Error Propagation of Capon’s Minimum Variance Estimator

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 wh...

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Bibliographic Details
Main Authors: S. Toepfer, Y. Narita, D. Heyner, U. Motschmann
Format: Article
Language:English
Published: Frontiers Media S.A. 2021-06-01
Series:Frontiers in Physics
Subjects:
Online Access:https://www.frontiersin.org/articles/10.3389/fphy.2021.684410/full
Description
Summary: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.
ISSN:2296-424X