshold
property). If the detection already has a known
classification (i.e., the ObjectClassID
field of the returned track is
nonzero), that corresponding track is confirmed immediately. When a track is confirmed, the
tracker considers the track to represent a physical object. If detections are not assigned to
the track within a specifiable number of updates, the track is deleted.
To track targets using this object:
Create the trackerJPDA
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? (MATLAB).
tracker = trackerJPDA
tracker = trackerJPDA(Name,Value)
creates a
tracker
= trackerJPDAtrackerJPDA
System
object with default property values.
sets properties for the tracker using one or more namevalue pairs. For example,
tracker
= trackerJPDA(Name,Value
)trackerJPDA('FilterInitializationFcn',@initcvukf,'MaxNumTracks',100)
creates a multiobject tracker that uses a constantvelocity, unscented Kalman filter and
allows a maximum of 100 tracks. Enclose each property name in quotes.
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 (MATLAB).
FilterInitializationFcn
— Filter initialization function@initcvekf
(default)  function handle  character vectorFilter initialization function, specified as a function handle or as a character vector containing the name of a valid filter initialization function. The tracker uses a filter initialization function when creating new tracks.
Sensor Fusion and Tracking Toolbox™ supplies many initialization functions that you can use to specify
FilterInitializationFcn
for a trackerJPDA
object.
Initialization Function  Function Definition 

initcvkf  Initialize constantvelocity linear Kalman filter. 
initcakf  Initialize constantacceleration linear Kalman filter. 
initcvabf  Initialize constantvelocity alphabeta filter 
initcaabf  Initialize constantacceleration alphabeta filter 
initcvekf  Initialize constantvelocity extended Kalman filter. 
initcaekf  Initialize constantacceleration extended Kalman filter. 
initrpekf  Initialize constantvelocity rangeparametrized extended Kalman filter. 
initapekf  Initialize constantvelocity angleparametrized extended Kalman filter. 
initctekf  Initialize constantturnrate extended Kalman filter. 
initcackf  Initialize constantacceleration cubature filter. 
initctckf  Initialize constantturnrate cubature filter. 
initcvckf  Initialize constantvelocity cubature filter. 
initcvukf  Initialize constantvelocity unscented Kalman filter. 
initcaukf  Initialize constantacceleration unscented Kalman filter. 
initctukf  Initialize constantturnrate unscented Kalman filter. 
initcvmscekf  Initialize constantvelocity extended Kalman filter in modified spherical coordinates. 
initekfimm  Initialize tracking IMM filter. 
You can also write your own initialization function using the following syntax:
filter = filterInitializationFcn(detection)
objectDetection
. The output of this function must be an object belonging to
one of the filter classes: trackingKF
, trackingEKF
, trackingUKF
, trackingCKF
,
trackingGSF
,
trackingIMM
,
trackingMSCEKF
, or trackingABF
.
For guidance in writing this function, use the type
command to
examine the details of builtin MATLAB^{®}
functions. For example:
type
initcvekf
trackerJPDA
does not accept all filter initialization functions
in Sensor Fusion and Tracking Toolbox. The full list of filter initialization functions available in
Sensor Fusion and Tracking Toolbox are given in Initialization.
Data Types: function_handle
 char
EventGenerationFcn
— Feasible joint events generation function@jpdaEvents
(default)  function handle  character vectorFeasible joint events generation function, specified as a function handle or as a
character vector containing the name of a feasible joint events generation function. A
generation function generates feasible joint event matrices from admissible events
(usually given by a validation matrix) of a tracking scenario. A validation matrix is a
binary matrix listing all possible detectionstotrack associations. For details, see
jpadEvents
.
You can also write your own generation function. The function must have the following syntax:
FJE = myfunction(ValidationMatrix)
jpdaEvents
. For guidance in writing this function, use the
type
command to examine the details of
jpdaEvents
:
type jpdaEvents
Example:
@myfunction
or 'myfunction'
Data Types: function_handle
 char
MaxNumTracks
— Maximum number of tracks100
(default)  positive integerMaximum number of tracks that the tracker can maintain, specified as a positive integer.
Data Types: single
 double
MaxNumSensors
— Maximum number of sensors20
(default)  positive integerMaximum number of sensors that can be connected to the tracker, specified as a
positive integer. MaxNumSensors
must be greater than or equal to
the largest value of SensorIndex
found in all the detections used to
update the tracker. SensorIndex
is a property of an objectDetection
object. The MaxNumSensors
property
determines how many sets of ObjectAttributes
each track can
have.
