Using local redundancy to improve GNSS absolute positioning in harsh scenario

In GNSS context, absolute positioning is a widespread operational mode, largely used in many field activities as automotive, aerospace and ships navigation. The functional model of absolute positioning, relating pseudorange measurements to unknowns, is well defined, while its stochastic model, defining the behavior of measurement error, is currently under investigation and is the core of this work. A realistic model of measurement error can be used to define a weighting scheme, able to reduce the positioning errors; a weighted approach is mainly necessary in signal-degraded scenario, where pseudorange accuracies are significantly different and equally weighting all the measurements would yield very large errors. The quality indicators, commonly adopted to define a pseudorange error model, are the signal-to-noise ratio and the satellite elevation angle. In this work, an additional indicator, the redundancy number, is introduced. The redundancy numbers are the diagonal elements of the redundancy matrix and they represent the degree of controllability of the measurements; a large value of the redundancy number corresponds to a well-controlled measurement, while a small one corresponds to a leverage observation, with a high potential to influence the solution. The benefits of using the proposed weighting schemes is demonstrated in urban canyon and with single (GPS only) or multiple (GPS/Glonass) constellations.