An estimation accuracy of state observers under uncertain initial conditions

: pp. 320–332
Received: September 23, 2019
Revised: October 03, 2019
Accepted: October 05, 2019

Mathematical Modeling and Computing, Vol. 6, No. 2, pp. 320–332 (2019)

Lviv Polytechnic National University
Lviv Polytechnic National University
University of Alabama at Birmingham
Lviv Polytechnic National University
US Army CCDC Ground Vehicle Systems Center, Warren, MI

A fast convergence speed of an observer helps improve the capability to track the states of a system for an arbitrary divergence between a real and an estimated initial conditions.  This property of the observers is significantly useful if a system has fast dynamics and its states change rapidly.  Thus, the convergence time is one of the main performance criteria of linear and non-linear state observers.

This article presents a comparative analysis of observers for both linear and nonlinear systems in terms of the time of convergence of the observers.  The following observers was chosen for this study: the Kalman filter (KF), extended Kalman filter (EKF), unscented Kalman filter (UKF), particle filter (PF), Luenberger observer (LO), and fuzzy-based Luenberger observer (Fuzzy-LO).  The listed observers were studied using a non-linear mathematical model of an open-link locomotion module, which movements were studied in stochastic terrain conditions.  The mathematical model was then simplified and simulated as a linear model with the purpose to estimate the efficiency of the linear observers.  The Fuzzy-LO with an adaptive gain to the estimation error gives better results than the LO, especially in steady states.  The PF with a simple Gaussian distribution provides a lower convergence speed than the KF, EKF, and UKF.  To faster the convergence of the PF, a novel approach, PF*, that utilizes mixture probability density function of the distribution of initial particles was introduced in the article.

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