Spherical functions are continuous functions defined on the surface of a sphere. They are relevant in modelling a range of spherical phenomena that appear across many disciplines of science and engineering. This paper considers the problem of robust estimation of spherical functions from acoustical datasets that may be noisy and incomplete. Employing a spherical harmonic model representation, and using a Bayesian formulation, prior covariance structures are designed for the spherical harmonic coefficients to reflect the prior knowledge which exists in this estimation setting. Taking an empirical Bayes approach, the prior distributions are optimized based on the available data to maintain a robust and flexible framework, and the final model estimate and confidence bounds can be obtained analytically from a well-defined posterior distribution. Numerical examples are presented for the estimation of head related transfer functions (HRTFs) and a sound source directivity pattern, demonstrating the favourable performance of the proposed method under challenging experimental conditions, especially when compared with common existing estimation techniques.
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