# Range Measurement from Range signal downlink

How is accurate time of round-travel determined from downlinked ranging signal?

AFAIK Ranging signal, used to determine distance of a spacecraft is usually a reference wave modulated and uplinked, passed through PLL (Phase Locked Loop) thus demodulated and then again modulated to a downlink signal which is demodulated by PLL at receiving ground station.

What are the steps that follow in calculating the distance of the spacecraft? How exactly is time of round trip calculated accurately ? How is time tagged to the wave downlinked?

A brief reference to Radiometric Tracking Techniques for Deep Space Navigation - C Thornton, J Border (Wiley, 2003) helped me to get this:

A Phase Locked Loop at receiving station produces a reference signal coherent with received signal. This reference signal is used by the ranging assembly to demodulate the downlink signal. The received range code is compared against a model of the transmitted range code to determine the round trip transit time. range measurements are quantized in steps referred to as range units(RU). The size of an RU depends on the frequency of the highest component of code, and is currently about 28cm. Doppler data are obtained by differencing the received reference signal with the station frequency reference.

Maybe I am connecting the dots wrong and completely unable to understand the process.

The transmitted ranging signal is generated by coherent frequency division from the frequency reference used to generate the uplink carrier. Usually a code consisting of a succession of frequencies is generated, starting with approximately 1 MHz and decreasing by factors of two to as low as approximately 1 Hz.

The spacecraft returns this uplinked time-varying code back to Earth. That the highest frequency is 1 MHz limits the range determination to 300 meter accuracy (at best). That's not bad for a spacecraft that is many astronomical units from Earth. The received downlink from the satellite provides the basis by which the receiving station determines the range to the satellite. Simply look for the transition between frequencies, and voila! the range is determined.

Actually, it's not as simple as that. The linked document goes into details as to why it's not that simple. But that is the basic concept.

• Thank you. I'd look up the reference to see the detailed process. On the second note, i think i have come across frequency response very often and i suppose 2MHz was mentioned, mostly while describing the pass band filter in the spacecraft transponder. I wish you check that out. Jan 28, 2015 at 15:34
• Maybe with techniques such as psuedo code ranging in modern times 1MHz might be the value they use but AFAIK most references (Mainly, those corresponding to the age of development of DSN) mention 2MHz when talking about ranging system operation. Jan 28, 2015 at 15:37
• The wavelength of a code with 1 MHz symbol rate is indeed 300 meters, but with reasonable SNR the symbol phasing can be determined to a small fraction (perhaps 2%) of the symbol period, i.e. 6 meters. Witness GPS, with a 1.023 MHz chipping rate and pseudorange accuracies in the single-digit meters - and that is with quite poor SNR. Jan 28, 2015 at 19:22
• @pericynthion you said "chipping rate" which means you know more than I do - can you take a look at my question here - I don't like to call an acceleration / deceleration of the received chipping rate due to relative velocity as a "Doppler shift" per se, is there another word for it?
– uhoh
Jul 26, 2016 at 1:29
• The link to the DSTSE.pdf document is much appreciated! Quite a lot of good reading there!
– uhoh
Jul 26, 2016 at 1:31