Weighted Total Least Squares RAIM Algorithm Using Carrier Phase Measurements

This paper proposes a weighted total least squares approach based on both pseudorange and carrier phase measurements. The paper makes use of the weighted total least squares solution to solve the global positioning system (GPS) navigation equation determining the user position. The total least squares estimation considers both measurements vector and observable data matrix errors which common least squares approach not. This means that the total least squares approach provides a value that evaluates the "magnitude" of the mismatch between the observable ephemerides data and the measurements. This value can be used as a measure for fault detection in a receiver autonomous integrity monitoring (RAIM) algorithm. Another output given by the total least squares, uncorrelated with the first one, provides another test statistic to the RAIM algorithm. The RAIM algorithm focus was the position vertical component that is actually the critical component on the position estimation as well as for navigation purposes, since it produces the highest error in the overall error budget. The minimum requirements, for the Global Navigation Satellite System (GNSS) guide in aviation, will be the performance metrics of the RAIM algorithm proposed. A comparison between the receiver autonomous integrity monitoring algorithm based on the total least squares and the proposed one that considers also the carrier phase measurements was made, proving a better precision on the positioning accuracy and higher performance concerning the receiver autonomous integrity monitoring of the combined measurements (code and carrier).