Theoretically correct decimation of GPS data

As the spectrum of GPS applications continuously widens, it becomes usual to collect GPS data at a high rate and to decimate them to slower rates depending on the applications. It is shown in this paper that the decimation process is not as trivial as it sounds. Some important rules are presented that have to be observed for the decimation to be theoretically correct. Two decimation algorithms are proposed. The first one follows these rules, but it is shown that it gives rather poor results in terms of measurement noise (yielding a noise reduction by a factor of 2 for a decimation from 1 to 30 seconds). The second one is not perfectly “correct”, but is more successful in reducing the noise (achieving a reduction by a factor of 5.5 for a 1–30 decimation), and it proves to be adequate for all practical purposes.