An alternative approach to non-linear filtering†

Abstract The following non-linear filtering problem is discussed. Consider a process {Xt, t≥0}, determined by the stochastic differential equation with the noisy observations of this process given by dy = h(x) dt + y(x) dB, t> 0, yϵRr, where W and B are Rm valued and Rr valued Wiener processes respectively and q is a zero-mean Poisson random measure on [0, ∞) × Rm. An observer is required of the form dz = j(z) dt + G(z) (dy — h(z) dt), t>0, zϵRm, where the ‘ gain matrix ” G has yet to be determined. Let DeRIm be a given centrally symmetric open and bounded domain with the origin at its centre, and let t be the first time that (Xt; Zi)D given that (X0, Z0)ϵD (Zt is the state of the observer). The approach adopted here is to choose a matrix G*, of a bang-bang type, in such a manner that tho expected value of A{t:0≤t 0 is given. Sufficient conditions on the maximizing gain matrix are deriv...

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