A system consisting of a base GPS receiver with a clear view of the sky, one or more remote GPS receivers with restricted views of the sky and a processing center that batch processes range information provided by the GPS receivers determines the positions of the remote GPS receivers to within tight tolerances. The base GPS receiver and the remote GPS receivers produce range information based on the satellite signals that the respective receivers can track at a given time, and provide the range information to the processing center. The range information includes both code and carrier measurements for each of the signals that are being tracked by the respective GPS receivers. The center collects the range information over an extended period of time, for example, hours, days or weeks, and then batch processes the collected information in multiple passes through the data, to calculate the precise latitude, longitude and height of the receiver. The center batch processes the data using a floating ambiguity filter that, after a first pass through the data, is initialized with the position calculated in an earlier pass. The center also calculates the quality of the collected range information by fixing the position and position covariance of the floating ambiguity filter and using double differences with the base GPS receiver measurements, to ensure that the information used in subsequent position calculations is sufficiently reliable.