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Component-Wise Conditionally Unbiased Estimation

Combining classical and Bayesian estimation


Project leader
Univ.-Prof. Dr. Mario Huemer

Project staff
DI Oliver Lang

Project start

Project description
In this project the class of conditionally unbiased linear estimators are studied and compared against linear unbiased estimators and linear minimum mean square error estimators.
An estimator calculates a guess of an unknown parameter vector based on a measurement vector in the presence of noise. This experiment can be repeated many times with different noise values. If the mean of these resulting estimates is equal to the true parameter vector, then the estimator is called unbiased (in the classical sense). Softening this classical unbiased constraint can in many cases lead to a better performance of the estimator (in the Bayesian sense) if the parameter vector is a random variable with known statistics. This leads to the component-wise conditionally unbiased (CWCU) constraint. This CWCU constraint ensures unbiasedness for one component of the parameter vector at a time. This approach allows in many cases using prior knowledge about the statistics of the parameter vector, leading to a better performance (in the Bayesian sense).
In this project we investigate the prerequisites, the behavior and the performance of linear CWCU estimators. Also a widely linear extension is currently under investigation. (FoDok)

Estimator comparison


4) Huemer M., Lang O., Hofbauer C.: "Component-Wise Conditionally Unbiased Widely Linear MMSE Estimation," in: Signal Processing, Volume 133, Page(s) 227-239, 2017. Open Access.

3) Lang O., Huemer M., Hofbauer C.: On the Log-Likelihood Ratio Evaluation of CWCU Linear and Widely Linear MMSE Data Estimators, in: Proceedings of the ASILOMAR Conference on Signals, Systems, and Computers, IEEE, 2016.

2) Lang O., Huemer M.: "CWCU LMMSE Estimation Under Linear Model Assumptions", in: Lecture Notes in Computer Science (LNCS): Computer Aided Systems Theory - EUROCAST 2015, Volume 9520, Page(s) 537-545, Springer International Publishing, 2015, PDF

1) Huemer M., Lang O.: On Component-Wise Conditionally Unbiased Linear Bayesian Estimation, in: Proceedings of the ASILOMAR Conference on Signals, Systems, and Computers, Page(s) 879-885, 2014.