On Estimating Map Model Errors and GPS Position Errors: (Applying More Science to the Art of Navigation)

In order to decide whether a desired manoeuver can or cannot be safely undertaken, a prudent navigator must be aware of both the current spatial uncertainty of his vehicle's positioning system and the spatial uncertainty of the navigational map model being used to depict the theatre of operations. From this safety to navigation perspective, knowledge of data accuracy is as important as the data itself. This paper discusses the Electronic Chart (EC) implications of both GPS vehicle positioning errors and the relatively large data modeling errors specific to bathymetric map models (charts). It proposes and demonstrates software solutions which statistically evaluate both of these spatial uncertainties and graphically integrates the two stochastic models within an EC environment. The paper also documents an experiment carried out by the Canadian Hydrographic Service, designed to insure that real-time DGPS users compute statistically valid position error estimates. The experiment ground truthed the position error estimates obtained using a conventional real-time error analysis of pseudo-range redundancy. Using this ground-truth information, an improved pseudo-range error model was empirically determined. The new pseudorange error model is continually updated using the estimated pseudo-range variances computed by the Novatel GPS receiver rather than applying the constant a priori pseudo-range variance typical in least-squares adjustments. This dynamic range error model effectively reduced the statistical bias between the observed errors and their predicted error estimates. The improved range error model also significantly improved the performance of the position solution. All DGPS positions computed by the modified software had a positional accuracy of better than 0.5 metres