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Determining signal parameter values or a probability distribution's parameters are the simplest estimation problems. Their fundamental utility in signal processing, much less array processing, is unquestioned. How do we estimate noise power? What is the best estimator of signal amplitude? How should array outputs be effectively combined to estimate propagation delay? Examination of useful estimators, and evaluation of their properties and performances constitute a case study of estimation problems. As expected, many of these issues are interrelated and serve to highlight the intricacies that arise in estimation theory.
All parameters of concern here have unknown values; we classify
parameter estimation problems according to whether the parameter
is stochastic or not. If so, then the parameter has a
probability density and choosing the density, as we have said so
often, narrows the problem considerably, suggesting that
measurement of the parameter's density would yield something
like what was assumed! If the density is not known, the
parameter is termed nonrandom, and its values range
unrestricted over some interval. The resulting
nonrandom-parameter estimation problem differs greatly from the
random-parameter problem. We consider first the latter problem,
letting