# residual

Measurement residual and residual noise from tracking filter

Since R2021a

## Syntax

``[zres,rescov] = residual(filter,zmeas)``
``[zres,rescov] = residual(filter,zmeas,measparams)``

## Description

````[zres,rescov] = residual(filter,zmeas)` computes the residual and residual covariance of the current given measurement, `zmeas`, with the predicted measurement in the tracking filter, `filter`. This function applies to filters that assume a Gaussian distribution for noise.```
````[zres,rescov] = residual(filter,zmeas,measparams)` specifies additional parameters that are used by the `MeasurementFcn` of the filter.If `filter` is a `trackingKF` object, then you cannot use this syntax.```

## Input Arguments

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Filter for object tracking, specified as one of these objects:

Current measurement of a tracked object, specified as a vector or matrix.

Parameters for measurement function, specified as a cell array. The parameters are passed to the measurement function that is defined in the `MeasurementFcn` property of the input `filter`. If `filter` is a `trackingKF` object, then you cannot specify `measparams`.

## Output Arguments

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Residual between current and predicted measurement, returned as a matrix.

Residual covariance, returned as a matrix.

## Algorithms

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The residual is the difference between a measurement and the value predicted by the filter. For Kalman filters, the residual calculation depends on whether the filter is linear or nonlinear.

### Linear Kalman Filters

Given a linear Kalman filter with a current measurement of z, the residual zres is defined as

zres = zHx,

where:

• H is the measurement model set by the `MeasurementModel` property of the filter.

• x is the current filter state.

The covariance of the residual, S, is defined as

S = R + HPHT,

where:

• P is the state covariance matrix.

• R is the measurement noise matrix set by the `MeasurementNoise` property of the filter.

### Nonlinear Kalman Filters

Given a nonlinear Kalman filter with a current measurement of z, the residual zres is defined as:

zres = zh(x),

where:

• h is the measurement function set by the `MeasurementFcn` property.

• x is the current filter state.

The covariance of the residual, S, is defined as:

S = R + Rp,

where:

• R is the measurement noise matrix set by the `MeasurementNoise` property of the filter.

• Rp is the state covariance matrix projected onto the measurement space.

## Version History

Introduced in R2021a