FIXED LAG SMOOTHING ,JN NONLINEAR DYNAMICAL SYSTEMS

Abstract

The earliest stimulus for the development of the estimation theory was apparently provided by astronomical studies in which the motion of the planets and comets was studied uintelesóopie measurement data,The thotion of these bodies cn be characterized by six parameters and the estimation problem àousiderd was that of obtaining the values of these parameters from the measurement data. The first contribution in thifl area appears to be that due to Gauss who, in 1795 invented the least squares approach and applied to this estimation problem. This was followed by the maximum likelihood method introduced by Fisher,in 1912, It was not until 1942 that Kolmogorov and Weiner independently developed a linear minimum meanusquare estimation technique that received considerable Interest and attention not only in the field of space science but also in the field of statistical communication as well and provided the foundation for the subsequent develop merit of Kalman filter theory in 1960(1). During the period (1940..1960), the clasica1 control technique involving Laplace and Fourier transforms gave way to the present day control theory employing the state space approach. Although the two approaches are mathematically equivalent, it is more convenient to deal with the differential or difference equation rather then integral equations, because of the ease of manipu1ting such equations on the digital computer...