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Constant-acceleration motion model

returns the updated state, `updatedstate`

= constacc(`state`

)`state`

, of a constant acceleration
Kalman filter motion model for a step time of one second.

specifies the time step, `updatedstate`

= constacc(`state`

,`dt`

)`dt`

.

also specifies the state noise, `updatedstate`

= constacc(`state`

,`w`

,`dt`

)`w`

.

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.

`constaccjac`

|`cameas`

|`cameasjac`

|`constturn`

|`constturnjac`

|`ctmeas`

|`ctmeasjac`

|`constvel`

|`constveljac`

|`cvmeas`

|`cvmeasjac`