On joint detection, estimation and system identification: discrete data case

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Abstract
The recent results of Lainiotis (1971 a, b, 1971) on single-shot, as well as multishot, joint detection, estimation and system identification for continuous data and dynamics are extended to multishot, discrete data and discrete dynamical systems. The results are given for the signals generated by the linear dynamical systems with unknown parameter vectors and driven by white gaussian sequences, where the observation contains additive white gaussian noise. Specifically, it is shown that the above problem constitutes a class of non-linear mean-square estimation problems. By utilizing the adaptive approach, closed-form integral expressions are obtained for simultaneously optimal detection, estimation and system identification. In addition, several approximate algorithms that utilize linear Kalman estimators are presented to limit the storage requirement to finite size and reduce computational requirements. The results presented in this paper are applicable to both independent and Markov signalling sources

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