residual

Measurement residual and residual noise from tracking filter

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

filter — Filter for object tracking

trackingKF object | trackingEKF object | trackingUKF object

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

• trackingKF — Linear Kalman filter

• trackingEKF — Extended Kalman filter

• trackingUKF — Unscented Kalman filter

zmeas — Current measurement of tracked object

vector | matrix

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

measparams — Parameters for measurement function

cell array

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

zres — Residual between current and predicted measurement

matrix

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

rescov — Residual covariance

matrix

Residual covariance, returned as a matrix.

Algorithms

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 z_res is defined as

z_res = z – Hx,

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 + HPH^T,

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 z_res is defined as:

z_res = z – h(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 + R_p,

where:

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

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2018a