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initcaekf

Create constant-acceleration extended Kalman filter from detection report

Since R2021a

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Syntax

filter = initcaekf(detection)

Description

filter = initcaekf(detection) creates and initializes a constant-acceleration extended Kalman filter from information contained in a detection report. For more details, see Algorithms and trackingEKF.

example

Examples

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Open Live Script

Create and initialize a 3-D constant-acceleration extended Kalman filter object from an initial detection report.

Create the detection report from an initial 3-D measurement, (-200;30;0) , of the object position. Assume uncorrelated measurement noise.

detection = objectDetection(0,[-200;-30;0],'MeasurementNoise',2.1*eye(3), ...
    'SensorIndex',1,'ObjectClassID',1,'ObjectAttributes',{'Car',2});

Create the new filter from the detection report and display its properties.

filter = initcaekf(detection)
filter = 
  trackingEKF with properties:

                          State: [9x1 double]
                StateCovariance: [9x9 double]

             StateTransitionFcn: @constacc
     StateTransitionJacobianFcn: @constaccjac
                   ProcessNoise: [3x3 double]
        HasAdditiveProcessNoise: 0

                 MeasurementFcn: @cameas
         MeasurementJacobianFcn: @cameasjac
         HasMeasurementWrapping: 1
               MeasurementNoise: [3x3 double]
    HasAdditiveMeasurementNoise: 1

                MaxNumOOSMSteps: 0

                EnableSmoothing: 0

Show the filter state.

filter.State
ans = 9×1

  -200
     0
     0
   -30
     0
     0
     0
     0
     0

Show the state covariance matrix.

filter.StateCovariance
ans = 9×9

    2.1000         0         0         0         0         0         0         0         0
         0  100.0000         0         0         0         0         0         0         0
         0         0  100.0000         0         0         0         0         0         0
         0         0         0    2.1000         0         0         0         0         0
         0         0         0         0  100.0000         0         0         0         0
         0         0         0         0         0  100.0000         0         0         0
         0         0         0         0         0         0    2.1000         0         0
         0         0         0         0         0         0         0  100.0000         0
         0         0         0         0         0         0         0         0  100.0000
Open Live Script

Initialize a 3D constant-acceleration extended Kalman filter from an initial detection report made from an initial measurement in spherical coordinates. If you want to use spherical coordinates, then you must supply a measurement parameter structure as part of the detection report with the Frame field set to 'spherical'. Set the azimuth angle of the target to 45∘, the elevation to 22∘, the range to 1000 meters, and the range rate to -4.0 m/s.

frame = 'spherical';
sensorpos = [25,-40,-10].';
sensorvel = [0;5;0];
laxes = eye(3);

Create the measurement parameters structure. Set 'HasVelocity' and 'HasElevation' to true. Then, the measurement vector consists of azimuth, elevation, range, and range rate.

measparms = struct('Frame',frame,'OriginPosition',sensorpos, ...
    'OriginVelocity',sensorvel,'Orientation',laxes,'HasVelocity',true, ...
    'HasElevation',true);
meas = [45;22;1000;-4];
measnoise = diag([3.0,2.5,2,1.0].^2);
detection = objectDetection(0,meas,'MeasurementNoise', ...
    measnoise,'MeasurementParameters',measparms)
detection = 
  objectDetection with properties:

                     Time: 0
              Measurement: [4x1 double]
         MeasurementNoise: [4x4 double]
              SensorIndex: 1
            ObjectClassID: 0
    ObjectClassParameters: []
    MeasurementParameters: [1x1 struct]
         ObjectAttributes: {}


filter = initcaekf(detection);

Display the state vector.

disp(filter.State)
  680.6180
   -2.6225
         0
  615.6180
    2.3775
         0
  364.6066
   -1.4984
         0

Input Arguments

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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])

Output Arguments

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Extended Kalman filter, returned as a trackingEKF object.

Algorithms

  • The function initializes a trackingEKF object with a constacc motion model and a cameas measurement model. The state of the filter is defined as [x; vx; ax; y; vy; ay; z; vz; az], in which x, y, z are the position coordinates, vx, vy, vz are the corresponding velocities, and ax, ay, az are the corresponding accelerations.

  • The detection input can be an objectDetection object of Cartesian or spherical measurement:

    • For a Cartesian measurement,

      • By default, the function assumes the measurement is a 3-D position measurement ([x; y; z]). The function uses the position measurement to initialize the position state of the filter and sets the velocity and acceleration components of the filter state as 0. For the state error covariance matrix of the filter, the function sets the position components same as those of the measurement noise matrix and sets the velocity and acceleration components as 100 m2/s2 and 100 m2/s4, respectively. The function sets all the cross-components of the state error covariance matrix as 0.

      • You can also use a 6-D measurement ([x; y; z; vx; vy; vz]) by specifying the MeasurementParameters property of the objectDetection object. Specify the HasVelocity field of the measurement parameter structure as true so that the initcaekf function can recognize the 6-D measurement. In this case, the position and velocity components of the state and the state error covariance matrix are the same as the measurement and measurement noise matrix of the detection, respectively. The function sets the acceleration states as 0 and sets the acceleration components of the state error covariance matrix as 100 m2/s4.

    • For a spherical measurement, you must specify the Frame field in the MeasurementParameters property of the objectDetection object as "Spherical". Also, use the MeasurementParameters property to specify if the detection has azimuth, elevation, range, and range rate. A full spherical measurement has four elements [az, el, r, rr], representing azimuth in degrees, elevation in degrees, range in meters, and range-rate in meters per second, respectively. Some of the four elements can be missing.

      • If the detection has elevation, the function uses the elevation measurement and its covariance to construct the position components of the filter state and state error covariance after performing coordinate transformation from the spherical frame to the Cartesian frame. Without elevation, the function sets the elevation as 0 and set its covariance as 1802/12 deg2 before performing the coordinate transformation.

      • If the detection has range-rate, the function uses the range-rate measurement and its covariance to construct the velocity components of the filter sate and state error covariance. The function also assumes the velocity covariance of the cross-range direction is 100 m2/s2. Without range-rate, the function sets the velocity states of the filter as 0 and its corresponding covariances as 100 m2/s2.

    • The function sets the acceleration component of the filter state as 0 and set the acceleration components of the state error covariance matrix as 100 m2/s4. The function sets all the cross-components (for example between position and velocity) of the state error covariance matrix as 0.

    • You can use other fields of the MeasurementParameters property of an objectDetection object, such as OriginPosition and OriginaVelocity, to further specify the measurement coordinates.

  • The function models the process noise as non-additive and computes the process noise matrix assuming a unit acceleration increment per step following the Weiner-sequence acceleration model.

  • The measurement noise matrix in the initialized filter is the same as that in the detection.

  • You can use this function as the FilterInitializationFcn property of a radarTracker object.

Extended Capabilities

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

Version History

Introduced in R2021a

See Also

Functions

Objects