This chapter presents the minimum mean square error (MMSE) estimation of Gaussian random vectors and the linear MMSE estimator for arbitrarily distributed random vectors. The estimation of unknown constant vectors according to the least squares (LS) criterion is discussed. The batch and recursive versions are derived and the results are applied to polynomial fitting. The statistical tools for deciding what is the appropriate order of the polynomial when fitting a set of data points is detailed, followed by a realistic example of the localization of a target. A problem solving section appears at the end of the chapter.


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