Nonlinear Filters

3Observers

3.1 Introduction

State of a system refers to the minimum amount of information, which is required at the current time instant to uniquely describe the dynamic behavior of the system in the future, given the inputs and parameters. Parameters reflect the physical properties used in a model as a description of the system under study. Inputs or actions are manipulated variables that act on the dynamic system as forcing functions. Outputs or observations are variables that can be directly measured. In many practical situations, the full state of a dynamic system cannot be directly measured. Hence, the current state of the system must be reconstructed from the known inputs and the measured outputs. State estimation is deployed as a process to determine the state from inputs and outputs given a dynamic model of the system. For linear systems, reconstruction of system state can be performed by deploying the well‐established optimal linear estimation theory. However, for nonlinear systems, we need to settle for sub‐optimal methods, which are computationally tractable and can be implemented in real‐time applications. Such methods rely on simplifications of or approximations to the underlying nonlinear system in the presence of uncertainty [9]. In this chapter, starting from deterministic linear state estimation, the stage will be set for nonlinear methods, and then, unknown inputs such as faults and attacks will be discussed. Since state estimators are usually implemented ...