Constrained Linear Minimum MSE Estimation

—We address the problem of linear minimum meansquared error (LMMSE) estimation under constraints on the lter or the estimated signal. We develop a general formula that leads to closed form solutions for a wide class of constrained LMMSE problems. The results are applicable to both nite dimensional problems as well as to the Wiener ltering setup, in which in nitely-many measurements are available. Our approach generalizes previous known results such as the generalized Karhunen-Loeve transform (GKLT), the causal Wiener lter and more. As an application of our framework, we develop Wiener type lters under various restrictions, which allow for practical implementations. Index Terms—Estimation, Wiener ltering, Constrained Estimation.