A Note on Capon's Minimum Variance Projection for Multi-Spacecraft Data Analysis

Abstract

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Capon's minimum variance projection for the multi-point measurements is revisited using the method of likelihood function to derive the minimum variance projection and a simplified error estimate analytically. Theoretical construction of the minimum variance projection assumes a Gaussian form of the likelihood function and also regards the data covariance as a proxy of the noise covariance. The minimum variance projection is extended to the problem of two-spacecraft mode decomposition in the Mercury magnetosphere in which the magnetic field is a superposition of the constant field from the current sheet and the dipolar field from the planet. The extension of the Capon estimator (the data-variance projection) can identify the signal amplitudes of the different fields with a sufficient accuracy when the statistical averaging is properly done. The Capon estimator serves as a powerful analysis tool when the spatial resolution is limited to only a few points.

Keywords

• adaptive filter theory
• Capon estimator
• multi-spacecraft data analysis
• waves and turbulence
• mode decomposition