Nonlinear Multidimensional Bayesian Estimation with Fourier Densities

Dietrich Brunn, Felix Sawo, Uwe D. Hanebeck
2006 Proceedings of the 45th IEEE Conference on Decision and Control  
Efficiently implementing nonlinear Bayesian estimators is still an unsolved problem, especially for the multidimensional case. A trade-off between estimation quality and demand on computational resources has to be found. Using multidimensional Fourier series as representation for probability density functions, so called Fourier densities, is proposed. To ensure non-negativity, the approximation is performed indirectly via Ψ-densities, of which the absolute square represent the Fourier density.
more » ... t is shown that Ψ-densities can be determined using the efficient fast Fourier transform algorithm and their coefficients have an ordering with respect to the Hellinger metric. Furthermore, the multidimensional Bayesian estimator based on Fourier densities is derived in closed form. That allows an efficient realization of the Bayesian estimator where the demands on computational resources are adjustable.
doi:10.1109/cdc.2006.377378 dblp:conf/cdc/BrunnSH06 fatcat:puod55qva5fzbadd5ui4zqcbw4