Computation of Filters by Sampling and Quantization.

Abstract

Various approximation procedures of filters by sampling and quantization are considered for effective computation. The correspond~ing approximation degrees are estimated without the boundedness condition on the modulated signal. Section 5 considers approximations of the signal by sampling and quantizat ion. ELECTESection 6 derives the approximation bounds for filters corresponding to various approximations of the signal and presents a method of quantization of the observation process preserving the degree of the previous approximations. MODEL AND FILTERThroughout this work the follow 4 ng usual signal and observation model is considered.The signal process is a q-dimensional continuous Markov diffusion defined P is the probability measure on Iq x BI T x YT = : FT induced by (xoby).We suppose that all the probability spaces are complete. We put n = Iq x B x Y. Therefore. (fl.FTP) is the probability space on which all the random processes under consideration are defined. We denote by F t (resp. Yt) the sub-c-fields generated by {(x 0 bs.ys); s t} (resp. {ys; s t}.According to the Girsanov theorem [14]. there is a probability measure P 0 on F T , equivalent to P. under which y is a Brownian motion independent of (xo,b) whose probability distribution, denoted by Q, remains unchanged. The corresponding Radon-Nikodym derivative is given by O r % 00P.

Interacting particle systems approximations of the Kushner-Stratonovitch equation

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Branching and interacting particle systems approximations of feynman-kac formulae with applications to non-linear filtering

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