Abstract
Using the methods of the Markov theory of nonlinear filtering, the problem of optimal estimation in discrete time of the time instant of occurrence of a random impulse disturbance in a signal observed against a background of white noise has been solved. It is shown that the optimal estimate in the mean-square sense for the impulse occurrence can be represented as the sum of two conditional estimates calculated in current time with the help of a system of recurrent equations with a posteriori probability of the impulse occurrence and auxiliary probability densities. A simplified approximate estimation algorithm has been developed using a Gaussian approximation of the auxiliary probability densities.
Published Version
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