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It is shown that the only cryptodeterministic estimation problems with exact finite dimensional filters are those in which the input-output model is a "subsystem" of a linear system. This generalizes a result of 0. Hijab [1], which covers the special case of time-invariant plant models. Moreover, the proof is much simpler than Hijab's, as it is an elementary calculation using Bayes rule...
A new nonlinear filter is derived for continuous time processes with discrete time measurements. The filter is exact, and it can be implemented in real-time with a computational complexity that is comparable to the Kalman filter. This new filter includes both the Kalman filter and the discrete time version of the Bene?? filter as special cases. Moreover, the new theory can handle a large class of...
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