Chapter

Three Decades of Progress in Control Sciences

pp 203-213

Sequential Bayesian Filtering via Minimum Distortion Quantization

  • Graham C. GoodwinAffiliated withSchool of Electrical Engineering and Computer Science, The University of Newcastle
  • , Arie FeuerAffiliated withElectrical Engineering Department, Technion-Israel Institute of Technology
  • , Claus MüllerAffiliated withSchool of Electrical Engineering and Computer Science, The University of Newcastle

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Summary

Bayes Rule provides a conceptually simple, closed form, solution to the sequential Bayesian nonlinear filtering problem. The solution, in general, depends upon the evaluation of high dimensional multivariable integrals and is thus computationally intractable save in a small number of special cases. Hence some form of approximation is inevitably required. An approximation in common use is based upon the use of Monte Carlo sampling techniques. This general class of methods is referred to as Particle Filtering. In this paper we advocate an alternative deterministic approach based on the use of minimum distortion quantization. Accordingly we use the term Minimum Distortion Nonlinear Filtering (MDNF) for this alternative class of algorithms. Here we review the theoretical support for MDNF and illustrate its performance via simulation studies.