A Method to Estimate the Ionospheric bias by Using the New GNSS Frequencies: An Analysis of its Theoretical Accuracy in a PPP Context

The modernization of the Global Positioning System (GPS) and the advent of the European Project Galileo will lead to a multifrequency Global Navigation Satellite System (GNSS). Single GNSS receiver observations could be used to estimate the ionospheric bias and smoothed pseudoranges which, in turn, can be exploited to better estimate the absolute position of the receiver and its clock correction. In fact, if we consider the satellite ephemerides and satellite clock corrections as perfect quantities (i. e. not affected by errors), the adjustment of GNSS observations is broken down into two parts. In addition, the least squares (LS) theory leads to a feasible adjustment in two steps, where covariance matrices can be explicitly written, studied and propagated from one step to the other, so that, a rigorous solution is finally obtained. This paper deals with the analytic representation of the above mentioned LS procedure and provides theoretical limits for the achievable accuracies of the parameter estimated considering different scenarios, including modernized GPS and Galileo systems. Furthermore, numerical tests with Galileo data simulated by GSSF (Galileo System Simulation Facility) have been carried out.