Abstract
In this paper, two types of nonlinear filters which are constructed without the limitation of Gaussian distribution are presented for discrete noisy nonlinear systems. These filters are based on the nonlinear estimation theory derived by using the Hermite expansion or orthogonal projection method. In these cases, the a posteriori density functions, which are approximately represented by a finite number of terms, are modified so as to have the fundamental properties of a probability density function. Therefore, the merits of our filters are as follows;
1) Since the nonlinear theory is used and the moments are considered up to the higher order ones by the characteristics of non-Gaussian distribution, the filters enable us to estimate the states properly for systems with rather high nonlinearities.
2) One cause of divergence in estimation is eliminated by introducing the modified density function. In particular, negative values for the even moments (variance etc.) are avoided.
The simulation results by a digital computer indicate that these filters are superior to ordinary filters in performance.