Data Types: single
 double
AssignmentThreshold
— Detection assignment threshold30*[1 Inf]
(default)  positive scalar  1by2 vector of positive valuesDetection assignment threshold (or gating threshold), specified as a positive scalar
or 1by2 vector of
[C_{1},C_{2}],
where C_{1} ≤
C_{2}. 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
C_{2}. Also, the tracker can only assign a
detection to a track if the accurate normalized distance between them is less than
C_{1}. See the distance
method of each tracking filter (such as trackingCKF
and trackingEKF
) for explanation of the distance
calculation.
Tips:
Increase the value of C_{2} if there are track and detection combinations that should be calculated for assignment but are not. Decrease this value if cost calculation takes too much time.
Increase the value of C_{1} 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).
DetectionProbability
— Probability of detection0.9
(default)  scalar in the range [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.
Example: 0.85
Data Types: single
 double
InitializationThreshold
— Threshold to initialize a track0
(default)  scalar in the range [0,1]The probability threshold to initialize a new track, specified as a scalar in the
range [0,1]. If the probabilities of associating a detection with any of the existing
tracks are all smaller than InitializationThreshold
, the detection
will be 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
Data Types: single
 double
TrackLogic
— Track confirmation and deletion logic type'History'
(default)  'Integrated'
Confirmation and deletion logic type, specified as:
'History'
– Track confirmation and deletion is based on the
number of times the track has been assigned to a detection in the latest tracker
updates.
'Integrated'
– Track confirmation and deletion is based on
the probability of track existence, which is integrated in the assignment
function.
ConfirmationThreshold
— Threshold for track confirmationThreshold for track confirmation, specified as a scalar or a 1by2 vector. The
threshold depends on the type of track confirmation and deletion logic you set with the
TrackLogic
property:
'History'
– Specify the confirmation threshold as 1by2
vector [M
N]. A track is confirmed if it recorded at least
M hits in the last N updates. The
trackerJPDA
registers a hit on a track’s history logic
according to the HitMissThrehold
. The default value is
[2 3]
.
'Integrated'
– Specify the confirmation threshold as a
scalar. A track is confirmed if its probability of existence is greater than or
equal to the confirmation threshold. The default value is
0.95
.
Data Types: single
 double
DeletionThreshold
— Threshold for track deletionThreshold for track deletion, specified as a scalar or a realvalued 1by2 vector.
The threshold depends on the type of track confirmation and deletion logic you set with
the TrackLogic
property:
'History'
– Specify the confirmation threshold as
[P
R]. A track is deleted if it recorded at least
P misses in the last R updates. The
trackerJPDA
will register a miss on a track’s history logic
according to the HitMissThrehold
property. The default value
is [5,5]
.
'Integrated'
– Specify the deletion threshold as a scalar.
A track is deleted if its probability of existence drops below the threshold. The
default value is 0.1
.
Example: 0.2
or [5,6]
Data Types: single
 double
HitMissThreshold
— Threshold for registering hit or missThreshold for registering a hit or miss, specified as a scalar in the range [0,1].
The track history logic will register a miss and the track will be coasted if the sum of
the marginal probabilities of assignments is below the
HitMissThreshold
. Otherwise, the track history logic will
register a hit.
Example: 0.3
To enable this argument, set the TrackLogic
property to
'History'
.
Data Types: single
 double
ClutterDensity
— Spatial density of clutter measurements1e6
(default)  positive scalarSpatial density of clutter measurements, specified as a positive scalar. The clutter
density describes the expected number of false positive detections per unit volume. It
is used as the parameter of a Poisson clutter model. When
TrackLogic
is set to 'Integrated'
,
ClutterDensity
is also used in calculating the initial
probability of track existence.
Example: 1e5
Data Types: single
 double
NewTargetDensity
— Spatial density of new targets1e5
(default)  positive scalarSpatial density of new targets, specified as a positive scalar. The new target density describes the expected number of new tracks per unit volume in the measurement space. It is used in calculating the probability of track existence during track initialization.
Example: 1e3
To enable this argument, set the TrackLogic
property to
'Integrated'
.
