A Survey of Observers for Nonlinear Dynamical Systems - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 1

Chapter 1
A Survey of Observers for Nonlinear Dynamical
Systems

Wei Kang, Arthur J. Krener, Mingqing Xiao, and Liang Xu

Abstract The Kalman filter, invented initially for control systems, has been widely
used in science and engineering including data assimilation. For the last several
decades, the estimation theory for dynamical systems has been actively developed
in control theory. In this paper, we survey several observers, including Kalman
filters, for nonlinear systems. We also review some fundamental concepts on the
observability of systems defined by either differential equations or a numerical
model. The hope is that some of these ideas will inspire research that can benefit
the area of data assimilation.

Keywords Observers and estimation • Nonlinear systems • Observability

1.1 Introduction

In modern control theory, the term Observer has a technical meaning. An observer
is a system defined by differential or difference equations and associated computa-
tional algorithms which accepts the measured data from another system as input and