IMPROVED DIRECT SOLUTION OF THE GLOBAL POSITIONING SYSTEM EQUATION

A known direct solution of the global positioning system (GPS) equatio n, which yields user position and clock bias, is examined and tested u sing real GPS data, A comparison of the position computed using this s olution with that obtained using the popular iterated least-squares so lution reveals that the direct solution is in error by up to 4 m. An i mproved direct solution is presented, which takes into account the noi se associated with the pseudorange measurements. The position error ob tained when using this solution is an order of magnitude smaller than that generated by the direct solution, Finally, an iterated solution, which is based on the improved direct solution, is presented. The accu racy of the latter is comparable to that of the iterated least-squares solution of the GPS equation, The advantage of the new algorithm over that of the iterated least-squares solution is in its fast convergenc e rate. This advantage could be particularly important in space missio ns, where the initial guess may be far off from the real position.