AUTHOR=Toepfer S. , Narita Y. , Heyner D. , Motschmann U. TITLE=Error Propagation of Capon’s Minimum Variance Estimator JOURNAL=Frontiers in Physics VOLUME=9 YEAR=2021 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.684410 DOI=10.3389/fphy.2021.684410 ISSN=2296-424X ABSTRACT=

The error propagation of Capon’s minimum variance estimator resulting from measurement errors and position errors is derived within a linear approximation. It turns out, that Capon’s estimator provides the same error propagation as the conventionally used least square fit method. The shape matrix which describes the location depence of the measurement positions is the key parameter for the error propagation, since the condition number of the shape matrix determines how the errors are amplified. Furthermore, the error resulting from a finite number of data samples is derived by regarding Capon’s estimator as a special case of the maximum likelihood estimator.