Returns both the filtered values and smoothed values for the state-space model.
Ksmooth0(num, y, A, mu0, Sigma0, Phi, cQ, cR)
number of observations
data matrix, vector or time series
time-invariant observation matrix
initial state mean vector
initial state covariance matrix
state transition matrix
Cholesky-type decomposition of state error covariance matrix Q -- see details below
Cholesky-type decomposition of observation error covariance matrix R -- see details below
state smoothers
smoother mean square error
initial mean smoother
initial smoother covariance
initial value of the J matrix
the J matrices
one-step-ahead prediction of the state
mean square prediction error
filter value of the state
mean square filter error
the negative of the log likelihood
last value of the gain
https://www.stat.pitt.edu/stoffer/tsa4/
See also https://www.stat.pitt.edu/stoffer/tsa4/chap6.htm for an explanation of the difference between levels 0, 1, and 2.