ConstantAccelerationModel

Constant acceleration state transition model

Since R2025a

Description

A ConstantAccelerationModel object defines the constant-acceleration 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 ConstantAccelerationModel, the associated state conventions follow.

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

• 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.

• ax, ay, and az represent the acceleration components in different directions in meters per second squared.

Creation

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

stateTransModel = targetStateTransitionModel("constant-acceleration")

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

AccelerationMean — Mean of prior acceleration

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

Mean of prior acceleration in each dimension, specified as an N-by-1 real column vector. The dimension N must be the same as the NumMotionDimensions. Units are in m/s². This property assists in track initialization by providing initial estimates for the object's state.

Example: [2 1.6]

Data Types: single | double

AccelerationVariance — Variance of prior acceleration

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

Variance of prior acceleration, specified as an N-by-N real matrix. The dimension N must be the same as the NumMotionDimensions. Units are in m²/s⁴. This property assists in track initialization by providing initial estimates for the object's state.

Example: 1.5*eye(2)

Data Types: single | double

AccelerationIncrementVariance — Variance of unknown acceleration increment

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

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

Example: eye(2)

Data Types: single | double

Algorithms

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

$$\left[\begin{array}{c}{x}_{k+1}\\ v{x}_{k+1}\\ a{x}_{k+1}\\ y_{k+1}\\ v{y}_{k+1}\\ a{y}_{k+1}\end{array}\right]=\left[\begin{array}{cccccc}1& T& \frac{1}{2}{T}^2& 0& 0& 0\\ 0& 1& T& 0& 0& 0\\ 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 1& T& \frac{1}{2}{T}^2\\ 0& 0& 0& 0& 1& T\\ 0& 0& 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_k\\ v{x}_k\\ a{x}_k\\ y_k\\ v{y}_k\\ a{y}_k\end{array}\right]$$

The block for each spatial dimension has this form:

$$\left[\begin{array}{ccc}1& T& \frac{1}{2}{T}^2\\ 0& 1& T\\ 0& 0& 1\end{array}\right]$$

For each additional spatial dimension, add an identical block.

Version History

Introduced in R2025a