Nonlinear filtering in discrete time : A particle convolution approach

In this paper a new generation of particle filters for nonlinear discrete time processes is proposed, based on convolution kernel probability density estimation. The main advantage of this approach is to be free from the limitations met by the current particle filters when the likelihood of the observation variable is analytically unknown or when the observation noise is null or too small. To illustrate this convolution kernel approach two convolution filters, counterparts of the well-known sequential importance sampling (SIS) and sequential importance sampling-resampling (SIS-R) filters, are considered and their stochastic convergence to the optimal filter under different modes are proved. Their good behaviour with respect to that of the SIS and the SIS-R filters is shown on several simulated case studies.

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