Summary

Differencing is an ingenious approach to minimizing the effect of biases in both pseudorange and carrier phase measurements. It is a technique that largely overcomes the impossibility of perfect time synchronization. Double differencing is the most widely used formulation. Double differencing still contains the initial integer ambiguities, of course. And the estimates of the ambiguities generated by the initial processing are usually not integers; in other words, some orbital errors and atmospheric errors remain. But with the knowledge that the ambiguities ought to be integers, during subsequent processing, it is possible to force estimates for the ambiguities that are, in fact, integers. When the integers are so fixed, the results are known as a fixed solution, rather than a float solution. It is the double differenced carrier phase based fixed solution that makes the very high accuracy possible with GPS.

However, it is important to remember that multipath, cycle slips, incorrect instrument heights, and a score of other errors whose effects can be minimized or eliminated by good practice are simply not within the purview of differencing at all. The unavoidable biases that can be managed by differencing— including clock, atmospheric, and orbital errors—can have their effects drastically reduced by the proper selection of baselines, the optimal length of the observation sessions, and several other considerations included in the design of a GPS survey. But such decisions require an understanding of the sources of these biases and the conditions that govern their magnitudes. The adage of, “garbage in, garbage out,” is as true of GPS as any other surveying procedure. The management of errors cannot be relegated to mathematics alone.