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.
Highlights
The reconstruction of model parameters from a given set of measurements is one of the most important tasks in geophysical and space science studies
The analysis of the error propagation is of major importance for the application of linear inversion methods
Upper bounds for the errors of Capon’s estimator resulting from measurement errors and measurement position errors are derived. These upper bounds solely depend on known quantities, i.e., measurements and measurement positions, whereas the true estimation error cannot be calculated within the practical application of the method, since the accurate estimator is unavailable
Summary
The reconstruction of model parameters from a given set of measurements is one of the most important tasks in geophysical and space science studies. The measurements are always affected by measurement errors which result in estimation errors for the wanted model parameters. Since Capon’s method is based on the evaluation of statistically averaged data, the spectrum is affected by errors resulting from a finite number of samples [6]. Concerning the application of the Capon method for the analysis of planetary magnetic fields, the error propagation of Capon’s estimator itself is of major importance for assessing the quality of the reconstructed model parameters. As a follow-up of the generalized derivation of Capon’s method [3] and the error estimation of the power spectrum [6], in this work the effects of measurement errors, measurement position errors as well as finite sample sizes on Capon’s estimator are considered
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
