ABSTRACT
This chapter discusses the Gauss-Hermite rule of integration and how it is solving the filtering problems. It utlizes the Gauss quadrature method to evaluate the said integral. More specifically, as the weighting function is exponential the Gauss-Hermite quadrature rule will be useful. With this different method of numerical integration a new filtering algorithm was developed which is known as Gauss-Hermite filter (GHF). Although the Gauss-Hermite rule of integration is quite old in the literature, its application in filtering and estimation problems is recent and mainly due to the work of Kazufumi Ito and K. Xiong. The GHF makes use of the Gauss-Hermite Quadrature rule of integration. Using the Gauss-Hermite quadrature rule, an integration of an arbitrary function over an exponential weighting function can be evaluated as a weighted sum over a set of sample points known as Gauss-Hermite quadrature points. Hermann Singer introduces generalization of the GHF in which is claimed to be better than GHF.
