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constacc

State transition function for constant-acceleration motion model

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Syntax

predictedState = constacc(state)
predictedState = constacc(state,dt)
predictedState = constacc(state,w,dt)

Description

predictedState = constacc(state) returns the predicted state, predictedState, obtained from the current state, state, based on the constant-acceleration motion model. The default time step is 1 second.

example

predictedState = constacc(state,dt) specifies the time step, dt.

example

predictedState = constacc(state,w,dt) also specifies the state noise, w.

Examples

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Open Live Script

Define an initial state for 2-D constant-acceleration motion.

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

Predict the state 1 second later.

state = constacc(state)
state = 6×1

    2.5000
    2.0000
    1.0000
    3.0000
    1.0000
         0
Open Live Script

Define an initial state for 2-D constant-acceleration motion.

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

Predict the state 0.5 s later.

state = constacc(state,0.5)
state = 6×1

    1.6250
    1.5000
    1.0000
    2.5000
    1.0000
         0

Input Arguments

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Current state for constant-acceleration motion, specified as a real-valued 3D-by-N matrix. D is the number of spatial degrees of freedom of motion and N is the number states. For each spatial degree of motion, the state vector, as a column of the state matrix, takes the form shown in this table.

Spatial DimensionsState 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 meters/second. Acceleration coordinates are in meters/second2.

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

Data Types: double

Time step interval, specified as a positive scalar. Time units are in seconds.

Example: 0.5

Data Types: single | double

State noise, specified as a scalar or real-valued D-by-N matrix. D is the number of spatial degrees of freedom of motion and N is the number of state vectors. If specified as a scalar, the scalar value is expanded to a D-by-N matrix.

Data Types: single | double

Output Arguments

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Predicted state, returned as a real-valued vector or real-valued matrix with same number of elements and dimensions as the input state vector.

Algorithms

For a two-dimensional constant-acceleration process, the state transition matrix after a time step, T, is block diagonal:

[xk+1vxk+1axk+1yk+1vyk+1ayk+1]=[1T12T200001T0000010000001T12T200001T000001][xkvxkaxkykvykayk]

The block for each spatial dimension has this form:

[1T12T201T001]

For each additional spatial dimension, add an identical block.

Extended Capabilities

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

Version History

Introduced in R2017a

See Also

Functions

  • (Sensor Fusion and Tracking Toolbox) | (Sensor Fusion and Tracking Toolbox) | (Sensor Fusion and Tracking Toolbox) | (Sensor Fusion and Tracking Toolbox) | (Sensor Fusion and Tracking Toolbox) | (Sensor Fusion and Tracking Toolbox) | (Sensor Fusion and Tracking Toolbox) | (Sensor Fusion and Tracking Toolbox) | (Sensor Fusion and Tracking Toolbox)

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