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

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1 Author(s)
H. Ruskeepaa ; University of Turku, Turku, Finland

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.

Published in:

IEEE Transactions on Automatic Control  (Volume:30 ,  Issue: 8 )