A system for determining positions of fixed-position GPS receives that have restricted views of the sky includes a data recording and control center, and one or more base GPS receivers with associated antennas with a substantially unrestricted views of the sky. The system batch processes range information provided by the fixed-position GPS receivers over an extended period of time; determining which of the range data from the fixed-position receivers are valid, and using the valid range data to determine position. In this way, the precise positions of the respective fixed-position slave GPS receivers can be calculated, even if the fixed-position GPS receivers are able to observe and collect data from sets of two or more satellites for only three or four relatively short time intervals at various sky positions during the extended period.