A numerically efficient algorithm for risk-sensitive filters (known to be robust to model uncertainties) of nonlinear plants, using central difference approximation is proposed. The proposed filter, termed central difference risk-sensitive filter (CDRSF), overcomes several disadvantages associated with the extended risk-sensitive filter (ERSF), reported earlier. The theory of formulation and the algorithm of the CDRSF are presented. With an example, it is demonstrated that the proposed new filter would give much better tracking performance compared to the ERSF for certain nonlinear systems. The CDRSF would be nearly as fast as the ERSF, thus making it more preferable for real-time applications compared to the risk-sensitive particle filter.

Most versions of the Peterson-Gorenstein-Zierler (PGZ) decoding algorithm are not true bounded distance decoding algorithms in the sense that when a received vector is not in the decoding sphere of any codeword, the algorithm does not always declare a decoding failure. For a t-error-correcting BCH code, if the received vector is at distance i, i/spl les/t from a codeword in a supercode with BCH distance t+i+1, the decoder will output that codeword from the supercede. If that codeword is not a member of the t-error-correcting code, then decoder malfunction is said to have occurred. We describe the necessary and sufficient conditions for decoder malfunction, and show that malfunction can be avoided in the PGZ decoder by checking t-/spl nu/ equations, where /spl nu/ is the number of errors hypothesized by the decoder. A formula for the probability of decoder malfunction is also given, and the significance of decoder malfunction is considered for PGZ decoders and high-speed Berlekamp-Massey decoders.>