تلخیص
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.
Syed Amer A. Gilani, P. L. Palmer. (2019) Sequential Monte Carlo Bayesian Estimation Using Gram Charlier Series Mixture Model, Journal of Space Technology , Volume 9, Issue 1.
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