An Iterative Filter for a Class of Multi-Channel Nonlinear Systems with Multiplicative Noise

An iterative state filtering algorithm was proposed for a class of multi-channel nonlinear systems in the presence of multiplicative noise. The system is under the condition that the multiplicative noise sequence of observation model is in the form of diagonal stochastic matrix, and the multiplicative noises of all observation channels are correlated with each other at the same time. Based on linearization, iterative idea and the principle of linear minimum-variance, the algorithm is optimal for the linearized system in the sense of linear minimum-variance, and is suboptimal with respect to the original nonlinear system. A simulation example of two channels was given to demonstrate the effectiveness of the proposed algorithm