# singerProcessNoise

Process noise matrix for Singer acceleration model

Since R2020b

## Syntax

``processNoise = singerProcessNoise(state)``
``processNoise = singerProcessNoise(state,dt)``
``processNoise = singerProcessNoise(state,dt,tau)``
``processNoise = singerProcessNoise(state,dt,tau,sigma)``

## Description

example

````processNoise = singerProcessNoise(state)` returns the process noise matrix for the Singer acceleration model based on the current `state`. For more details, see Reference .```
````processNoise = singerProcessNoise(state,dt)` specifies the time step `dt`. The default time step is 1 second.```
````processNoise = singerProcessNoise(state,dt,tau)` specifies the target maneuver time constant `tau`. The default maneuver time constant is 20 seconds.```
````processNoise = singerProcessNoise(state,dt,tau,sigma)` specifies the target maneuver standard deviation `sigma`. The default maneuver standard deviation is 1 meter per second squared.```

## Examples

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Obtain the Singer process noise for a 3-D Singer state that has a default time step, a target maneuver time constant, and a standard deviation.

`Q1 = singerProcessNoise((1:9)')`
```Q1 = 9×9 0.0049 0.0121 0.0159 0 0 0 0 0 0 0.0121 0.0321 0.0476 0 0 0 0 0 0 0.0159 0.0476 0.0952 0 0 0 0 0 0 0 0 0 0.0049 0.0121 0.0159 0 0 0 0 0 0 0.0121 0.0321 0.0476 0 0 0 0 0 0 0.0159 0.0476 0.0952 0 0 0 0 0 0 0 0 0 0.0049 0.0121 0.0159 0 0 0 0 0 0 0.0121 0.0321 0.0476 0 0 0 0 0 0 0.0159 0.0476 0.0952 ```

Set the time step as 2 seconds. Set the target maneuver time constant as 10 seconds in x- and y- axes and as 100 seconds in z-axis. Set the target maneuver standard deviation as 1$\mathrm{m}/{\mathrm{s}}^{2}$ in x- and y- axes and 0 $\mathrm{m}/{\mathrm{s}}^{2}$ in z-axis.

`Q2 = singerProcessNoise((1:9)', 2, [10 10 100], [1 1 0])`
```Q2 = 9×9 0.2868 0.3508 0.2188 0 0 0 0 0 0 0.3508 0.4603 0.3286 0 0 0 0 0 0 0.2188 0.3286 0.3297 0 0 0 0 0 0 0 0 0 0.2868 0.3508 0.2188 0 0 0 0 0 0 0.3508 0.4603 0.3286 0 0 0 0 0 0 0.2188 0.3286 0.3297 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```

## Input Arguments

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Current state, specified as a real-valued 3N-by-1 vector. N is the spatial degree of the state. The state vector takes the different forms based on its dimensions.

Spatial DegreesState Vector Structure
1-D`[x;vx;ax]`
2-D`[x;vx;ax;y;vy;ay]`
3-D`[x;vx;ax;y;vy;ay;z;vz;az]`

For example, `x` represents the x-coordinate, `vx` represents the velocity in the x-direction, and `ax` represents the acceleration in the x-direction. If the motion model is in one-dimensional space, the y- and z-axes are assumed to be zero. If the motion model is in two-dimensional space, values along the z-axis are assumed to be zero. Position coordinates are in meters. Velocity coordinates are in m/s. Acceleration coordinates are in m/s2.

Example: `[5;0.1;0.01;0;-0.2;-0.01;-3;0.05;0]`

Time step, specified as a positive scalar in seconds.

Example: `0.5`

Target maneuver time constant, specified as a positive scalar or an N-element vector of scalars in seconds. N is the spatial degree of the state. When specified as a vector, each element applies to the corresponding spatial dimension.

Example: `30`

Maneuver standard deviation, specified as a positive scalar or an N-element vector of scalars in m/s2. N is the spatial degree of the state. When specified as a vector, each element applies to the corresponding spatial dimension.

Example: `3`

## Output Arguments

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Process noise for a Singer acceleration model, returned as an N-by-N matrix of nonnegative scalars. N is the spatial dimension of the `state` input.

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

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

 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.