State estimation of nonlinear dynamical systems by an asymptotic method
type: Item
instance of: scholarly article
title: State estimation of nonlinear dynamical systems by an asymptotic method
zbMATH Open document ID: 0919.93071
author: A. S. Gol'tsov
published in: Journal of Computer and Systems Sciences International
publication date: 1999-09-07T00:00:00Z
review text: Consider the finite-dimensional dynamic system with noises \[ {dx(t)\over dt}= f(x(t), t)+ G(x(t),t) w(t) \] with initial conditions \(E[x(0)]= \widehat x_0\), \(\text{Cov}[x(0)]= V_0\). The output signal is measured, \[ y(t)= m(x(t), t)+ n(t),\quad t\in [0,t_N]. \] The components \(w_j(t)\), \(j= 1,\dots, p\), and \(n_i(t)\), \(i= 1,\dots, r\) of noises are stationary stochastic processes with arbitrary probability distribution laws. The estimation problem of the phase vector \(x(t)\) is solved. By the Fourier series expansion of covariance functions of the processes \(w_j(t)\) and \(n_i(t)\) and by an asymptotic method of analyses of differential equations with small parameters, an estimation algorithm with minimum variance of the estimation error is obtained. As an example, the problem of determining the value of the heat flow with the help of the battery heat flow meter is investigated. The numerical results show that the proposed algorithm yields unbiased consistent estimators that have a rapid rate of convergence and a variance of estimation error that is less than in the recursive least square method and in the Kalman filter.
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 1274253
zbMATH Keywords: Fourier series expansion of covariance functions
zbMATH Keywords: differential equations with small parameters
zbMATH Keywords: estimation algorithm
zbMATH Keywords: minimum variance
reviewed by: A. Kukush
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1274253