A quasi-linear estimation method--Application to Kalman filtering with stochastic regressors
Heikki Ruskeepää · IEEE Transactions on Automatic Control · 1985
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 vectorsyandzis defined to be of the formp + Qy, where the vectorpand the matrixQare\sigma(z)-measurable. Orthogonal projections are used to derive the quasi-linear minimum mean square error estimator. This estimator isE(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.