Implementation of non-linear estimators using quadrature formulae†

Abstract

Abstract A new method of non-linear estimator implementation called quadrature formula method is presented. It is different from other methods in that emphasis is placed directly upon approximating the weighted integral of the conditional density function rather than the function itself. Valuable perspective is developed by relating this method to certain former methods based on density function approximation. In particular, it is shown that the point mass representation method is included as a special ease of the quadrature formula method with an accuracy consistent with that of a rectangular rule. The fundamental spline approximation method when formulated in the context of quadrature formula method turns out to be comparable to a trapezoidal rule. Of significant practical interest is the fact that improved accuracy can he achieved with essentially the same amount of labour required by the point mass representation method, an amount which practically is the minimum of all the existing methods. In additi...