A New Gaussian-Like Density Model and Its Application to Object-Tracking

Probability density function (PDF) plays a vital role in many applications involving stochastic process. A good approximation for real-time PDF conditioned on certain performance criterion could help to acquire unknown information about the system. With the help of this kind of information, which was not available earlier, many features of various models that describe the real system can be estimated effectively, especially for non-linear non-Gaussian stochastic system. In this paper, we elucidate some PDFs with only one parameter that have a definite physical meaning based on Tsallis entropy. The PDFs that we calculated here are all Gaussian-like, and Gaussian distribution is attained when the parameter of Tsallis entropy approaches zero. Based on these explicit form of Gaussian-like PDFs we calculated here, an extension of Gaussian particle filter (GPF) called Gaussian-like particle filter (GLPF) is proposed and the simulation results show that the GLPF is a more effective way to estimate the state of non-linear stochastic system compared with the GPF.