SingerAccelerationModel

Singer acceleration state transition model

Since R2025a

Description

A SingerAccelerationModel object defines the Singer acceleration state transition model, which assumes the target acceleration decays over time. 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 SingerAccelerationModel, 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 SingerAccelerationModel object, use the targetStateTransitionModel function with the "singer-acceleration" input argument. For example:

stateTransModel = targetStateTransitionModel("singer-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

ManeuverTimeConstant — Time constant of target maneuver

[20;20;20] (default) | N-by-1 positive column vector

Time constant of target maneuver in each dimension, specified as an N-by-1 positive column vector. The dimension N must be the same as the NumMotionDimensions. Units are in seconds.

Example: [15;15;15]

Data Types: single | double

ManeuverStandardDeviation — Standard deviation of target maneuver

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

Standard deviation of target maneuver, specified as an N-by-1 positive column vector. This property defines the process noise in the Weiner-sequence constant acceleration model. The dimension N must be the same as the NumMotionDimensions. Units are in meters per second squared.

Example: eye(2)

Data Types: single | double

Algorithms

The Singer acceleration model assumes the acceleration at time step k+1, which depends on the acceleration at time step k with exponential decay as:

$$a(k+1)=a(k)*\exp (-T/\tau )$$

where a(k) is the acceleration at time step k, T is the time step, and τ is the target maneuver time constant.

For a 1-D singer model state p = [x, vx, ax]^T, the state propagation is:

$$p(k)=\left[\begin{array}{ccc}1& T& (\alpha T-1-e^{-\alpha T})/{\alpha }^2\\ 0& 1& (1-e^{-\alpha T})/\alpha \\ 0& 0& e^{-\alpha T}\end{array}\right]p(k)+w(k)$$

where α = 1/τ is the reciprocal of the target maneuver time constant and w(k) is the Singer model process noise at time step k.

References

[1] Singer, Robert A. "Estimating optimal tracking filter performance for manned maneuvering targets." IEEE Transactions on Aerospace and Electronic Systems 4 (1970): 473-483.

[2] Blackman, Samuel S., and Robert Popoli. "Design and analysis of modern tracking systems." (1999).

[3] 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.

Version History

Introduced in R2025a