Data Types: single
 double
DeathRate
— Time rate of target deaths0.01
(default)  scalar in the range [0,1]Time rate of target deaths, specified as a scalar in the range [0,1].
DeathRate
describes the probability with which true targets
disappear. It is related to the propagation of the probability of track existence
(PTE) :
where δt is the time interval since the previous update time t.
To enable this argument, set the TrackLogic
property to
'Integrated'
.
Data Types: single
 double
InitialExistenceProbability
— Initial probability of track existence0.9
(default)  scalar in the range [0,1]This property is readonly.
Initial probability of track existence, specified as a scalar in the range [0,1] and
calculated as InitialExistenceProbability =
NewTargetDensity*DetectionProbability/(ClutterDensity +
NewTargetDensity*DetectionProbability)
.
To enable this property, set the TrackLogic
property to
'Integrated'
. When the TrackLogic
property
is set to 'History'
, this property is not available.
Data Types: single
 double
HasCostMatrixInput
— Enable cost matrix inputfalse
(default)  true
Enable a cost matrix, specified as false
or
true
. If true
, you can provide an assignment cost
matrix as an input argument when calling the object.
Data Types: logical
HasDetectableTrackIDsInput
— Enable input of detectable track IDsfalse
(default)  true
Enable the input of detectable track IDs at each object update, specified as
false
or true
. Set this property to
true
if you want to provide a list of detectable track IDs. This
list informs the tracker of all tracks that the sensors are expected to detect and,
optionally, the probability of detection for each track.
Data Types: logical
NumTracks
— Number of tracks maintained by trackerThis property is readonly.
Number of tracks maintained by the tracker, returned as a nonnegative integer.
Data Types: single
 double
NumConfirmedTracks
— Number of confirmed tracksThis property is readonly.
Number of confirmed tracks, returned as a nonnegative integer. If the
IsConfirmed
field of an output track structure is
true
, the track is confirmed.
Data Types: single
 double
TimeTolerance
— Absolute time tolerance between detections1e5
(default)  positive scalarAbsolute time tolerance between detections for the same sensor, specified as a
positive scalar. Ideally, trackerJPDA
expects detections from a sensor
to have identical time stamps. However, if the time stamps differences between
detections of a sensor are within the margin specified by
TimeTolerance
, these detections will be used to update the track
estimate based on the average time of these detections.
Data Types: double
To process detections and update tracks, call the tracker with arguments, as if it were a function (described here).
confirmedTracks = tracker(detections,time)
confirmedTracks = tracker(detections,time,costMatrix)
confirmedTracks = tracker(___,detectableTrackIDs)
[confirmedTracks,tentativeTracks,allTracks] = tracker(___)
[confirmedTracks,tentativeTracks,allTracks,analysisInformation] = tracker(___)
returns a list of confirmed tracks that are updated from a list of detections at the
update time. Confirmed tracks are corrected and predicted to the update time.confirmedTracks
= tracker(detections
,time
)
also specifies a cost matrix. confirmedTracks
= tracker(detections
,time
,costMatrix
)
To enable this syntax, set the HasCostMatrixInput
property to
true
.
also specifies a list of expected detectable tracks given by
confirmedTracks
= tracker(___,detectableTrackIDs
)detectableTrackIDs
. This argument can be used with any of the
previous input syntaxes.
To enable this syntax, set the HasDetectableTrackIDsInput
property to true
.
[
also returns a list of tentative tracks and a list of all tracks. You can use any of the
input arguments in the previous syntaxes.confirmedTracks
,tentativeTracks
,allTracks
] = tracker(___)
[
also returns analysis information that can be used for track analysis. You can use any of
the input arguments in the previous syntaxes.confirmedTracks
,tentativeTracks
,allTracks
,analysisInformation
] = tracker(___)
detections
— Detection listobjectDetection
objectsDetection 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.
time
— Time of updateTime of update, specified as a scalar. The tracker updates all tracks to this time. Units are in seconds.
time
must be greater than or equal to the largest
Time
property value of the objectDetection
objects in the input detections
list.
time
must increase in value with each update to the
tracker.
Data Types: single
 double
costMatrix
— Cost matrixCost matrix, specified as a realvalued
MbyN matrix, where M is
the number of existing tracks in the previous update, and N is the
number of current detections. The cost matrix rows must be in the same order as the
list of tracks, and the columns must be in the same order as the list of detections.
