The integrated Doppler offset, in the phased locked link systems, is of course the number of RF cycles that can fit into the round trip time delay. The physical distance measurement is no more precise (as an absolute measurement) than the frequency control used to create the Radio Frequency. As noted earlier, with care, this can easily approach one part per million, and with a “GPS Disciplined, Ovenized crystal oscillator”, can approach one part per billion. But only CHANGES in distance are determined by counting the “cycles” of Doppler Shift. A variety of space applications will have unavoidable interruptions, and this will create a multi cycle indeterminacy in the distance measurement. Using these techniques to quantify orbital flight is one example, with no signal for a large fraction of each orbit.

Yet is it possible to modify these techniques to identify the integral cycle count, and then add the fractional cycle phase data for ultimate resolution. (Exactly this is done with GPS systems capable of analyzing “Carrier Phase” for millimeter differential resolution. Those techniques, however, rely on a phenomenally accurate onboard clock rather than round trip, phase lock, corrections. We will not duplicate that technique in our tiny spacecraft.)

The key to doing this is to modify the link signals so that they are NOT an continuous, single frequency. Any detectable modulation of course does this. Any data echoed from the command uplink to the telemetry downlink will of course demonstrate and confirm the total path delay. But with low power, narrow band systems, it may be difficult to analyze this delay to an accuracy better than 30 microseconds, corresponding to almost 10 km path uncertainty or 5 km range. We need 10,000 times better accuracy to eliminate the cycle count indeterminacy.

For relatively static situations, one way to do this is to unlock the RF frequency from the reference, and slide it gradually to an offset frequency. Measuring the changing “integrated Doppler count” in the process gives us an estimate of the total path delay. (Count change = frequency change * path delay time). Gradually returning it to the initial frequency restores our desired measurement mode, and identifies small motions which may have occurred during the process. For highly dynamic situations, generating continuous offset frequencies is preferable.

This is surprisingly easy to accomplish. A small cyclic phase modulation will generate a pair of weak sidebands around the carrier. Since these have a predictable offset from carrier, very narrow band receiver techniques can be used to capture and identify the phase of these sidebands. (It is actually a challenge to PREVENT these sidebands in Digital RF Generator systems, like PLLs.) With no need to carry information, these sidebands may be - 40 dB (10,000 times lower power) relative to the carrier, and still be reliably captured. These can be looked at either as producing a “time code” to better measure the path delay, or as generating offset frequencies for analysis: two different conceptual views of the same process, which yield the same result. In fact, one or more intermediate frequencies (or more complex time codes) are desired to achieve the resolution we want. The maximum frequency in this subcarrier modulation should be about 1 MHz, in our 433 MHz link, to allow a one degree phase resolution to approach one “integrated Doppler cycle” of path delay. Once this is identified, the absolute distance uncertainty drops into the millimeter range, as discussed previously.

These procedures allow the full resolution of this technique to be used when the communications link is periodically interrupted, as it must be for a spacecraft traveling to the Moon and monitored from the Earth.