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Q-Gaussian Density Model and Its Application to State Estimation of Nonlinear Systems

Abstract Probability density function (PDF) plays a vital role in system analysis involving stochastic factors. A good estimate of true PDF conditioned under certain performance criterion could help acquire more information of the system. With help of the new information, many features of the system that we are concerning can be revealed effectively, especially for nonlinear non-Gaussian stochastic systems. In this paper, based on the Tsallis entropy, we derive a class of PDFs with explicit form called q-Gaussian PDFs. These PDFs have a parameter that indicates the fractal feature of the system. Based on the explicit form of q-Gaussian PDFs, we propose an extension of Gaussian particle filter (GPF) called q-Gaussian particle filter (q-GPF). The experimental results show that the q-GPF is a more effective method to estimate the state of nonlinear stochastic system compared with the GPF.