Brief paper: Distribution function tracking filter design using hybrid characteristic functions

Authors:
Jinglin Zhou;Donghua Zhou;Hong Wang;Lei Guo;Tianyou Chai
Affiliations:
Department of Automation, Tsinghua University, Beijing, China and College of Information Science and Technology, Beijing University of Chemical Technology, Beijing, China;Department of Automation, Tsinghua University, Beijing, China;School of Electrical and Electronics Engineering, The University of Manchester, Manchester, M60 1QD, UK and Research Centre of Automation, Northeastern University, Shenyang, China;School of Instrumentation and Opto-Electronics Engineering, Beihang University, Beijing, China;Research Centre of Automation, Northeastern University, Shenyang, China
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

A new tracking filtering algorithm for a class of multivariate dynamic stochastic systems is presented. The system is expressed by a set of time-varying discrete systems with non-Gaussian stochastic input and nonlinear output. A new concept, such as hybrid characteristic function, is introduced to describe the stochastic nature of the dynamic conditional estimation errors, where the key idea is to ensure the distribution of the conditional estimation error to follow a target distribution. For this purpose, the relationships between the hybrid characteristic functions of the multivariate stochastic input and the outputs, and the properties of the hybrid characteristic function, are established. A new performance index of the tracking filter is then constructed based on the form of the hybrid characteristic function of the conditional estimation error. An analytical solution, which guarantees the filter gain matrix to be an optimal one, is then obtained. A simulation case study is included to show the effectiveness of the proposed algorithm, and encouraging results have been obtained.