Abstract
This paper presents the new approach to the discrete nonlinear estimation, which enables us to estimate the state of system more accurately, even if there will be rather high nonlinearities in the system.
This approach uses the method of the extended orthogonal projection, in which the optimal nonlinear estimation is assumed to be performed with a polynomial series about the past and present observations.
The estimated values are sequentially obtained by the resulting estimate equation, and are always optimal in the sense of mean square even though the series of observations is truncated at any finite order term.
In the remainder of the paper, an algorithm of a sequential nonlinear filter is derived. This filter contains the observation errors up to the second order term in both the state estimate equation and the covariance equation.
Experimental simulations by a digital computer are also demonstrated, and the results better than those obtained by the ordinary filters are obtained in our special examples.
