SS.solve.SMW: Optimal Estimation
In SSsimple: State Space Models

Description Usage Arguments Details Value Note Examples

Solve a state space system using the Kalman Filter.

1	SS.solve.SMW(Z, F, H, Q, inv.R, length.out, P0, beta0=0)

`Z`	A T x n data matrix.
`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.
`length.out`	Scalar integer.
`P0`	Initial a priori prediction error.
`beta0`	Initial state value. A scalar, or a vector of length d.

H is the master argument from which system dimensionality is determined. Otherwise identical to SS.solve, except that the Woodbury identity is used for inversion. This method offers a computationally reduced means of solving the system realization of interest; however, this method must be supplied with the inverse of the measurement variance matrix, R – not R.

A named list.

`B.apri`	A T x d matrix, the ith row of which is the best state estimate prior to observing data at time i.
`B.apos`	A T x d matrix, the ith row of which is the best state estimate given the observation at time i.

For a definition of the system of interest, please see SSsimple.

set.seed(999)
H <- matrix(1)
R <- 7
inv.R <- 1 / R
x <- SS.sim( 1, H, 1, R, 100, 0 )
y <- SS.solve.SMW( x$Z, 1, H, 1, inv.R, 100, 10^5, 0 )

z.hat <- t( H %*% t( y$B.apri ) )

plot( x$Z, type="l", col="blue" )
points( z.hat[ ,1], type="l", col="red" )