Approximations of the nonlinear filter by periodic sampling and quantization

Korezlioglu, H.; Mazziotto, G.

doi:10.1007/bfb0004980

Cited by 9 publications

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“…as in [3] and [11]. where 6 is the sampling period but, because of the widening of the conditions, the bounds are better.…”

Section: Introductionmentioning

confidence: 99%

“…For a quick proof of these formulas, derived in [11]. it is enough to 6 5 notice that Z t is the ratio of the probability densities of (yn; n and define the conditional kernel L n 5 (X(n-1)6'-) on by (3.8)…”

Section: Ihn2)mentioning

confidence: 99%

“…On the other hand, the reference probability method has been very useful in developing approximation procedures ( [3]. [11], [13], [19]. [20]) some of which are exposed here.…”

Section: Introductionmentioning

confidence: 99%

“…In order to eliminate this difficulty and to 3 help computations we propose a quantization of the signal and the observation processes. The proposed approximation schemes follow those of [11] and go as follows in the decreasing order of difficulty for computations, i) Periodic sampling of the observation. ii) periodic sampling of the signal, iii) Euler approximation of the signal, iv) quantization of the signal, v) quantization of the observation.…”

Section: Introductionmentioning

confidence: 99%

“…The estimation of the approximation degrees was considered in [3], [11], [19] and [20]. but always with the boundedness condition on the modulated signal h or some restrictive conditions on the likelihood ratio excluding the linear model from the approximation procedures.…”

Section: Introductionmentioning

confidence: 99%

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Computation of Filters by Sampling and Quantization.

Korezlioglu¹

1987

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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.

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“…as in [3] and [11]. where 6 is the sampling period but, because of the widening of the conditions, the bounds are better.…”

Section: Introductionmentioning

confidence: 99%

Section: Ihn2)mentioning

confidence: 99%

“…On the other hand, the reference probability method has been very useful in developing approximation procedures ( [3]. [11], [13], [19]. [20]) some of which are exposed here.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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