State variable and parameter estimation

Abstract

The development of methods designed to produce continuous solutions to linear, ordinary differential equations is described. These solutions are based on a set of orthogonal polynomials. This work is then incorporated into state estimation theory and a continuous filter is developed. A new sequential adaptive filter is then developed which effectively compensates for errors in the mathematical description of the process. This adaptive filter finds the mean and covariance of ‘fictitious inputs' and uses these parameters to compensate for the model errors. The results show the application of the above topics to some simple linear and non-linear systems and demonstrate the effectiveness of the adaptive filter in situations involving poor models. The adaptive filter also provides information concerning the nature of the model errors which may be used to improve the model formulation.