Abstract
In this paper discrete time nonlinear Bayesian filter using Gram Charlier Series Mixture (GCSM) model has been developed. Optimal nonlinear sequential state estimation can be described in a unified way by recursive Bayes’ formula. The most important quantity of interest in Bayesian recursive formulation is state probability distribution of the system conditioned on available measurements. Exact optimal solution to Bayesian filtering problem is intractable as it requires an infinite dimensional process. Bayes’ probability distribution can be approximated by orthogonal expansion of probability density function in terms of higher order moments of the distribution. In general, better series approximations to Bayes’ distribution can be achieved by using higher order moment terms and Hermite polynomials termed as Gram Charlier Series (GCS). Sequential Monte Carlo (SMC) method has been adopted for approximating state predictive and filtering distributions parameterized as GCSM. GCSM based parametric bootstrap particle filters are derived for flexible use depending on inference problems under sparse measurement environment. Application of these sequential filters for satellite orbit determination using radar measurements is presented. The results have shown better/comparable performances over other SMC filtering methods such as Particle Filter and Gaussian Mixture Particle Filter (GMPF) under sparse measurement availability.
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