Rethinking Biased Estimation: Improving Maximum Likelihood and the Cramér–Rao Bound
Foundations and Trends in Signal Processing
Worst-case robust MIMO transmission with imperfect channel knowledge
IEEE Transactions on Signal Processing
Generalized SURE for exponential families: applications to regularization
IEEE Transactions on Signal Processing
Robust THP transceiver designs for multiuser MIMO downlink
WCNC'09 Proceedings of the 2009 IEEE conference on Wireless Communications & Networking Conference
Robust THP transceiver designs for multiuser MIMO downlink with imperfect CSIT
EURASIP Journal on Advances in Signal Processing - Multiuser MIMO Transmission with Limited Feedback, Cooperation, and Coordination
Brief paper: Identification for robust H2 deconvolution filtering
Automatica (Journal of IFAC)
Structured least squares problems and robust estimators
IEEE Transactions on Signal Processing
Prediction of defect distribution based on project characteristics for proactive project management
Proceedings of the 6th International Conference on Predictive Models in Software Engineering
Competitive linear estimation under model uncertainties
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
EURASIP Journal on Advances in Signal Processing
Structured Total Maximum Likelihood: An Alternative to Structured Total Least Squares
SIAM Journal on Matrix Analysis and Applications
Theory and Applications of Robust Optimization
SIAM Review
IEEE/ACM Transactions on Networking (TON)
Robust Mobile Location Estimation Using Hybrid TOA/AOA Measurements in Cellular Systems
Wireless Personal Communications: An International Journal
Robust estimation in flat fading channels under bounded channel uncertainties
Digital Signal Processing
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We consider the problem of estimating an unknown parameter vector x in a linear model that may be subject to uncertainties, where the vector x is known to satisfy a weighted norm constraint. We first assume that the model is known exactly and seek the linear estimator that minimizes the worst-case mean-squared error (MSE) across all possible values of x. We show that for an arbitrary choice of weighting, the optimal minimax MSE estimator can be formulated as a solution to a semidefinite programming problem (SDP), which can be solved very efficiently. We then develop a closed form expression for the minimax MSE estimator for a broad class of weighting matrices and show that it coincides with the shrunken estimator of Mayer and Willke, with a specific choice of shrinkage factor that explicitly takes the prior information into account. Next, we consider the case in which the model matrix is subject to uncertainties and seek the robust linear estimator that minimizes the worst-case MSE across all possible values of x and all possible values of the model matrix. As we show, the robust minimax MSE estimator can also be formulated as a solution to an SDP. Finally, we demonstrate through several examples that the minimax MSE estimator can significantly increase the performance over the conventional least-squares estimator, and when the model matrix is subject to uncertainties, the robust minimax MSE estimator can lead to a considerable improvement in performance over the minimax MSE estimator.