A new method based on polytopic linear inclusion for nonlinear filter with non-Gaussian noise

This paper presents a new method based on the polytopic linear differential inclusion and the robust mixed H₂/H_∞ filtering for the design of the nonlinear filter with non-Gaussian noises. The main goal is to solve the problems of the complexity and large calculation number in the general nonlinear filter and the filtering design problem for systems with the non-Gaussian noises. The noises considered in the paper involve two different kinds of noises: white noises and energy bounded noises. Differing from the linearization in most nonlinear filters, the estimation error system for the nonlinear system is represented by an uncertain polytopic linear model, based on which, the rectification equations for the predicted errors are designed following the robust mixed H₂/H_∞ filtering. The state estimates for the nonlinear system are given through updating the predictions by the rectified quantities, where, the state predicted quantities of the nonlinear system are gained by the prediction equation of the EKF. The evident advantage of the new filter is the filter coefficients of the rectification equation are constant, without the need to evaluate the Jacobian matrixes. As a result, the calculation number for the new filter is decreased much and the real-time performance of the new filter is much better than the EKF, though the accuracy is a little decline. Its effectiveness is demonstrated by using an example and the statistics result of the calculation number for the filters in the example.