Improvement of Positioning Accuracy with GNSS Using User Range Accuracy and Posterior Variance Model

Abstract

Although Global Navigation Satellite System (GNSS) has found extensive applications in civil aviation operation, it could not meet the requirements of positioning accuracy when aircraft are in the approaching phase, especially in the vertical direction. Further improving the positioning accuracy of GNSS is of significance in pushing forward the applications of GNSS in this area. Weight estimation matrix in the least squares algorithm helps in further improving the accuracy of positioning with GNSS. A great weight indicates the ranging error from a satellite is less than that from other satellites. Researchers aiming at improving the accuracy with weight matrix usually take the reciprocal of ranging standard deviations or elevation angles from satellites as weight elements in a weight estimation matrix for the least squares iterative algorithm. User range accuracy (URA) is a factor indicating the quality of ranging from a satellite to a receiver. Positioning accuracy could be expected to be improved by taking this index combined with the elevation angle and other considerations as weight elements in the weight estimation matrix. For implementing the idea above, the weight estimation model based on satellite elevations and user range accuracy is implemented. With GPS alone, a weight element estimation model is set and a weight matrix is established. Data for positioning calculation are extracted from navigation messages in a receiver. Positioning errors from each iterative calculation are plotted according to three coordinate axes and the comparisons are made with the results with considering user range accuracy index. The means and the standard deviations in each coordinate axis are given by analyzing the positioning results. Circular error probable (CEP) is also shown for well comparing the accuracy of positioning with/without taking into account factors that affect weight matrix. The same procedure is made with the posterior variance model based on pseudo-range deviation value, showing the improvement of accuracy with this model. Experimental results show that the positioning accuracy of posterior variance model is better than traditional least squares positioning algorithm. The positioning algorithms which adopt weights estimation model and posterior weight model have the potential in airborne GNSS receivers to improve the position accuracy.