A stochastic sigma model for GLONASS Satellite pseudorange

The GLONASS (Global Navigation Satellite System) is a satellite positioning system able to provide various numbers of air, marine, and any other type of users with all-weather three-dimensional positioning, velocity measuring, and timing anywhere in the world or near-earth space. As known, a GLONASS receiver performs passive measurements of pseudoranges and pseudorange rate of at least four GLONASS satellites as well as receives and processes navigation messages contained within navigation signals of the satellites. The navigation message supplies the satellites' position both in space and in time. Combined processing of the measurements and the navigation messages of the four (three) GLONASS satellites allows users to determine three (two) position coordinates, three (two) velocity vector constituents, and to refer user time scale to the national reference time UTC (SU). The purpose of this work was to define a stochastic model for pseudorange variances of GLONASS satellites able to provide its estimation. This evaluation is made for all satellites as a function of the elevation, independently of the user position, starting from real data. To achieve this goal, a suitable software tool MATLAB® is developed. The tool is able to create a GLONASS sky from the broadcast ephemeris, to compute the pseudorange error and to process it. The used data are extracted from observation and navigation RINEX files (containing both GPS and GLO-NASS measures). From the known receiver position and the computed satellite coordinates, the geometric range is obtained and compared with the pseudorange measurement, in order to achieve the pseudorange variance and build the model. In order to validate the sigma stationary stochastic model, the results are compared with further data obtained from different stations. The purpose of this work was the creation of an σ model particularly adapted in application as personal navigation device, characterized by the need of a real-time positioning and by a low computational power. The accuracy in real-time positioning can be improved, using a weighted least square (WLS) method for GNSS (GPS, GLONASS, and in the future GALILEO or other feasible systems) measurements. For GPS measurements, several suitable σ models for the WLS implementation are already in use; for GLONASS (or GLONASS-GPS together), the same is not available. So, there is need of studies about this topic. © Società Italiana di Fotogrammetria e Topografia (SIFET) 2011.