The Linear Minimum Mean-Square Error Estimation with Constraints and Its Applications

The minimum mean-square error (MMSE) is an important optimization criterion, which is widely applied to many fields in signal processing and others, such as waveforms estimation, signal detection and system identification. In many practical scenarios, the optimal solutions are usually expected to locate in some especial subspace. So, it is significant to study the MMSE detector or estimator with various constraints. A rigorous analytic method to incorporate the optimal estimation with linear equality constraints is developed in the most general case. It can be directly applied to the Kalman filtering with state equality constraints, in which the assumption of the states and noises to be Gaussian can be avoided