Abstract
This chapter investigates the idea of using Luenberger's minimal-order observer as an alternate to the Kalman filter for obtaining state estimates in linear discrete-time stochastic systems. One of the major results presented in the chapter is the development of the general solution to the problem of constructing an optimal minimalorder observer for linear discrete-time stochastic systems where optimality is in the mean-square sense. The approach taken in the development which follows leads to a completely unified theory for the design of optimal minimum-order observers and is applicable to both time-varying and timeinvariant linear discrete systems.
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