Estimation theory and, in the same breath, filtering theory is vast and rich in the literature and is central to a wide variety of disciplines, including control, communications, and signal processing. Also, it is relevant to such diverse areas as statistics, economics, bioengineering, and operations research. The terms estimation and filtering evoke many and varied responses among engineers and scientists. In its primary level, “estimation” is the process of arriving at a value for a desired and unknown variable from certain observations or measurements of other variables related to the desired one but contaminated with noise. Although one could trace the origins of estimation back to ancient times, Karl Friederich Gauss is generally acknowledged to be the forefather of what is now referred to as estimation theory. In his quest to predict the motions of planets and comets from telescopic measurements, Gauss at the age of 18 formulated the now well-known method of least squares. In modern times and in particular in the second half of the twentieth century, filtering theory has become synonymous with estimation theory mainly in the engineering literature. It might look odd that the term “filter” would apply to an “estimator”. In its common use, a “filter” is a physical device that can separate the wanted and unwanted fractions of a mixture. In electronics, a filter is seen as a circuit with a frequency-selective behavior, and thus can attenuate certain undesired components of the input signal and pass to the output certain desired components of the input signal.
KeywordsWhite Noise Power Spectral Density Transfer Matrix Noise Input Fault Estimation
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