functionUKF

Unscented Kalman filter design function

Extends from Modelica.Icons.Function (Icon for functions).

Information

Syntax

(x_est, y_est, P, K) = DiscreteStateSpace.Design.UKF(x_pre, u_pre, y, P_pre, Q, R, alpha, beta, kappa, Ts)

Description

Function UKF computes one recursion of the Unscented Kalman filter. Unscented Kalman filters are similar to Extended Kalman filters but using statistical linearization where extended Kalman filter apply the user-provided derivation of the system equation. Instead of explicit derivation linear regression between spcifically chosen sample points (sigma points). See [1] for more information.

See also UKF_SR, where the square root method to deal with positive definite matrices is applied to solve the mathematically identical problem.

References

[1]: http://en.wikipedia.org/wiki/Kalman_filter#Unscented_Kalman_filter.

Inputs

Type	Name	Default	Description
Real[:]	xpre		State at instant k-1
Real[:]	upre		Input at instant k-1
Real[:]	y		Output at instant k
Real[size(xpre, 1),size(xpre, 1)]	Ppre		Error covariance matrix at instant k-1
Real[size(xpre, 1),size(xpre, 1)]	Q	identity(size(xpre, 1))	Weighted covariance matrix of the associated process noise (FQF')
Real[size(y, 1),size(y, 1)]	R	identity(size(y, 1))	Covariance matrix of the measurement noise
Real	alpha	0.1	Spread of sigma points
Real	beta	2	Characteristic of the distribution of x
Real	kappa	0	Kurtosis scaling of sigma point distribution
Modelica.Units.SI.Time	Ts		Sample time

Outputs

Type	Name	Description
Real[size(xpre, 1)]	x_est	Estimated state vector
Real[size(y, 1)]	y_est	Estimated output
Real[size(Ppre, 1),size(Ppre, 1)]	P	Error covariance matrix
Real[size(xpre, 1),size(y, 1)]	K	Kalman filter gain matrix

Name	Description
predict
update
estimate

Revisions

Date	Author	Comment
2010-06-11	Marcus Baur, DLR-RM	Realization