Backward smoothing for precise GNSS applications

The Extended Kalman filter is widely used for its robustness and simple implementation. Parameters estimated for solving dynamical systems usually require certain time to converge and need to be smoothed by a dedicated algorithms. The purpose of our study was to implement smoothing algorithms for processing both code and carrier phase observations with Precise Point Positioning method. We implemented and used the well known Rauch–Tung–Striebel smoother (RTS). It has been found out that the RTS suffer from significant numerical instability in smoothed state covariance matrix determination. We improved the processing with algorithms based on Singular Value Decomposition, which was more robust. Observations from many permanent stations have been processed with final orbits and clocks provided by the International GNSS service (IGS), and the smoothing improved stability and precision in every cases. Moreover, (re)convergence of the parameters were always successfully eliminated.