Obtain the correct order of the list of tracks from the third output argument,
allTracks
, when the tracker is updated.
At the first update of the tracker or when the tracker has no previous tracks,
specify the cost matrix to be empty with a size of
[0,numDetections]
. Note that the cost must be given so that lower
costs indicate a higher likelihood of assigning a detection to a track. To prevent
certain detections from being assigned to certain tracks, you can set the appropriate
cost matrix entry to Inf
.
To enable this argument, set the HasCostMatrixInput
property to true
.
Data Types: double
 single
detectableTrackIDs
— Detectable track IDs Detectable track IDs, specified as a realvalued Mby1 vector
or Mby2 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 contains the corresponding
detection probability for the track. The detection probability is either reported by a
sensor or, if not reported, obtained from the
DetectionProbability
property.
Tracks whose identifiers are not included in
detectableTrackIDs
are considered undetectable. In this case,
the track deletion logic does not count the lack of detection for that track as a
missed detection for track deletion purposes.
To enable this input argument, set the detectableTrackIDs
property to true
.
Data Types: single
 double
confirmedTracks
— Confirmed tracksConfirmed tracks updated to the current time, returned as a structure or array of structures. Each structure corresponds to a track. The confirmation of a track depends on the track logic.
'History'
– A track is confirmed if it recorded enough
hits during the last few updates to satisfy the
ConfirmationThreshold
.
'Integrated'
– A track is confirmed if its probability of
existence is higher than the ConfirmationThreshold
property
value.
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 tracksTentative tracks, returned as a structure or array of structures. Each structure
corresponds to a track. A track is tentative if the track is not assigned to enough
detections and the track cannot be associated with any classified object given by the
ObjectClassID
. 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 tracksAll tracks, returned as a structure or 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 updatesAdditional information for analyzing track updates, returned as a structure. The fields of this structure are:
Field  Description 
TrackIDsAtStepBeginning  Track IDs when step began. 
CostMatrix  Cost matrix for assignment. 
Clusters  Cell array of cluster reports. 
InitiatedTrackIDs  IDs of tracks initiated during the step. 
DeletedTrackIDs  IDs of tracks deleted during the step. 
TrackIDsAtStepEnd  Track IDs when the step ended. 
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 jpadEvents 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. 
Data Types: struct
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)
trackerJPDA
predictTracksToTime  Predict track state 
getTrackFilterProperties  Obtain track filter properties 
setTrackFilterProperties  Set track filter properties 
Construct a trackerJPDA object with a default constant velocity Extended Kalman Filter and 'History' track logic. Set AssignmentThreshold to 100 to allow tracks to be jointly associated.
tracker = trackerJPDA('TrackLogic','History', 'AssignmentThreshold',100,... 'ConfirmationThreshold', [4 5], ... 'DeletionThreshold', [10 10]);
Specify the true initial positions and velocities of the two objects.
pos_true = [0 0 ; 40 40 ; 0 0]; V_true = 5*[cosd(30) cosd(30) ; sind(30) sind(30) ;0 0];
Create a theater plot to visualize tracks and detections.
tp = theaterPlot('XLimits',[1 150],'YLimits',[50 50]); trackP = trackPlotter(tp,'DisplayName','Tracks','MarkerFaceColor','g','HistoryDepth',0); detectionP = detectionPlotter(tp,'DisplayName','Detections','MarkerFaceColor','r');
To obtain the position and velocity, create position and velocity selectors.
positionSelector = [1 0 0 0 0 0; 0 0 1 0 0 0; 0 0 0 0 0 0]; % [x, y, 0] velocitySelector = [0 1 0 0 0 0; 0 0 0 1 0 0; 0 0 0 0 0 0 ]; % [vx, vy, 0]
Update the tracker with detections, display cost and marginal probability of association information, and visualize tracks with detections.
