Application of Supporting Integral Curves and Generalized Invariant Unbiased Estimation for the Study of a Multidimensional Dynamical System

Abstract

The well-known methods of supporting integral curves and generalized invariant unbiased estimation are used to find numerical-analytical representations of the solution to an equation describing a dynamical system and its measured output and to compute optimal values of continuous linear functionals (numerical characteristics) of measured parameters based on incorrect data involving both a fluctuation error and a singular disturbance. A two-step method is developed for this purpose. Numerical-analytical representations depending continuously on all parameters of the system are formed at the first stage, and numerical characteristics of the system that are invariant under the singular disturbance are estimated at the second stage. The method ensures the maximum possible decomposition of the numerical procedures involved; moreover, it does not require traditional linearization or initial guess choice and does not involve the computation of spectral coefficients in finite linear combinations (with given basis functions) describing the integral curves, measured parameters, and the singular disturbance. The random and systematic errors are analyzed, an illustrative example is given, and recommendations on practical application of the results are made.