New sigma point filtering algorithms for nonlinear stochastic systems with correlated noises |
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Authors: | Xiao-xu Wang Quan Pan Yong-mei Cheng and Chun-hui Zhao |
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Affiliation: | College of Automation, Northwestern Polytechnical University, Xi'an 710072, China |
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Abstract: | New sigma point filtering algorithms, including the unscented Kalman filter (UKF) and the divided difference filter (DDF),
are designed to solve the nonlinear filtering problem under the condition of correlated noises. Based on the minimum mean
square error estimation theory, the nonlinear optimal predictive and correction recursive formulas under the hypothesis that
the input noise is correlated with the measurement noise are derived and can be described in a unified framework. Then, UKF
and DDF with correlated noises are proposed on the basis of approximation of the posterior mean and covariance in the unified
framework by using unscented transformation and second order Stirling’s interpolation. The proposed UKF and DDF with correlated
noises break through the limitation that input noise and measurement noise must be assumed to be uncorrelated in standard
UKF and DDF. Two simulation examples show the effectiveness and feasibility of new algorithms for dealing with nonlinear filtering
issue with correlated noises. |
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Keywords: | nonlinear system correlated noise sigma point unscented Kalman filter divided difference filter |
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