**Abstract**

The chapter describes effective algorithms that are often used in processing data measurements in Global Navigation Satellite Systems (GNSSs). Existing effective algorithm was developed for detection and elimination of outliers from GNSS data measurements. It is based on searching for a so-called optimal solution for which standard deviation and maximum absolute deviation of the measured data from mean values do not exceed specified threshold values, and the number of the detected outliers is minimal. A modification of this algorithm with complexity of *N* log <sup>2</sup>*N* is discussed. Generalization of the existing algorithm to the case when data series included some unknown trend will be presented. The processing trend is assumed to be described by an unknown function of time. The generalized algorithm includes the outlier detection algorithm and trend searching algorithm that has been tested using simulated data. A new algorithm will be presented for cycle slip repair using Melbourne-Wübbena linear combination formed from GNSS data measurements on two carrier frequencies. Test results for repair data in the case of multiple (cascade) cycle slips in actual observation data will also be presented in this chapter.

**Keywords:** global navigational satellite systems (GNSSs), GNSS measurements, outliers, data screening, optimal solution, trend function, Melbourne-Wübbena combination, cycle slips
