constvel

State transition function for constant-velocity motion model

Syntax

predictedState = constvel(state)

predictedState = constvel(state,dt)

predictedState = constvel(state,w,dt)

Description

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

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

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

Examples

Update State for Constant-Velocity Motion

Update the state of two-dimensional constant-velocity motion for a time interval of one second.

state = [1;1;2;1];
state = constvel(state)

state = 4×1

     2
     1
     3
     1

Update State for Constant-Velocity Motion with Specified Time Step

Update the state of two-dimensional constant-velocity motion for a time interval of 1.5 seconds.

state = [1;1;2;1];
state = constvel(state,1.5)

state = 4×1

    2.5000
    1.0000
    3.5000
    1.0000

Input Arguments

state — Current state

real-valued 2D-by-N matrix

Current state for constant-velocity motion, specified as a real-valued 2D-by-N matrix. D is the number of spatial degrees of freedom of motion and N is the number states. The state is expected to be Cartesian state. For each spatial degree of motion, the state vector, as a column of the state matrix, takes the form shown in this table.

Spatial Dimensions	State Vector Structure
1-D	[x;vx]
2-D	[x;vx;y;vy]
3-D	[x;vx;y;vy;z;vz]

For example, x represents the x-coordinate and vx represents the velocity in the x-direction. If the motion model is 1-D, values along the y and z axes are assumed to be zero. If the motion model is 2-D, values along the z axis are assumed to be zero. Position coordinates are in meters and velocity coordinates are in meters/sec.

Example: [5;.1;0;-.2;-3;.05]

Data Types: single | double

dt — Time step interval

1.0 (default) | scalar

Time step interval, specified as a scalar. Time units are in seconds. If dt is negative, this function performs retrodiction and propagates the state estimate and covariance backward in time.

Example: 0.5

Data Types: single | double

w — State noise

scalar | real-valued D-by-N matrix

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. For example, D = 2 for the 2-D motion. If specified as a scalar, the scalar value is expanded to a D-by-N matrix.

Data Types: single | double

Output Arguments

predictedState — Predicted state at next time step

real-valued column or row vector | real-valued matrix

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-velocity process, the state transition matrix after a time step, T, is block diagonal as shown here.

$$\left[\begin{array}{c}{x}_{k+1}\\ v_{x,k+1}\\ y_{k+1}\\ v_{y,k+1}\end{array}\right]=\left[\begin{array}{cccc}1& T& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& T\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_k\\ v{x}_k\\ y_k\\ v{y}_k\end{array}\right]$$

The block for each spatial dimension is:

$$\left[\begin{array}{cc}1& T\\ 0& 1\end{array}\right]$$

For each additional spatial dimension, add an identical block.

References

[1] 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™.

Version History

Introduced in R2018b