Augmented GNSS Differential Corrections Minimum Mean Square Error Estimation Sensitivity to Spatial Correlation Modeling Errors

Railway signaling is a safety system that has evolved over the last couple of centuries towards autonomous functionality. Recently, great effort is being devoted inthis field, towards the use and exploitation of Global Navigation Satellite System (GNSS)signals and GNSS augmentation systems in view of lower railway track equipments andmaintenance costs, that is a priority to sustain the investments for modernizing the local andregional lines most of which lack automatic train protection systems and are still manuallyoperated. The objective of this paper is to assess the sensitivity of the Linear Minimum MeanSquare Error (LMMSE) algorithm to modeling errors in the spatial correlation function thatcharacterizes true pseudorange Differential Corrections (DCs). This study is inspired bythe railway application; however, it applies to all transportation systems, including the roadsector, that need to be complemented by an augmentation system in order to deliver accurateand reliable positioning with integrity specifications. A vector of noisy pseudorange DCmeasurements are simulated, assuming a Gauss-Markov model with a decay rate parameterinversely proportional to the correlation distance that exists between two points of a certainenvironment. The LMMSE algorithm is applied on this vector to estimate the true DC, andthe estimation error is compared to the noise added during simulation. The results show thatfor large enough correlation distance to Reference Stations (RSs) distance separation ratiovalues, the LMMSE brings considerable advantage in terms of estimation error accuracy and precision. Conversely, the LMMSE algorithm may deteriorate the quality of the DCmeasurements whenever the ratio falls below a certain threshold.