ctrectjac

Jacobian of constant turn-rate rectangular target motion model

Description

Jx = ctrectjac(state) returns the Jacobian matrix of the constant turn-rate rectangular motion model with respect to the state vector. The default time step is 1 second.

example

Jx = ctrectjac(state,dt) specifies the time step dt in seconds.

[Jx,Jw] = ctrectjac(state,w,dt) also specifies the process noise w.

Examples

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Define a state vector for the model.

state = [1;2;2;30;1;4.7;1.8];

Compute the Jacobian. dt = 1 second.

jac = ctrectjac(state)
jac = 7×7

1.0000         0    0.8616   -0.0177   -0.0089         0         0
0    1.0000    0.5075    0.0301    0.0150         0         0
0         0    1.0000         0         0         0         0
0         0         0    1.0000    1.0000         0         0
0         0         0         0    1.0000         0         0
0         0         0         0         0    1.0000         0
0         0         0         0         0         0    1.0000

Compute the Jacobian. dt = 0.1 second without noise.

jac = ctrectjac(state,0.1)
jac = 7×7

1.0000         0    0.0866   -0.0017   -0.0001         0         0
0    1.0000    0.0501    0.0030    0.0002         0         0
0         0    1.0000         0         0         0         0
0         0         0    1.0000    0.1000         0         0
0         0         0         0    1.0000         0         0
0         0         0         0         0    1.0000         0
0         0         0         0         0         0    1.0000

Compute the Jacobian. dt = 0.1 second with noise.

jac = ctrectjac(state,0.01,0.1)
jac = 7×7

1.0000         0    0.0866   -0.0017   -0.0001         0         0
0    1.0000    0.0501    0.0030    0.0002         0         0
0         0    1.0000         0         0         0         0
0         0         0    1.0000    0.1000         0         0
0         0         0         0    1.0000         0         0
0         0         0         0         0    1.0000         0
0         0         0         0         0         0    1.0000

Input Arguments

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Current state, specified as a 1-by-7 real-valued vector. The sate of the constant-turn rectangular target model is [x; y; s; θ; ω; L; W]. The meaning of these variables and their units are:

 Variable Meaning Unit x Position of the rectangle center in x direction m y Position of the rectangle center in y direction m s Speed in the heading direction m/s θ Orientation angle of the rectangle with respect to x direction degree ω Turn-rate degree/s L Length of the rectangle m W Width of the rectangle m Example: [1;2;2;30;1;4.7;1.8]

Data Types: single | double

Time step, specified as a real-valued positive scalar in second.

Data Types: single | double

Process noise, specified as a 2-element real-valued vector. The first element specifies the process noise in linear acceleration (m/s2). The second element specifies the process noise in yaw acceleration (degrees/s2).

Data Types: single | double

Output Arguments

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Jacobian matrix with respect to state, returned as a 7-by-7 matrix.

Data Types: double

Jacobian with respect to process noise, returned as a 7-by-2 matrix.

Data Types: double