ConstantVelocityModel

Constant velocity state transition model

Since R2025a

Description

A ConstantVelocityModel object defines the constant-velocity state transition model. You can use this model to define the state transition model for a CustomTarget. The state transition model of the CustomTarget specification defines the state convention for trackers initialized with it. For a ConstantVelocityModel, the associated state conventions follow.

Motion Dimension	State Convention
1	[x;vx]
2	[x;vx;y;vy]
3	[x;vx;y;vy;z;vz]

• x, y, and z represent the x-, y-, and z-coordinates in meters.

• vx, vy, and vz represent the velocity components in different directions in meters per second.

Creation

To create a ConstantVelocityModel object, use the targetStateTransitionModel function with the "constant-velocity" input argument. For example:

stateTransModel = targetStateTransitionModel("constant-velocity")

Properties

NumMotionDimensions — Number of motion dimensions

3 (default) | 2

Number of motion dimensions, specified as 3 or 2.

Example: 3

Data Types: single | double

VelocityMean — Mean of prior velocity

[0;0;0] (default) | N-by-1 real column vector

Mean of prior velocity in each dimension, specified as an N-by-1 real column vector. The dimension N must be the same as NumMotionDimensions. Units are in m/s. This property assists in track initialization by providing initial estimates for the object's state.

Example: [25 16]

Data Types: single | double

VelocityVariance — Variance of prior velocity

100*eye(3) (default) | N-by-N real matrix

Variance of prior velocity, specified as an N-by-N real matrix. The dimension N must be the same as NumMotionDimensions. Units are in (m/s)². This property assists in track initialization by providing initial estimates for the object's state.

Example: 75*eye(2)

Data Types: single | double

AccelerationVariance — Variance of unknown acceleration

eye(3) (default) | N-by-N real matrix

Variance of unknown acceleration, specified as an N-by-N real matrix. This property defines the process noise of the model. The dimension N must be the same as NumMotionDimensions. Units are in m²/s⁴. This property defines the level of uncertainty in the model.

Example: 2.5*eye(2)

Data Types: single | double

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.

Version History

Introduced in R2025a