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Jacobian of Singer acceleration motion model

Given the dimension of the state space, the Jacobian of a Singer model takes different forms.

For 1-D state space, the Jacobian matrix is calculated as

$${J}_{1}=\left[\begin{array}{ccc}1& T& {\tau}^{2}(-T/\tau +\beta )\\ 0& 1& \tau (1-\beta )\\ 0& 0& 0\end{array}\right]$$

where *T* is the time step interval, *τ*
is the target maneuver time constant, and *β* =
*exp*(*-T/τ*).

For 2-D state space, the Jacobian matrix is calculated as

$${J}_{2}=\left[\begin{array}{cc}{J}_{1}& 0\\ 0& {J}_{1}\end{array}\right]$$

For 3-D state space, the Jacobian matrix is calculated as

$${J}_{3}=\left[\begin{array}{ccc}{J}_{1}& 0& 0\\ 0& {J}_{1}& 0\\ 0& 0& {J}_{1}\end{array}\right]$$

[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.

`initsingerekf`

| `singer`

| `singermeas`

| `singermeasjac`

| `singerProcessNoise`