The weak elastic string and some applications in geodesy

Abstract

This paper presents an edge detecting filter, known as “the weak elastic string”, and some of its possible applications in locating slips and outliers in geodetic time series. Basically, the weak elastic string is a mechanical rather than a stochastic filter. It is based on the concept of a weak continuity constraint, that is, a constraint that prefers the continuity of a function, but allows for occasional discontinuities if they simplify the overall description of the function. The performance of the filter is controlled by a few parameters that tune the filtering to the noise level in the data. Unlike methods based on statistical testing, the efficiency of the weak elastic string depends on the noise level. If the data are precise, the algorithm is extremely efficient due to its mechanical nature. In addition, the filter does not require mathematical modeling of the shape of the data. The algorithm is applied to edit time series of completely different nature: satellite altimetry sea surface heights and combinations of GPS phase and pseudo-range data. Finally, the filter is incorporated in the linear least squares estimator resulting in a completely geometric, robust and efficient least squares algorithm.