Main Content

Constant velocity state update

returns the updated state, `updatedstate`

= constvel(`state`

)`state`

, of a constant-velocity Kalman
filter motion model after a one-second time step.

specifies the time step, `updatedstate`

= constvel(`state`

,`dt`

) `dt`

.

also specifies state noise, `updatedstate`

= constvel(`state`

,`w`

,`dt`

)`w`

.

For a two-dimensional constant-velocity process, the state transition matrix after a time
step, *T*, is block diagonal as shown here.

$$\left[\begin{array}{c}{x}_{k+1}\\ {v}_{x,k+1}\\ {y}_{k+1}\\ {v}_{y,k+1}\end{array}\right]=\left[\begin{array}{cccc}1& T& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& T\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{k}\\ v{x}_{k}\\ {y}_{k}\\ v{y}_{k}\end{array}\right]$$

The block for each spatial dimension is:

$$\left[\begin{array}{cc}1& T\\ 0& 1\end{array}\right]$$

For each additional spatial dimension, add an identical block.

`cameas`

|`cameasjac`

|`constacc`

|`constaccjac`

|`constturn`

|`constturnjac`

|`constveljac`

|`ctmeas`

|`ctmeasjac`

|`cvmeas`

|`cvmeasjac`