Improved Framework of Gaussian Filter for Nonlinear System with Correlated Noises

This paper investigates the stochastic uncertain system with correlated noise. The stochastic uncertainties are caused by the multiplicative noises existing in the state function. Moreover, the multiplicative noises and the measurement noises are synchronously cross-correlated. A novel framework of Gaussian filter (GF) is proposed for this kind of stochastic uncertain systems. As the probability of multiplicative noises conditioned on measurement noises contains more correlation information than its original probability, the conditional Gaussian distributions is utilized to improve the GF accuracy. What is more, the spherical-radial cubature rule is exploited to calculate the Gaussian quadrature. The cubature Kalman filter with multiplicative correlated noises (CKF-MCN) is designed. The numeral example shows the accuracy and effectiveness of the CKF-MCN.