# initcackf

Create constant acceleration tracking cubature Kalman filter from detection report

## Description

example

ckf = initcackf(detection) initializes a constant acceleration cubature Kalman filter for object tracking based on information provided in an objectDetection object, detection.

The function initializes a constant acceleration state with the same convention as constacc and cameas, [x vx ax y vy ay z vz az].

## Examples

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Create a constant acceleration tracking cubature Kalman filter object, trackingCKF, from an initial detection report. The detection report is made from an initial 3-D position measurement of the Kalman filter state in rectangular coordinates. You can obtain the 3-D position measurement using the constant acceleration measurement function, cameas.

This example uses the coordinates, x = 1, y = 3, z = 0 and a 3-D position measurement noise of [1 0.2 0; 0.2 2 0; 0 0 1].

detection = objectDetection(0, [1;3;0], 'MeasurementNoise', [1 0.2 0; 0.2 2 0; 0 0 1]);

Use initcackf to create a trackingCKF filter initialized at the provided position and using the measurement noise defined above.

ckf = initcackf(detection)
ckf =
trackingCKF with properties:

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

StateTransitionFcn: @constacc
ProcessNoise: [3x3 double]

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

EnableSmoothing: 0

Check the values of the state and the measurement noise. Verify that the filter state, ckf.State, has the same position components as the detection measurement, detection.Measurement.

ckf.State
ans = 9×1

1
0
0
3
0
0
0
0
0

Verify that the filter measurement noise, ckf.MeasurementNoise, is the same as the detection.MeasurementNoise values.

ckf.MeasurementNoise
ans = 3×3

1.0000    0.2000         0
0.2000    2.0000         0
0         0    1.0000

Create a constant acceleration tracking cubature Kalman filter object, trackingCKF, from an initial detection report. The detection report is made from an initial 3-D position measurement of the Kalman filter state in spherical coordinates. You can obtain the 3-D position measurement using the constant acceleration measurement function, cameas.

This example uses the coordinates, az = 30, e1 = 5, r = 100, rr = 4 and a measurement noise of diag([2.5, 2.5, 0.5, 1].^2).

meas = [30;5;100;4];
measNoise = diag([2.5, 2.5, 0.5, 1].^2);

Use the MeasurementParameters property of the detection object to define the frame. When not defined, the fields of the MeasurementParameters struct use default values. In this example, sensor position, sensor velocity, orientation, elevation, and range rate flags are default.

measParams = struct('Frame','spherical');
detection = objectDetection(0,meas,'MeasurementNoise',measNoise,...
'MeasurementParameters',measParams)
detection =
objectDetection with properties:

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

Use initcackf to create a trackingCKF filter initialized at the provided position and using the measurement noise defined above.

ckf = initcackf(detection)
ckf =
trackingCKF with properties:

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

StateTransitionFcn: @constacc
ProcessNoise: [3x3 double]

MeasurementFcn: @cameas
HasMeasurementWrapping: 1
MeasurementNoise: [4x4 double]

EnableSmoothing: 0

Verify that the filter state produces the same measurement as above.

meas2 = cameas(ckf.State, measParams)
meas2 = 4×1

30.0000
5.0000
100.0000
4.0000

## 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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Constant acceleration cubature Kalman filter for object tracking, returned as a trackingCKF object.

## Algorithms

• The function computes the process noise matrix assuming a unit standard deviation for the acceleration change rate.

• You can use this function as the FilterInitializationFcn property of trackerTOMHT and trackerGNN System objects.

## Version History

Introduced in R2018b