initcaekf

Create constant-acceleration extended Kalman filter from detection report

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.

Examples

Initialize 3-D Constant-Acceleration Extended Kalman Filter

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

Create 3D Constant Acceleration EKF from Spherical Measurement

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 $$45^{\circ }$$, the elevation to $$22^{\circ }$$, 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

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 constacc motion model and a cameas measurement model. The state of the filter is defined as [x; v_x; a_x; y; v_y; a_y; z; v_z; a_z], in which x, y, z are the position coordinates, v_x, v_y, v_z are the corresponding velocities, and a_x, a_y, a_z 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; 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 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 multiObjectTracker object.

Extended Capabilities

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

Version History

Introduced in R2017a