Robust Adaptive Central Difference Particle Filter

Robust Adaptive Central Difference Particle Filter

Li Xue (School of Physics and Electronics Information Engineering, Ningxia University, Yin Chuan, China), Shesheng Gao (School of Automatics, Northwestern Polytechnical University, Xi'an, China), Yongmin Zhong (School of Aerospace, Mechanical and Manufacturing Engineering, RMIT Univeristy, Bundoora, Australia), Reza Jazar (School of Aerospace, Mechanical and Manufacturing Engineering, RMIT Univeristy, Bundoora, Australia) and Aleksandar Subic (School of Aerospace, Mechanical and Manufacturing Engineering, RMIT Univeristy, Bundoora, Australia)
Copyright: © 2014 |Pages: 16
DOI: 10.4018/ijrat.2014010102
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Abstract

This paper presents a new robust adaptive central difference particle filtering method for nonlinear systems by combining the concept of robust adaptive estimation with the central difference particle filter. This method obtains system state estimate and covariances using the principle of robust estimation. Subsequently, the importance density is obtained by adjusting the state estimate and covariances through the equivalent weight function and adaptive factor constructed from predicted residuals to control the contributions to the new state estimation from measurement and kinematic model. The proposed method can not only minimize the variance of the importance density distribution to resist the disturbances of systematic noises, but it also fully takes advantage of present measurement information to avoid particle degeneration. Experiments and comparison analysis with the existing methods demonstrate the improved filtering accuracy of the proposed method.
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A significant amount of research efforts have been dedicated to the problem of nonlinear filtering. The extended Kalman filter (EKF) is an approximation method, in which nonlinear system equations are linearized by the Taylor series and the linear states are assumed to obey the Gaussian distribution. The linearization stage of the state equations may lead to the problem of divergence or instability (Cappe, Godsill, & Moulines, 2007). The EKF also requires the calculation of Jacobian matrix, which is a difficult and time-consuming process. Jacobian matrix may not even exist in some cases.

The unscented Kalman filter (UKF) and central difference Kalman filter (CDKF) are belonged to a single family of non-derivative Kalman filters. Both are based on statistical approximations of system equations without requiring the calculation of Jacobian matrix. Therefore, they have the higher accuracy and convergent speed than the EKF. The UKF combines the concept of unscented transform with the linear update structure of the Kalman filtering. However, it considers the second-order system momentum only, leading to the limited accuracy (Cappe, Godsill, & Moulines, 2007; Sarkka, 2007; Del Moral, Doucet, & Jasra, 2006; van der Merwe, Doucet, de Freitas, & Wan, 2000; Tenne, & Singh, 2003; Gordon, Salmond, & Smith, 1993). The CDKF approximates the state estimation and covariances of stochastic variables through central difference transformation. Its approximation accuracy is at least in the second order, leading to the higher filtering accuracy than the UKF. The CDKF also has a much simple structure than the UKF, as only one single scaling parameter is required for the CDKF while three parameters for the UKF. However, both CDKF and UKF require the system state obey the Gaussian distribution. Further, if the nonlinearity of a dynamic system is strong, both will lead to the biased or even divergent filtering solution (Simon, 2006).

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