Robust Adaptive Unscented Particle Filter

Robust Adaptive Unscented Particle Filter

Li Xue (School of Automatics, Northwestern Polytechnical University, Xi’an, China), Shesheng Gao (School of Automatics, Northwestern Polytechnical University, Xi’an, China) and Yongmin Zhong (School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Bundoora, VIC, Australia)
Copyright: © 2013 |Pages: 12
DOI: 10.4018/ijimr.2013040104
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Abstract

This paper presents a new robust adaptive unscented particle filtering algorithm by adopting the concept of robust adaptive filtering to the unscented particle filter. In order to prevent particles from degeneracy, this algorithm adaptively determines the equivalent weight function according to robust estimation and adaptively adjusts the adaptive factor constructed from predicted residuals to resist the disturbances of singular observations and the kinematic model noise. It also uses the unscented transformation to improve the accuracy of particle filtering, thus providing the reliable state estimation for improving the performance of robust adaptive filtering. Experiments and comparison analysis demonstrate that the proposed filtering algorithm can effectively resist disturbances due to system state noise and observation noise, leading to the improved filtering accuracy.
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1. Introduction

The problem of nonlinear filtering is common in many areas such as integrated navigation system, geodetic positioning, automatic control, information fusion and signal processing. The extended Kalman filtering is a commonly used filtering method to nonlinear systems (Julier, Uhlmann & Durrant-Whyte, 2000; Lefebvre, Bruyninckx & Schutter, 2004). This is an approximation method, in which nonlinear system equations are linearized by the Taylor expansion and the linearized states are assumed to obey the Gaussian distribution. The linearization stage of the state equations may lead to a problem of divergence or instability (Simon, 2006). Especially, when the practical probability function has multiple peak values, the estimated state error is very large or even divergent (Grewal & Andrews, 2008). The unscented Kalman filtering (UKF) method combines the concept of unscented transform with the Kalman filtering (Julier & Uhlmann, 2004; Wan & van der Merwe, 2000). This method inherits the linear update structure of the Kalman filtering. It uses only the second-order system moments, which may not be sufficient for some nonlinear systems.

The particle filtering (PF) is an optimal recursive Bayesian filtering method based on Monte Carlo simulation (Doucet, Godsill & Andrieu, 2000; Rawlings & Bakshi, 2006). This method aims to produce a sample of independent random variables distributed according to the conditional probability distribution. It is not limited by the linearized errors and the assumption of Gaussian noise, and thus can deal with nonlinear system models and non-Gaussian noise (Rawlings & Bakshi, 2006). It is also easier to implement, even for high dimensional problems. Therefore, particle filtering has been widely used in the fields of navigation, target tracking, fault detection, robotic control and computer vision (Zhang, Chen, Zhou & Li, 2007; Oppenheim & Philippe & de Rigal, 2008). However, the accuracy of the PF method largely depends on the choice of importance sampling density and resampling scheme (Yang, Tian, Jin & Zhang, 2005; Arulampalam, Maskell, Gordon & Clapp, 2002; Watzenig, Brandner & Steiner, 2007).

Recently, various methods have been proposed to design a good importance sampling density or modify the resampling scheme (Yang, Tian & Jin, 2006; Zhang, Tian & Jin, 2006; Budhiraja, Chen & Lee, 2007; Ning & Fang, 2008). The unscented particle filtering (UPF) method uses unscented transformation to get a better importance sampling density (van der Merwe, Doucet, Freitas & Wan, 2000; Liang, Ma & Dai, 2008; Ning & Fang, 2008; Ali & Fang, 2009). The unscented transformation calculates the statistics of a random variable that undergoes a nonlinear transform (Julier & Uhlmann, 2004). It enables the estimation of state mean and variance to achieve the third-order accuracy, thus providing higher accuracy for filtering. However, the particle degeneracy phenomenon could occur if a dynamic system has very small noise or the observational noise has very small variance (Oppenheim & Philippe & de Rigal, 2008; Ning & Fang, 2008; Ali & Fang, 2009). In fact, it is unavoidable in practical engineering applications that a dynamic system has small systematic noise due to the disturbances caused by singular observations and uncertain factors.

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