Abstract | It is a trivial notion that all measurements contain error or noise. To derive meaningful physical units from our measurements we need to keep error and noise as small as possible and we need to know how to handle them. How much of a problem noise is, depends on its nature. We are using laser altimetry data to derive tidal parameters 1–3. In our simulations, Gaussian noise has been shown to be have only a low impact on the resulting Love numbers. However, the Cauchy distributed noise strongly affects our results. The Cauchy distribution has long tails which translates to outliers in the data. Cauchy distribution is a “pathological” distribution: it has no defined expectant value or variance; simply cutting out outliers won’t improve results. We look into weighted nuclear norm minimization (WNNM) for regularization of our input data, an approach that has recently been used in regularization of images with Cauchy noise4.
1. Thor, R. N. et al. Determination of the lunar body tide from global laser altimetry data. J. Geod. 95, 4 (2020).
2. Thor, R. N. et al. Prospects for measuring Mercury’s tidal Love number h2 with the BepiColombo Laser Altimeter. Astron. Astrophys. 633, A85 (2020).
3. Stenzel, O. J., Hall, I. & Hilchenbach, M. Mercury Tide Parameter Estimation from Laser Altimeter Records. 2678, 1990 (2022).
4. Kim, G., Cho, J. & Kang, M. Cauchy Noise Removal by Weighted Nuclear Norm Minimization. J. Sci. Comput. 83, 15 (2020).
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