dt = 0.2; for time = 0:dt:30 % Update the true positions of objects. pos_true = pos_true + V_true*dt; % Create detections of the two objects with noise. detection(1) = objectDetection(time,pos_true(:,1)+1*randn(3,1)); detection(2) = objectDetection(time,pos_true(:,2)+1*randn(3,1)); % Step the tracker through time with the detections. [confirmed,tentative,alltracks,info] = tracker(detection,time); % Extract position, velocity and label info. [pos,cov] = getTrackPositions(confirmed,positionSelector); vel = getTrackVelocities(confirmed,velocitySelector); meas = cat(2,detection.Measurement); measCov = cat(3,detection.MeasurementNoise); % Update the plot if there are any tracks. if numel(confirmed)>0 labels = arrayfun(@(x)num2str([x.TrackID]),confirmed,'UniformOutput',false); trackP.plotTrack(pos,vel,cov,labels); end detectionP.plotDetection(meas',measCov); drawnow; % Display the cost and marginal probability of distribution every eight % seconds. if time>0 && mod(time,8) == 0 disp(['At time t = ' num2str(time) ' seconds,']); disp('The cost of assignment was: ') disp(info.CostMatrix); disp(['Number of clusters: ' num2str(numel(info.Clusters))]); if numel(info.Clusters) == 1 disp('The two tracks were in the same cluster.') disp('Marginal probabilities of association:') disp(info.Clusters{1}.MarginalProbabilities) end disp('') end end
At time t = 8 seconds, The cost of assignment was: 1.0e+03 * 0.0020 1.1523 1.2277 0.0053 Number of clusters: 2  At time t = 16 seconds, The cost of assignment was: 1.3968 4.5123 2.0747 1.9558 Number of clusters: 1 The two tracks were in the same cluster. Marginal probabilities of association: 0.8344 0.1656 0.1656 0.8344 0.0000 0.0000  At time t = 24 seconds, The cost of assignment was: 1.0e+03 * 0.0018 1.2962 1.2664 0.0013 Number of clusters: 2 
Track information is returned as an array of structures having the following fields:
Field  Description 
TrackID  Unique integer that identifies the track. 
UpdateTime  Time to which the track is updated. 
Age  Number of times the track was updated with either a hit or a miss. 
State  Value of state vector at the update time. 
StateCovariance  Uncertainty covariance matrix. 
TrackLogic  The track logic used. The value is either

TrackLogicState  The current state of the track logic.

IsConfirmed  True if the track is assumed to be of a real target. 
IsCoasted  True if the track has been updated without a detection (predicted). 
ObjectClassID  An integer value representing the object classification. Zero is reserved
for 
ObjectAttributes  A cell array of cells. Each cell captures the object attributes reported by the corresponding sensor. 
When a JPDA tracker processes detections, track creation and management follow these steps.
The tracker divides detections into multiple groups by originating sensor.
For each sensor:
The tracker calculates the distances from detections to existing tracks and
forms a costMatrix
.
The tracker creates a validation matrix based on the assignment threshold (or gate threshold) of the existing tracks. A validation matrix is a binary matrix listing all possible detectionstotrack associations. For details, see Feasible Joint Events.
Tracks and detections are then separated into clusters. A cluster can contain one track or multiple tracks if these tracks share common detections within their validation gates. A validation gate is a spatial boundary, in which the predicted detection of the track has a high likelihood to fall. For details, see Feasible Joint Events.
Update all clusters following the order of the mean detection time stamp within the cluster. For each cluster, the tracker:
Generates all feasible joint events. For details, see jpadEvents
.
Calculates the posterior probability of each joint event.
Calculates the marginal probability of each individual detectiontrack pair in the cluster.
Reports weak detections. Weak detections are the detections that are within the
validation gate of at least one track, but have probability association to all
tracks less than the IntitializationThreshold
.
Updates tracks in the cluster using correctjpda
.
Unassigned detections (these are not in any cluster) and weak detections spawn new tracks.
The tracker checks all tracks for deletion. Tracks are deleted based on the number
of scans without association using 'History'
logic or based on their
probability of existence using'Integrated'
track logic.
All tracks are predicted to the latest time value (either the time input if provided, or the latest mean cluster time stamp).
In the typical workflow for a tracking system, the tracker needs to determine if a detection can be associated with any of the existing tracks. If the tracker only maintains one track, the assignment can be done by evaluating the validation gate around the predicted measurement and deciding if the measurement falls within the validation gate. In the measurement space, the validation gate is a spatial boundary, such as a 2D ellipse or a 3D ellipsoid, centered at the predicted measurement. The validation gate is defined using the probability information (state estimation and covariance, for example) of the existing track, such that the correct or ideal detections have high likelihood (97% probability, for example) of falling within this validation gate.
However, if a tracker maintains multiple tracks, the data association process becomes more complicated, because one detection can fall within the validation gates of multiple tracks. For example, in the following figure, tracks T_{1} and T_{2} are actively maintained in the tracker, and each of them has its own validation gate. Since the detection D_{2} is in the intersection of the validation gates of both T_{1} and T_{2}, the two tracks (T_{1} and T_{2}) are connected and form a cluster. A cluster is a set of connected tracks and their associated detections.
To represent the association relationship in a cluster, the validation matrix is commonly used. Each row of the validation matrix corresponds to a detection while each column corresponds to a track. To account for the eventuality of each detection being clutter, a first column is added and usually referred to as "Track 0" or T_{0}. If detection D_{i} is inside the validation gate of track D_{j}, then the (j, i+1) entry of the validation matrix is 1. Otherwise, it is zero. For the cluster shown in the figure, the validation matrix Ω is
$$\Omega =\left[\begin{array}{ccc}1& 1& 0\\ 1& 1& 1\\ 1& 0& 1\end{array}\right]$$
Note that all the elements in the first column of Ω are 1, because any detection can be clutter or false alarm. One important step in the logic of joint probabilistic data association (JPDA) is to obtain all the feasible independent joint events in a cluster. Two assumptions for the feasible joint events are:
A detection cannot be emitted by more than one track.
A track cannot be detected more than once by the sensor during a single scan.
Based on these two assumptions, feasible joint events (FJEs) can be formulated. Each FJE is mapped to an FJE matrix Ω_{p} from the initial validation matrix Ω. For example, with the validation matrix Ω, eight FJE matrices can be obtained:
$$\begin{array}{l}{\Omega}_{1}=\left[\begin{array}{ccc}1& 0& 0\\ 1& 0& 0\\ 1& 0& 0\end{array}\right],\text{\hspace{0.17em}}\text{\hspace{0.05em}}\text{\hspace{0.17em}}{\Omega}_{2}=\left[\begin{array}{ccc}0& 1& 0\\ 1& 0& 0\\ 1& 0& 0\end{array}\right],\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\Omega}_{3}=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 1& 0& 0\end{array}\right],\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\Omega}_{4}=\left[\begin{array}{ccc}1& 0& 0\\ 0& 0& 1\\ 1& 0& 0\end{array}\right]\\ {\Omega}_{5}=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 1& 0& 0\end{array}\right],\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\Omega}_{6}=\left[\begin{array}{ccc}1& 0& 0\\ 1& 0& 0\\ 0& 0& 1\end{array}\right],\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\Omega}_{7}=\left[\begin{array}{ccc}0& 1& 0\\ 1& 0& 0\\ 0& 0& 1\end{array}\right],\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\Omega}_{8}=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]\end{array}$$
As a direct consequence of the two assumptions, the Ω_{p} matrices have
exactly one "1" value per row. Also, except for the first column which maps to clutter,
there can be at most one "1" per column. When the number of connected tracks grows in a
cluster, the number of FJE increases rapidly. The jpdaEvents
function
uses an efficient depthfirst search algorithm to generate all the feasible joint event
matrices.
[1] Fortmann, T., Y. BarShalom, and M. Scheffe. "Sonar Tracking of Multiple Targets Using Joint Probabilistic Data Association." IEEE Journal of Ocean Engineering. Vol. 8, Number 3, 1983, pp. 173184.
[2] Musicki, D., and R. Evans. "Joint Integrated Probabilistic Data Association: JIPDA." IEEE transactions on Aerospace and Electronic Systems . Vol. 40, Number 3, 2004, pp 10931099.
Usage notes and limitations:
See System Objects in MATLAB Code Generation (MATLAB Coder).
All the detections used with a multiobject tracker must have properties with the same sizes and types.
If you use the ObjectAttributes
field within an objectDetection
object, you must specify this field as a cell containing a
structure. The structure for all detections must have the same fields, and the values in
these fields must always have the same size and type. The form of the structure cannot
change during simulation.
If ObjectAttributes
are contained in the detection, the
SensorIndex
value of the detection cannot be greater than
10.
The first update to the multiobject tracker must contain at least one detection.
objectDetection
 trackHistoryLogic
 trackingABF
 trackingCKF
 trackingEKF
 trackingIMM
 trackingKF
 trackingUKF
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