Main Content

initapekf

Constant velocity angle-parameterized EKF initialization

collapse all in page

Syntax

filter = initapekf(detection)
filter = initapekf(detection,numFilters)
filter = initapekf(detection,numFilters,angleLimits)

Description

filter = initapekf(detection) configures the filter with 10 extended Kalman filters (EKFs). The function configures the process noise with unit standard deviation in acceleration.

The angle-parameterized extended Kalman filter (APEKF) is a Gaussian-sum filter (trackingGSF) with multiple EKFs, each initialized at an estimated angular position of the target. Angle-parametrization is a commonly used technique to initialize a filter from a range-only detection.

filter = initapekf(detection,numFilters) specifies the number of EKFs in the filter.

filter = initapekf(detection,numFilters,angleLimits) specifies the limits on angular position of the target.

example

Examples

collapse all

Open Live Script

The APEKF is a special type of filter that can be initialized using range-only measurements. When the 'Frame' is set to 'spherical', the detection has [azimuth elevation range range-rate] measurements. Specify the measurement parameters appropriately to define a range-only measurement.

measParam = struct('Frame','Spherical','HasAzimuth',false,'HasElevation',false,'HasVelocity',false,'OriginPosition',[100;10;0]);

The objectDetection class defines an interface to the range-only detection measured by the sensor. The MeasurementParameters field of objectDetection carries information about what the sensor is measuring. 

detection = objectDetection(0,100,'MeasurementNoise',100,'MeasurementParameters',measParam)
detection = 
  objectDetection with properties:

                     Time: 0
              Measurement: 100
         MeasurementNoise: 100
              SensorIndex: 1
            ObjectClassID: 0
    ObjectClassParameters: []
    MeasurementParameters: [1x1 struct]
         ObjectAttributes: {}

The initapekf function uses the range-only detection to initialize the APEKF.

apekf = initapekf(detection) %#ok
apekf = 
  trackingGSF with properties:

                     State: [6x1 double]
           StateCovariance: [6x6 double]

           TrackingFilters: {10x1 cell}
    HasMeasurementWrapping: [0 0 0 0 0 0 0 0 0 0]
        ModelProbabilities: [10x1 double]

          MeasurementNoise: 100

You can also initialize the APEKF with 10 filters and to operate within the angular limits of [-30 30] degrees.

angleLimits = [-30 30];
numFilters = 10;
apekf = initapekf(detection, numFilters, angleLimits)
apekf = 
  trackingGSF with properties:

                     State: [6x1 double]
           StateCovariance: [6x6 double]

           TrackingFilters: {10x1 cell}
    HasMeasurementWrapping: [0 0 0 0 0 0 0 0 0 0]
        ModelProbabilities: [10x1 double]

          MeasurementNoise: 100

You can also specify the initapekf function as a FilterInitializationFcn to the trackerGNN object.

funcHandle = @(detection)initapekf(detection,numFilters,angleLimits)
funcHandle = function_handle with value:
    @(detection)initapekf(detection,numFilters,angleLimits)


tracker = trackerGNN('FilterInitializationFcn',funcHandle);

Visualize the filter.

tp = theaterPlot;
componentPlot = trackPlotter(tp,'DisplayName','Individual sums','MarkerFaceColor','r');
sumPlot = trackPlotter(tp,'DisplayName','Mixed State','MarkerFaceColor','g');

indFilters = apekf.TrackingFilters;
pos = zeros(numFilters,3);
cov = zeros(3,3,numFilters);
for i = 1:numFilters
    pos(i,:) = indFilters{i}.State(1:2:end);
    cov(1:3,1:3,i) = indFilters{i}.StateCovariance(1:2:end,1:2:end);
end
componentPlot.plotTrack(pos,cov);

mixedPos = apekf.State(1:2:end)';
mixedPosCov = apekf.StateCovariance(1:2:end,1:2:end);
sumPlot.plotTrack(mixedPos,mixedPosCov);

Figure contains an axes object. The axes object with xlabel X (m), ylabel Y (m) contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Individual sums, Mixed State.

Open Live Script

Create an angle-parameterized EKF from an [az r] detection.

measParam = struct('Frame','Spherical','HasAzimuth',true,'HasElevation',false,'HasVelocity',false,'OriginPosition',[100;10;0]);

The objectDetection class defines an interface to the range-only detection measured by the sensor. The MeasurementParameters field of objectDetection carries information about what the sensor is measuring. 

det = objectDetection(0,[30;100],'MeasurementParameters',measParam,'MeasurementNoise',10);

The initapekf function parameterizes the apekf filter on the elevation measurement.

numFilters = 10;
apekf = initapekf(det,numFilters,[-30 30]);
indFilters = apekf.TrackingFilters;
pos = zeros(numFilters,3);
cov = zeros(3,3,numFilters);
for i = 1:numFilters
    pos(i,:) = indFilters{i}.State(1:2:end);
    cov(1:3,1:3,i) = indFilters{i}.StateCovariance(1:2:end,1:2:end);
end

Visualize the filter.

tp = theaterPlot;
componentPlot = trackPlotter(tp,'DisplayName','Individual sums','MarkerFaceColor','r');
sumPlot = trackPlotter(tp,'DisplayName','Mixed State','MarkerFaceColor','g');
componentPlot.plotTrack(pos,cov);
mixedPos = apekf.State(1:2:end)';
mixedPosCov = apekf.StateCovariance(1:2:end,1:2:end);
sumPlot.plotTrack(mixedPos,mixedPosCov);
view(3);

Figure contains an axes object. The axes object with xlabel X (m), ylabel Y (m) contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Individual sums, Mixed State.

Input Arguments

collapse all

Detection report, specified as an objectDetection object.

Example: detection = objectDetection(0,[1;4.5;3],'MeasurementNoise', [1.0 0 0; 0 2.0 0; 0 0 1.5])

Number of EKFs each initialized at an estimated angular position of the target, specified as a positive integer. When not specified, the default number of EKFs is 10.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Angular limits of the target, specified as a two-element vector. The two elements in the vector represent the lower and upper limits of the target angular position.

When the function detects:

  • Range measurements –– Default angular limits are [–180 180].

  • Azimuth and range measurements –– Default angular limits are [–90 90].

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Output Arguments

collapse all

Constant velocity angle-parameterized extended Kalman filter (EKF), returned as a trackingGSF object.

Algorithms

The function can support the following types of measurements in the detection.

  • Range measurements –– Parameterization is done on the azimuth of the target, and the angular limits are [–180 180] by default.

  • Azimuth and range measurements –– Parameterization is done on the elevation of the target, and the angular limits are [–90 90] by default.

References

[1] Ristic, Branko, Sanjeev Arulampalam, and James McCarthy. "Target motion analysis using range-only measurements: algorithms, performance and application to ISAR data." Signal Processing 82, no. 2 (2002): 273-296.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2018b

See Also

Functions

Objects