Bayesian and variational methods for discontinuity detection: theory overview and performance comparison

Discontinuity detection is of great relevance at different stages of the processing and analysis of geodetic time-series of data. This paper is essentially a review of two possible methods. The first method follows a stochastic approach and exploits the Bayesian theory to compute the posterior distributions of the discontinuity parameters. The epoch and the amplitude of the discontinuity are then selected as maximum a posteriori (MAP). The second method follows a variational approach based on the Mumford and Shah functional to segment the time-series and to detect the discontinuities. Whereas the original formulation was developed in a continuous form, discrete approaches are also available presenting some interesting connections with robust regressions. Both the methods have been applied to identify the occurrence of cycle-slips in GNSS phase measurements. Simulated and real data have been processed to compare the performance and to evaluate pros and cons of the two approaches. Results clearly show that both the methods can successfully identify cycle-slips.