Abstract
Abstract : Linear estimation theory has been applied extensively to nonlinear systems by assuming that perturbations from a reference solution can be described by linear equations. As long as the second order (and higher) terms in the perturbation equations are 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-discrete systems in which the second order effects are small but nonnegligible are considered. Recursion relations for the conditional mean and covariance 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 nonlinear system. Some results for a simple system are presented in which the response from linear and nonlinear filters is compared.
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