Hybrid Kalman Filtering Algorithm With Stochastic Nonlinearities and Multiple Missing Measurements

Abstract

In this paper, the hybrid Kalman filter is designed for a class of special nonlinear systems where the state equation is nonlinear and the measurement equation is linear. The stochastic nonlinearities, which are described by statistical means, are considered in the system model to reflect the multiplicative stochastic disturbances. The phenomenon of multiple missing measurements is depicted by a set of the Bernoulli distributed random variables with known conditional probabilities and the missing rates of every sensor are different. We need to compute the parameters to reduce the effects of the stochastic nonlinearities and the phenomenon of multiple missing measurements. In addition then, based on the recursive projection formula and the unscented transformation approach, a new hybrid Kalman filtering algorithm is proposed such that, for the stochastic nonlinearities and multiple missing measurements, the filtering error is minimized. By solving the recursive matrix equation, the filter gain matrices and the error covariance matrices can be obtained and the proposed results can be easily verified by using the standard numerical software. We finally provide a numerical example to show the performance of the proposed approach. INDEX TERMS Nonlinear systems, stochastic nonlinearities, multiple missing measurements, minimum mean square error, unscented transformation.