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singermeasjac

Jacobian of measurement function for Singer acceleration motion model

Since R2020b

Description

measurementjac = singermeasjac(state) returns the Jacobian of the measurement function, measurementjac, for a state based on the Singer acceleration motion model, which assumes the target acceleration decays over time. state specifies the current state of the track.

example

measurementjac = singermeasjac(state,frame) specifies the measurement Jacobian output coordinate system, frame.

measurementjac = singermeasjac(state,frame,sensorpos,sensorvel) specifies the sensor position, sensorpos, and the sensor velocity, sensorvel.

measurementjac = singermeasjac(state,frame,sensorpos,sensorvel,laxes) specifies the local sensor axes orientation, laxes.

measurementjac = singermeasjac(state,measurementParameters) specifies the measurement parameters, measurementParameters.

Examples

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Define a state for 2-D Singer acceleration motion.

state = [1;10;0;2;20;1];

Obtain the measurement Jacobian in a rectangular frame.

jacobian = singermeasjac(state)
jacobian = 3×6

     1     0     0     0     0     0
     0     0     0     1     0     0
     0     0     0     0     0     0

Obtain the measurement Jacobian in a spherical frame.

jacobian = singermeasjac(state, 'spherical')
jacobian = 4×6

  -22.9183         0         0   11.4592         0         0
         0         0         0         0         0         0
    0.4472         0         0    0.8944         0         0
    0.0000    0.4472         0    0.0000    0.8944         0

Obtain the measurement Jacobian in a spherical frame relative to a stationary sensor located at [1;-2;0].

jacobian = singermeasjac(state, 'spherical', [1;-2;0], [0;0;0])
jacobian = 4×6

  -14.3239         0         0         0         0         0
         0         0         0         0         0         0
         0         0         0    1.0000         0         0
    2.5000         0         0         0    1.0000         0

Obtain the measurement Jacobian in a spherical frame relative to a stationary sensor located at [1;-2;0] that is rotated by 90 degrees around the z axis relative to the global frame.

laxes = [0 -1 0; 1 0 0; 0 0 1];
jacobian = singermeasjac(state, 'spherical', [1;-2;0], [0;0;0], laxes)
jacobian = 4×6

  -14.3239         0         0         0         0         0
         0         0         0         0         0         0
         0         0         0    1.0000         0         0
    2.5000         0         0         0    1.0000         0

Input Arguments

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Input state, specified as a real-valued 3N-by-1 vector. N is the spatial degree of the state. The state vector takes the different forms based on its dimensions.

Spatial DegreesState Vector Structure
1-D[x;vx;ax]
2-D[x;vx;ax;y;vy;ay]
3-D[x;vx;ax;y;vy;ay;z;vz;az]

For example, x represents the x-coordinate, vx represents the velocity in the x-direction, and ax represents the acceleration in the x-direction. If the motion model is in one-dimensional space, the y- and z-axes are assumed to be zero. If the motion model is in two-dimensional space, values along the z-axis are assumed to be zero. Position coordinates are in meters. Velocity coordinates are in m/s. Acceleration coordinates are in m/s2.

Example: [5;0.1;0.01;0;-0.2;-0.01;-3;0.05;0]

Frame to report measurements, specified as 'rectangular' or 'spherical'. When you specify frame as 'rectangular', a measurement consists of x, y, and z Cartesian coordinates. When you specify frame as 'spherical', a measurement consists of azimuth, elevation, range, and range rate.

Data Types: char | string

Sensor position with respect to the navigation frame, specified as a real-valued 3-by-1 column vector. Units are in meters.

Data Types: single | double

Sensor velocity with respect to the navigation frame, specified as a real-valued 3-by-1 column vector. Units are in m/s.

Data Types: single | double

Local sensor axes coordinates, specified as a 3-by-3 orthogonal matrix. Each column specifies the direction of the local x-, y-, and z-axes, respectively, with respect to the navigation frame. The matrix is the rotation matrix from the global frame to the sensor frame.

Data Types: single | double

Measurement parameters, specified as a structure or an array of structures. For more details, see Measurement Parameters.

Data Types: struct

Output Arguments

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Jacobian of the measurement function, returned as a real-valued M-by-N matrix. The function constructs the Jacobian from the partial derivatives of the measurement vector with respect to the input state. The form of the measurement vector depends on the syntax.

  • When you do not specify the measurementParameters argument and set the frame argument to 'rectangular', the function outputs measurement vectors in the format of [x;y;z].

  • When you do not specify the measurementParameters argument and set the frame argument to 'spherical', the function outputs measurement vectors in the format of [az;el;r;rr].

  • When you specify the measurementParameters argument and set the frame field to 'rectangular', the size of the measurement vector depends on the value of the HasVelocity field in the measurementParameters structure. The measurement vector includes the Cartesian position and velocity coordinates of the tracked object with respect to the ego vehicle coordinate system.

    Rectangular Measurements

    HasVelocity = 'false'[x;y;z]
    HasVelocity = 'true'[x;y;z;vx;vy;vz]

    Position units are in meters and velocity units are in m/s.

  • When you specify the measurementParameters argument and set the frame field to 'spherical', the size of the measurement vector depends on the value of the HasVelocity, HasRange, and HasElevation fields in the measurementParameters structure. The measurement vector includes the azimuth angle, az, elevation angle, el, range, r, and range rate, rr, of the object with respect to the local ego vehicle coordinate system. Positive values for range rate indicate that an object is moving away from the sensor.

    Spherical Measurements

     HasRange = 'true'HasRange = 'false'
     HasElevation = 'false'HasElevation = 'true'HasElevation = 'false'HasElevation = 'true'
    HasVelocity = 'false'[az;r][az;el;r][az][az;el]
    HasVelocity = 'true'[az;r;rr][az;el;r;rr][az][az;el]

    Angle units are in degrees, range units are in meters, and range rate units are in m/s.

More About

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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

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

Version History

Introduced in R2020b