A new method of recursive estimation in discrete linear systems

Let the measurement
z(i)
at instant
i
be of form
z(i) = y(i) + \eta(i)
where
\eta(i)
is the noise and
y(i)
is the signal obeying a system of coupled linear difference equations. A method is given for computing the gains of the predictor and filter for the signal
y(i)
and the corresponding state
x(i)
. The gains are computed recursively from the previous gains without involving the covariance matrix of the state. The computational advantages of the scheme are also discussed.