ConstantAccelerationModel

Constant acceleration state transition model

Since R2025a

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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:

$[\begin{matrix} x_{k + 1} \\ v x_{k + 1} \\ a x_{k + 1} \\ y_{k + 1} \\ v y_{k + 1} \\ a y_{k + 1} \end{matrix}] = [\begin{matrix} 1 & T & \frac{1}{2} T^{2} & 0 & 0 & 0 \\ 0 & 1 & T & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & T & \frac{1}{2} T^{2} \\ 0 & 0 & 0 & 0 & 1 & T \\ 0 & 0 & 0 & 0 & 0 & 1 \end{matrix}] [\begin{matrix} x_{k} \\ v x_{k} \\ a x_{k} \\ y_{k} \\ v y_{k} \\ a y_{k} \end{matrix}]$

The block for each spatial dimension has this form:

$[\begin{matrix} 1 & T & \frac{1}{2} T^{2} \\ 0 & 1 & T \\ 0 & 0 & 1 \end{matrix}]$

For each additional spatial dimension, add an identical block.

Version History

Introduced in R2025a

See Also

Functions

targetStateTransitionModel

Objects

JIPDATracker | CustomTarget