Unscented Kalman Filter for Nonlinear Systems with One-step Randomly Delayed Measurements and Colored Measurement Noises

In this paper, a new unscented Kalman filter (Unscented Kalman filter, UKF) for nonlinear system with both one-step randomly delayed measurements and colored measurement noises is proposed. Firstly, the first-order Markov sequence model is used to whiten colored noise, at the same time, an independent and identically distributed Bernoulli variable is used to model the delay of measurement data transmission, then the model of nonlinear one-step randomly time delay system with colored noise whitening is established. Secondly, filter recursion formula of UKF under the above model is proposed through unscented transformation (Unscented transformation, UT) to calculate the posterior mean and covariance of the nonlinear state based on the Bayesian filter framework. The proposed new UKF method can effectively deal with the issue that traditional UKF is failure under the condition of one-step randomly delayed measurements and colored measurement noises. The efficiency and superiority of the proposed method are illustrated in a numerical example for a target tracking problem.