Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Statistics and Computing
Convex Optimization
Adaptive Approximation Based Control: Unifying Neural, Fuzzy and Traditional Adaptive Approximation Approaches (Adaptive and Learning Systems for Signal Processing, Communications and Control Series)
Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking
Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
MMSE estimation in a linear signal model with ellipsoidal constraints
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Comparison of SPARLS and RLS algorithms for adaptive filtering
SARNOFF'09 Proceedings of the 32nd international conference on Sarnoff symposium
Uniformly Improving the CramÉr-Rao Bound and Maximum-Likelihood Estimation
IEEE Transactions on Signal Processing
MSE Bounds With Affine Bias Dominating the CramÉr–Rao Bound
IEEE Transactions on Signal Processing - Part II
Comparing between estimation approaches: admissible and dominating linear estimators
IEEE Transactions on Signal Processing
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The adaptive estimation of a time-varying parameter vector in a linear Gaussian model is considered where we a priori know that the parameter vector belongs to a known arbitrary subset. We consider a family of efficient recursive estimators for this problem: the recursive constrained maximum likelihood (ML) estimator, the recursive affine minimax, and the recursive minimum mean square error (MMSE) estimator. We show that all three estimators can be substantially simplified by using the recursive weighted least squares (RWLS) algorithm in a first step as the RWLS computes the sufficient statistic for this estimation problem. The recursive constrained ML needs to solve an optimization problem in the second step for the case that the RWLS solution does not fulfill the constraint. In case of affine minimax, we have to solve an optimization problem and to perform an affine transform. The MMSE estimator needs to calculate the mean of a truncated Gaussian density in the second step which is done by Monte Carlo integration. A simple rejection scheme is used to take general constraints for the parameter vector into account. An example shows the superior performance of our proposed estimators in comparison to many other estimators.