Optimal Linear MMSE Estimation Under Correlation Uncertainty in Restricted Bayesian Framework

DÜLEK B., Topaloglu S. T., Gezici S.

IEEE Transactions on Aerospace and Electronic Systems, vol.59, no.4, pp.4744-4752, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.1109/taes.2023.3240672
  • Journal Name: IEEE Transactions on Aerospace and Electronic Systems
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, Civil Engineering Abstracts
  • Page Numbers: pp.4744-4752
  • Keywords: Correlation uncertainty, linear estimation, restricted Bayes, signal processing
  • Hacettepe University Affiliated: Yes

Abstract

A restricted Bayes approach is proposed for linear estimation of a scalar random parameter based on a scalar observation under uncertainty regarding the correlation between the parameter and the observation. In particular, the optimal linear estimator that minimizes the average mean-squared error (MSE) is derived under a constraint on the worst-case MSE by considering possible values of the correlation coefficient and its probability distribution. A closed-form expression is derived for the optimal linear estimator in the proposed restricted Bayesian framework by considering a generic statistical characterization of the correlation coefficient. Performance of the proposed estimator is evaluated via numerical examples and its benefits are illustrated in various scenarios. The proposed framework is also extended to the case of vector-valued observation and the properties of the optimal linear estimator are characterized.