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One of the problems considered in the report is to find the vector of weights W minimizing E the set((d(t)-W(sup T)X(T))) quantity squared subject to linear equality constraints on W, where X(t) is a vector of random variables measured at time t and d(t) is a random variable related to X(t). This is a classical problem in linear estimation theory, except that the statistics of the random variables are assumed unknown and must be learned through observations. The other problem considered is in the classical design of processors for sensor arrays whose purpose is signal detection and estimation, a receiver is optimized on the basis of the a prior knowledge of the statistics of its input signals. However, when the a priori knowledge is not available, the receiver's performance can still be improved by performing measurements on its input signals and incorporating this new information into its design. Such receivers are called adaptive. The purpose of this research is to develop and analyze a gradient-descent surface-searching algorithm for automatically adjusting (adapting) the parameters of a linear tapped-delay-line array processor in order to improve its performance in an unknown changing environment.