# residual

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

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 `insfilterErrorState` object and display its state.

```filter = insfilterErrorState; disp(filter.State')```
``` 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ```

Specify a measurement of altitude and vertical velocity.

```idx = [5 6 7]; measure = [10 20 30]; measureCov = 1e-2*diag([5 5 5]);```

Obtain the residual for the measurement.

`[res,rescov] = residual(filter,idx,measure,measureCov)`
```res = 1×3 10 20 30 ```
```rescov = 3×3 1.0500 1.0000 1.0000 1.0000 1.0500 1.0000 1.0000 1.0000 1.0500 ```

## Input Arguments

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`insfilterErrorState`, specified as an object.

State vector index of measurements to correct, specified as an N-element vector of increasing integers in the range [1, 17].

The state values represent:

StateUnitsIndex
Orientation (quaternion parts)N/A1:4
Position (NED)m5:7
Velocity (NED)m/s8:10
Accelerometer Bias (XYZ)m/s214:16
Visual Odometry Scale (XYZ)N/A17

Data Types: `single` | `double`

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