Enhanced pseudorange weighting scheme using local redundancy

The absolute positioning is the most common GNSS operational mode, being used, for instance, by ships satellite receivers; it is based on pseudorange measurements and its functional model, relating measurements to unknowns, is well defined. On the other hand the stochastic model, describing the measurement error behaviour, is currently under investigation and could be used to reduce the position errors, by defining a suitable weighting scheme. In signal-degraded scenario, as high density traffic harbours or canals, a weighted approach is especially suited, because the pseudorange accuracies are significantly different, so equally weighting all the measurements would bring to large errors. The redundancy numbers are the diagonal elements of the redundancy matrix and they represent the degree of controllability of the measurements; a large 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. In this work, the redundancy number is proposed as indicator, in addition to the largely adopted signal-to-noise ratio and satellite elevation angle, for defining a weighting scheme, based on the concept of limiting the effect of leverage measurements.