SS.stst.SMW {SSsimple}

Steady State using the Woodbury matrix identity

Description

Find steady state of system, i.e., locate when Kalman gain converges

Usage

SS.stst.SMW(F, H, Q, inv.R, P0, epsilon, verbosity=0)

Arguments

F

The state matrix. A scalar, or vector of length d, or a d x d matrix. When scalar, F is constant diagonal. When a vector, F is diagonal.

H

The measurement matrix. Must be n x d.

Q

The state variance. A scalar, or vector of length d, or a d x d matrix. When scalar, Q is constant diagonal. When a vector, Q is diagonal.

inv.R

The inverse of the measurement variance. A scalar, or vector of length n, or a n x n matrix. When scalar, inv.R is constant diagonal. When a vector, inv.R is diagonal.

P0

Initial a priori prediction error.

epsilon

A small scalar number.

verbosity

0, 1 or 2.

Details

Spiritually identical to SS.stst, except that the Woodbury identity is used for inversion. This method offers a computationally reduced means of finding the system steady state; however, this method must be supplied with the inverse of the measurement variance matrix, R – not R. Try comparing the example below with the evivalent example offered for SS.stst.

Value

A named list.

P.apri

A d x d matrix giving a priori prediction variance.

P.apos

A d x d matrix giving a posteriori prediction variance.

Examples

H <- matrix(1)

SS.stst.SMW(1, H, 1, 1, P0=10^5, epsilon=10^(-14), verbosity=1)