Recursive Filtering for Systems with Small but Non-negligible Non-linearities†

Publisher Website
Google Scholar
Abstract
Linear estimation theory has been applied extensively to non-linear systems by assuming that perturbations from a reference solution can be described by linear equutious. As long as the second-order (and higher) terms in the perturbation, equations me negligible, linear estimation techniques have been found to yield satisfactory response. Many examples have been encountered in which the linear theory is not satisfactory, however, and it is to this situation that attention is directed here. Time diserete systems in which the second-order effects are small but non-negligible are considered. Recursion relations for the conditional mean and covarianoo are developed. While these relations yield approximations to the true values of these moments, they are superior to the approximations provided by applying linear theory to a non-linear system. Some results for a simple system are presented in which the response from linear and non-linear filters is compared.

This publication has 2 references indexed in Scilit: