initctekf

Create constant turn-rate extended Kalman filter from detection report

Since R2021a

Syntax

filter = initctekf(detection)

Description

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

Examples

Initialize 2-D Constant Turn-Rate Extended Kalman Filter

Create and initialize a 2-D constant turn-rate extended Kalman filter object from an initial detection report.

Create the detection report from an initial 2-D measurement, (-250,-40), of the object position. Assume uncorrelated measurement noise.

Extend the measurement to three dimensions by adding a z-component of zero.

detection = objectDetection(0,[-250;-40;0],'MeasurementNoise',2.0*eye(3), ...
    'SensorIndex',1,'ObjectClassID',1,'ObjectAttributes',{'Car',2});

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

filter = initctekf(detection)

filter = 
  trackingEKF with properties:

                          State: [7×1 double]
                StateCovariance: [7×7 double]

             StateTransitionFcn: @constturn
     StateTransitionJacobianFcn: @constturnjac
                   ProcessNoise: [4×4 double]
        HasAdditiveProcessNoise: 0

                 MeasurementFcn: @ctmeas
         MeasurementJacobianFcn: @ctmeasjac
         HasMeasurementWrapping: 1
               MeasurementNoise: [3×3 double]
    HasAdditiveMeasurementNoise: 1

                MaxNumOOSMSteps: 0

                EnableSmoothing: 0

Show the state.

filter.State

ans = 7×1

  -250
     0
   -40
     0
     0
     0
     0

Show the state covariance matrix.

filter.StateCovariance

ans = 7×7

    2.0000         0         0         0         0         0         0
         0  100.0000         0         0         0         0         0
         0         0    2.0000         0         0         0         0
         0         0         0  100.0000         0         0         0
         0         0         0         0  100.0000         0         0
         0         0         0         0         0    2.0000         0
         0         0         0         0         0         0  100.0000

Create 2-D Constant Turn-rate EKF from Spherical Measurement

Initialize a 2-D constant turn-rate 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 degrees, 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 'HasElevation' to false. Then, the measurement consists of azimuth, range, and range rate.

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

detection = 
  objectDetection with properties:

                     Time: 0
              Measurement: [3×1 double]
         MeasurementNoise: [3×3 double]
              SensorIndex: 1
            ObjectClassID: 0
    ObjectClassParameters: []
    MeasurementParameters: [1×1 struct]
         ObjectAttributes: {}

filter = initctekf(detection);

Filter state vector.

disp(filter.State)

  732.1068
   -2.8284
  667.1068
    2.1716
         0
  -10.0000
         0

Input Arguments

detection — Detection report

objectDetection object

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

filter — Extended Kalman filter

trackingEKF object

Extended Kalman filter, returned as a trackingEKF object.

Algorithms

• The function initializes a trackingEKF object with a constturn motion model and a ctmeas measurement model. The state of the filter is defined as [x; v_x; y; v_y; ω; z; v_z], in which ω is the angular rate in the xy-plane, x, y, z are the position coordinates, and v_x, v_y, v_z are the corresponding velocities.

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

  • For a Cartesian objectDetection object,

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

    • You can also use a 6-D measurement ([x; y; z; v_x; v_y; v_z]) by specifying the MeasurementParameters property of the objectDetection object. Specify the HasVelocity field of the measurement parameter structure as true so that the initctekf function can recognize the 6-D measurement. In this case, the state and state error covariance matrix of the filter are the same as the measurement and measurement noise matrix of the detection, respectively.

    • Regardless of the dimension of the detection, the function sets the angular rate state ω of the filter as 0 and set its corresponding covariance as 100 deg²/s².

  • 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 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 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.

    • Regardless of the dimension of the detection, the function sets the angular velocity state ω of the filter as 0 and set its corresponding covariance as 100 deg²/s².

  • 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 an acceleration standard deviation of 1 m/s² and an angular acceleration standard deviation of 1 deg/s².

• 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