An embodiment of the present invention is a shipboard GPS positioning system having data links to outlying tailbuoys equipped with respective GPS receivers. On ship, an Intel 386-based microcomputer system collects data from various ship's equipment including the ship's GPS receiver and data from the several tailbuoy units. A computer-implemented process located in the microcomputer system controls the following processes. Periodically each GPS receiver produces updated pseudo ranges (PRs) and these are time-tagged. The time-tagged PRs for the ship are aligned according to their time tags with their counterpart PRs from the tailbuoys. The raw PRs are then passed through a Kalman mathematical filter to produce filtered pseudo-ranges (PRs). A position solution is then attempted for each GPS receiver using the PRs. The filters provide statistical data that is used to rate the quality of each PR in a weighted least squares solution process. Special measures are included to provide quality control/quality assurance, including the use of error ellipses on the display to present a graphic indication of expected solution accuracy, and the use of real time fault detection, isolation, and correction algorithms when redundant satellite information is available.