# residual

Residuals and residual covariances from direct state measurements for `ahrs10filter`

Since R2020a

## Syntax

``[res, resCov]= residual(FUSE,idx,measurement,measurementCovariance)``

## Description

example

````[res, resCov]= residual(FUSE,idx,measurement,measurementCovariance)` computes the residual, `res`, and the residual covariance, `resCov`, based on the direct state measurement and measurement covariance. The `measurement` maps directly to the states specified by indices, `idx`.```

## Examples

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`Create` an `ahrs10filter` object and display its state.

```filter = ahrs10filter; disp(filter.State')```
``` 1.0000 0 0 0 0 0 0 0 0 0 0 0 27.5550 -2.4169 -16.0849 0 0 0 ```

Specify a measurement of altitude and vertical velocity.

```idx = [5 6]; measure = [500 10]; measureCov = diag([5 1])*16-6;```

Obtain the residual for the measurement.

`[res,rescov] = residual(filter,idx,measure,measureCov)`
```res = 1×2 500 10 ```
```rescov = 2×2 74.0000 -6.0000 -6.0000 10.0000 ```

## Input Arguments

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`ahrs10filter`, specified as an object.

State vector index of measurement to correct, specified as an N-element vector of increasing integers in the range [1,18].

The state values represent:

StateUnitsIndex
Orientation (quaternion parts)N/A1:4
Altitude (NED)m5
Vertical Velocity (NED)m/s6
Delta Velocity Bias (XYZ)m/s10:12
Geomagnetic Field Vector (NED)μT13:15
Magnetometer Bias (XYZ)μT16:18

Direct measurement of state, specified as a N-element vector. N is the number of elements of the index argument, `idx`.

Covariance of measurement, specified as an N-by-N matrix. N is the number of elements of the index argument, `idx`.

## Output Arguments

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Measurement residual, returned as a 1-by-N vector of real values.

Residual covariance, returned as a N-by-N matrix of real values.

## Version History

Introduced in R2020a