A truncated nuclear norm regularization model for signal extraction from GNSS coordinate time series

Abstract

Precise signal extraction of Global Navigation Satellite System (GNSS) coordinate time series is of great significance for explaining geophysical phenomena. In this study, the low-rank characteristic of the Hankel matrix induced by the noise-free signals is utilized to recover the trend and seasonal signals from the observed GNSS coordinate time series. To this end, we first investigated the low rank characteristic of the Hankel matrix induced by the GNSS coordinate time series, then a Truncated Nuclear Norm Regularization (TNNR) technique was proposed by truncating the largest few singular values and minimizing the sum of the remaining singular values, so that the rank of matrix can be well approximated from its noisy data. To solve the minimization problem, an iterative technique called Accelerated Proximal Gradient Line-search (APGL) was employed by dividing the objective function into a closed non-smooth function and a convex smooth function. Further, an improved iterative procedure called TNNR-APGLM was proposed to boost the reconstruction performance of TNNR-APGL. Extensive experiments were carried out on simulated as well as real GNSS datasets to evaluate the performance of the TNNR-based methods. Experimental results indicate that the proposed scheme offers competitive performance with respect to the indicators such as misfit, trend uncertainty and residual power spectral density when compared with several State-Of-The-Art (SOTA) methods.