On the conditionally minimax nonlinear filtering concept development: Filter modification and analysis

The main result of the research is a new suboptimal filter developed from the conditionally minimax nonlinear filtering (CMNF) method for nonlinear stochastic systems in discrete time. The main idea of the proposed modification is to omit the time and resource consuming phase of a priori CMNF parameter calculation in favor of their online approximation together with the current state estimation. In the original CMNF filter, the simulation study is used in order to approximate dynamic system parameters' unconditional expectation and covariances, while the modified version deals with the conditional moments which are also calculated by means of the Monte-Carlo method. The proposed filter modification is provided with the minimax justification, similar to the underlying CMNF concept. Simulation examples show the proposed algorithm effectiveness and performance gain in comparison with the original conditionally minimax nonlinear filter.