We consider the problem of nonlinear filtering of one-dimensional diffusions from noisy measurements. The filter is said to lose lock if the estimation error exits a prescribed region. In the case of phase estimation this region is one period of the phase measurement function, e.g., [−π, π]. We show that in the limit of small noise the causal filter that maximizes the mean time to loose lock is...

Information filtering has become an important component of modern information systems due to significant increase in its applications. The objective of an information filtering is to classify/categorize documents as they arrive into the system. In this paper, we investigate an information filtering method based on steepest descent induction algorithm combined with a two-level preference relatio...

This paper shows that optimal set-membership filtering (SMF) is identical to minimax ( ) filtering, if optimal SMF corresponds to the smallest error bound specification that leads to a non-empty feasible solution. An adaptive minimax filtering algorithm that uses optimal quadratic approximations to the minimax cost function is proposed for adaptive implementation of optimal SMF. The proposed al...

This paper considers the problem of optimal filtering for several channels of observations occurring at different sampling rates. The problem is formulated in general terms with arbitrary sampling rates for the observations. The set of observation sequences (channels) are jointly cyclostationary and the resulting optimal filters are linear and periodically timevarying (LPTV). A formula for the ...

Estimation problems for linear time-invariant systems with noisy input and output are considered. The smoothing problem is a least norm problem. An efficient algorithm using a Riccati-type recursion is derived. The equivalence between the optimal filter and an appropriately modified Kalman filter is established. The optimal estimate of the input signal is derived from the optimal state estimate...