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Open AccessArticle

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

1
Department of Electronics and Telecommunications, Politecnico di Torino,Corso Duca degli Abruzzi 24, 10129 Turin, Italy
2
Ansaldo STS, S.p.A, Via Paolo Mantovani 3-5, 16151 Genoa, Italy
*
Author to whom correspondence should be addressed.
Sensors 2014, 14(6), 10258-10272; https://doi.org/10.3390/s140610258
Received: 17 April 2014 / Revised: 4 June 2014 / Accepted: 5 June 2014 / Published: 11 June 2014
(This article belongs to the Special Issue Positioning and Tracking Sensors and Technologies in Road Transport)
Railway signaling is a safety system that has evolved over the last couple of centuries towards autonomous functionality. Recently, great effort is being devoted in this field, towards the use and exploitation of Global Navigation Satellite System (GNSS) signals and GNSS augmentation systems in view of lower railway track equipments and maintenance costs, that is a priority to sustain the investments for modernizing the local and regional lines most of which lack automatic train protection systems and are still manually operated. The objective of this paper is to assess the sensitivity of the Linear Minimum Mean Square Error (LMMSE) algorithm to modeling errors in the spatial correlation function that characterizes true pseudorange Differential Corrections (DCs). This study is inspired by the railway application; however, it applies to all transportation systems, including the road sector, that need to be complemented by an augmentation system in order to deliver accurate and reliable positioning with integrity specifications. A vector of noisy pseudorange DC measurements are simulated, assuming a Gauss-Markov model with a decay rate parameter inversely proportional to the correlation distance that exists between two points of a certain environment. The LMMSE algorithm is applied on this vector to estimate the true DC, and the estimation error is compared to the noise added during simulation. The results show that for large enough correlation distance to Reference Stations (RSs) distance separation ratio values, the LMMSE brings considerable advantage in terms of estimation error accuracy and precision. Conversely, the LMMSE algorithm may deteriorate the quality of the DC measurements whenever the ratio falls below a certain threshold. View Full-Text
Keywords: GNSS; augmentation system; reference station; differential correction; linear MMSE; correlation distance GNSS; augmentation system; reference station; differential correction; linear MMSE; correlation distance
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Kassabian, N.; Lo Presti, L.; Rispoli, F. Augmented GNSS Differential Corrections Minimum Mean Square Error Estimation Sensitivity to Spatial Correlation Modeling Errors. Sensors 2014, 14, 10258-10272.

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