initsingerekf

Singer acceleration trackingEKF initialization

Since R2020b

Syntax

filter = initsingerekf(detection)

Description

filter = initsingerekf(detection) initializes an extended Kalman filter (trackingEKF) with the detection input, based on the Singer acceleration model, which assumes the target acceleration decays over time.

The function initializes an acceleration state [x v_x a_x y v_y a_y z v_z a_z] in the filter.

Examples

Initialize Singer Acceleration Extended Kalman Filter in Rectangular Frame

For a rectangular frame, the Singer acceleration measurement function, singermeas, assumes a position measurement in 3-D space. Define a position measurement [1;3;0] that has measurement noise [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 the initsingerekf function to create a trackingEKF filter using the measurements defined above.

ekf = initsingerekf(detection);

Verify the values of the state and measurement noise.

filterState = ekf.State

filterState = 9×1

     1
     0
     0
     3
     0
     0
     0
     0
     0

filterMeasureNoise = ekf.MeasurementNoise

filterMeasureNoise = 3×3

    1.0000    0.2000         0
    0.2000    2.0000         0
         0         0    1.0000

Input Arguments

detection — Object detection

objectDetection object

Object detection, specified as an objectDetection object. You can specify the following fields for the MeasurementParameters property of the objectDetection object. When you do not specify a field, the default value is used.

Field	Description	Default Value
Frame	Frame used to report measurements, specified as one of these values: 'rectangular' — Detections are reported in rectangular coordinates. 'spherical' — Detections are reported in spherical coordinates.	'rectangular'
OriginPosition	Position offset of the origin of the frame relative to the parent frame, specified as an [x y z] real-valued vector.	[0 0 0]
OriginVelocity	Velocity offset of the origin of the frame relative to the parent frame, specified as a [vx vy vz] real-valued vector.	[0 0 0]
Orientation	Frame rotation matrix, specified as a 3-by-3 real-valued orthonormal matrix.	[1 0 0; 0 1 0; 0 0 1]
HasAzimuth	Logical scalar indicating if azimuth is included in the measurement.	1
HasElevation	Logical scalar indicating if elevation is included in the measurement. For measurements reported in a rectangular frame, and if HasElevation is false, the reported measurements assume 0 degrees of elevation.	1
HasRange	Logical scalar indicating if range is included in the measurement.	1
HasVelocity	Logical scalar indicating if the reported detections include velocity measurements. For measurements reported in the rectangular frame, if HasVelocity is false, the measurements are reported as [x y z]. If HasVelocity is true, measurements are reported as [x y z vx vy vz].	0
IsParentToChild	Logical scalar indicating if Orientation performs a frame rotation from the parent coordinate frame to the child coordinate frame. When IsParentToChild is false, then Orientation performs a frame rotation from the child coordinate frame to the parent coordinate frame.	0

Output Arguments

filter — Extended Kalman filter

trackingEKF object

Extended Kalman filter, returned as a trackingEKF object.

Algorithms

• You can use the initsingerekf function as the FilterInitializationFcn property of trackingEKF.

• When creating the Kalman filter, the function configures the process noise assuming a target maneuver time constant, τ = 20s and a unit target maneuver standard deviation, σ = 1 m/s². The function uses the singerProcessNoise function.

• The Singer process noise assumes an invariant time step and additive process noise.

References

[1] Singer, Robert A. "Estimating optimal tracking filter performance for manned maneuvering targets." IEEE Transactions on Aerospace and Electronic Systems 4 (1970): 473-483.

[2] Blackman, Samuel S., and Robert Popoli. "Design and analysis of modern tracking systems." (1999).

[3] Li, X. Rong, and Vesselin P. Jilkov. "Survey of maneuvering target tracking: dynamic models." Signal and Data Processing of Small Targets 2000, vol. 4048, pp. 212-235. International Society for Optics and Photonics, 2000.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• The function returns a filter that uses anonymous functions to define the StateTransitionFcn and StateTransitionCovarianceFcn properties. As a result, the value of the target maneuver constant (τ = 20s) cannot be modified after construction. To create a Singer-based filter with a different value of τ, you must write your own filter initialization function similar as the initsingerekf function.

Version History

Introduced in R2020b