TABLE OF CONTENTS In the area of signal processing, we come across analogue and digital filtering concepts and methods. The real-life systems give rise to signals, which are invariably contaminated with the so-called random noise. This noise could arise due to measurement errors from the sensors, instruments, data transmission channels or human error. Some of these errors would be systematic, fixed or slowly varying with time. However, in most cases, the errors are random in nature and can be described best by a probabilistic model. A usual characteristic of such a random noise that affects the signal is Gaussian (normally distributed) noise with zero mean and some finite variance. This variance measures the power of the noise and it is often compared to the power of the signal that is influenced by the random noise. This leads to a measure called signal to noise ratio (SNR). Often the noise is assumed a white process (see Chapter 2). The aim is then to maximise SNR by filtering out the noise from the signal/data of the dynamical system. There are mainly two approaches: model free and model based. In the model free approach, no mathematical model (equations) is presumed to be fitted or used to estimate the signal from the signal plus noise. These techniques rely upon the concept of the correlation of various signals, like input-output signals and so on. In the present chapter, we use the model based approach and especially the approach based on the state-space model of a dynamical...
