Constrained Linear Minimum MSE Estimation
نویسندگان
چکیده
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 TermsEstimation, Wiener ltering, Constrained Estimation.
منابع مشابه
On Distributed Linear Estimation With Observation Model Uncertainties
We consider distributed estimation of a Gaussian source in a heterogenous bandwidth constrained sensor network, where the source is corrupted by independent multiplicative and additive observation noises, with incomplete statistical knowledge of the multiplicative noise. For multi-bit quantizers, we derive the closed-form mean-square-error (MSE) expression for the linear minimum MSE (LMMSE) est...
متن کاملMinimum mean-squared error covariance shaping
This paper develops and explores applications of a linear shaping transformation that minimizes the mean squared error (MSE) between the original and shaped data, i.e., that results in an output vector with the desired covariance that is as close as possible to the input, in an MSE sense. Three applications of minimum MSE shaping are considered, specifically matched filter detection, multiuser ...
متن کاملHard-constrained vs. soft-constrained parameter estimation
The paper aims at contrasting two different ways of incorporating a-priori information in parameter estimation, i.e. hard-constrained and soft-constrained estimation. Hardconstrained estimation can be interpreted, in the Bayesian framework, as Maximum A-posteriori Probability (MAP) estimation with uniform prior distribution over the constraining set, and amounts to a constrained Least-Squares (...
متن کاملNew Cramer-Rao-Type Bound for Constrained Parameter Estimation
Non-Bayesian parameter estimation under parametric constraints is encountered in numerous applications in signal processing, communications, and control. Mean-squared-error (MSE) lower bounds are widely used as performance benchmarks and for system design. The well-known constrained Cramér-Rao bound (CCRB) is a lower bound on the MSE of estimators that satisfy some unbiasedness conditions. In m...
متن کاملPerformance of LTE Channel Estimation Algorithms for Different Interpolation Methods and Modulation Schemes
In this paper, we present performance of pilot based channel estimation techniques such as Least Squares (LS) and Linear Minimum Mean Square Error (LMMSE) for different interpolation methods and modulation schemes. The performance is evaluated using the mean squared error (MSE) as the performance metric of interest for downlink LTE system. Simulation results show that for low SNR environment, a...
متن کامل