A quasi-linear estimation method--Application to Kalman filtering with stochastic regressors

An estimation method, called quasi-linear estimation, is presented. Quasi-linear estimation is aimed to give an intermediate possibility between linear and nonlinear estimation. A quasi-linear estimator of a parameter vector a given two observation vectors
y
and
z
is defined to be of the form
p + Qy
, where the vector
p
and the matrix
Q
are
\sigma(z)
-measurable. Orthogonal projections are used to derive the quasi-linear minimum mean square error estimator. This estimator is
E(a|z) + C(a, y|z)V(y|z)-[y- E(y|z)]
. Quasi-linear estimation is applied to derive a Kalman type filter for discrete-time dynamic linear models with stochastic regressors.