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Unscented Kalman Filtering for Nonlinear State Estimation with Correlated Noises and Missing Measurements

Long Xu, Kemao Ma*, and Hongxia Fan
International Journal of Control, Automation, and Systems, vol. 16, no. 3, pp.1011-1020, 2018

Abstract : "The unscented Kalman filtering problem is investigated for a class of nonlinear discrete stochastic systems subject to correlated noises and missing measurements. Here, a random variable obeying Bernoulli distribution with known conditional probability is introduced to depict the phenomenon of missing measurements occurring in a stochastic way. Due to taking the correlation of noises into account, a one-step predictor is designed by applying the innovative analysis and unscented transformation approach. And then, based on one-step predictor and the minimum mean square error principle, a new unscented Kalman filtering algorithm is proposed such that, for the correlated noises and 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.sensor faults by using the H∞ optimization technique. A FTC is secondly proposed to stabilize the faulty"

Keyword : "Correlated noises, minimum mean square error, missing measurements, nonlinear discrete stochastic systems, unscented transformation.internal model control (IMC)."

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