Wiener Filter Modifications for Gravity Field Data Using Different Resolution Levels and Non- Stationary Noise

Abstract. One of the most basic tools in optimal spectral gravity field modelling is the method of Wiener filtering. Originally developed for applications in analog signal analysis and communication engineering, Wiener filtering has become a standard linear estimation technique of mod-ern operational geodesy, either as an independent practical tool for data ‘de-noising ’ in the frequency domain or as an integral component of a more general signal estimation methodology (input-output systems theory). Its theoretical framework is based on the Wiener-Kolmogorov linear pre-diction theory for stationary random fields in the presence of additive external noise, and thus it is closely related to the (more familiar to geodesists) method of least-squares collocation with random observation errors. The main drawbacks of Wiener filtering that make its use in certain geodetic estimation applications problematic stem from the stationarity assumption for both the signal and the noise involved in the approximation problem. In this paper, we introduce a modified Wiener-type linear estimation filter that can be used with noisy data obtained from an arbitrary deterministic field under the masking of non-stationary random observation errors. In addition, the sampling reso-lution of the input data is explicitly taken into account within our estimation algorithm, resulting in a resolution-dependent optimal noise filter. 1 Introduction – Proble