I will hold off a bit on describing the complications of adding telemetry and control to this “Coherent” Radio Link (and Micro-Space success in mastering them), and jump ahead to the navigational benefits. With the drift in measuring rocket velocity nominally eliminated by synchronizing the Down Signal to the received, Up Link Reference, the net Doppler shift (Frequency Offset) provides a very precise measurement of the rocket's “Radial Velocity”. (This is a signed speed, not a true, three dimensional velocity vector.) The integral of this velocity gives an equally accurate measurement of the rocket's distance from the communications receiver. In a vertical launch situation this provides a very good value for the rocket's altitude with time (with a correction for the prelaunch distance of the rocket from the radio antennas). .

These measurements, and all such measurements within the atmosphere, are modified by a radio transmission velocity a bit lower than the free space “Speed of Light”. The better known, optical correction is 0.03 percent (300 parts per million) with about a one part per million per degree temperature coefficient. The correction for radio transmission is probably a bit larger, and somewhat more variable. These corrections are for near sea level and decrease nearly exponentially with altitude, paralleling air density. For high vertical flight the total correction approaches 7 feet (2 meters). Note that identical effects are involved in RADAR and GPS distance measurement. Using reliable, predicted corrections, rocket altitude can be determined to a precision approaching 10 centimeters!

Even better than the absolute distance measurement are the Velocity and Acceleration measurements. Changes in distance – beyond this relatively constant refractive correction – can be measured with a precision of as little as one millimeter. Analyzed over a modest time interval, the velocity can be determined to a fraction of a millimeter per second, and the acceleration to micro-g resolution. All these accuracies are dramatically improved if the tracking processes occur entirely in space. For sounding rockets, the ability to document air drag in near vacuum conditions is phenomenal, and the possibility of testing low thrust (Ion, Plasma or MHD) propulsion very real.

“Integrating” the Doppler Shift of course involves counting the cycles of “Phase Shift” created by the motion. Comparing the transmitted Reference signal with the returned Down Signal produces a changing phase relationship as the number of RF cycles “tied up” in transit (round trip) changes. If the separation distance is constant, then the time delay and number of cycles tied up in transit are also constant and the phase relationship is static. An increasing distance increases the delay, tying up more cycles in transit. This reduces the received Down Signal frequency, so that it falls behind the Reference signal with a steadily increasing phase delay. Counting “Cycles” can be done with the “Up/Down “ counter techniques used with rotary encoders. With 500 MHz radio signals, each cycle represents 1 foot (0.3 meters) of distance change (2 ft = 0.6 meters round trip path length change).

But “Phase Shift” need not just be counted in full cycles. Many instruments (including those used in color TV work) measure phase shift to much better than 1/360 cycle = 1 degree of phase angle. This accuracy can even be maintained with fairly week RF signals (18 dB Signal to Noise ratio) if averaged over 100 times the communications “Data Bit” time window. (With a barely usable communications signal, the same phase accuracy could be maintained with a longer averaging interval.) And this “Phase Shift” resolution produces the 1 millimeter distance resolution mentioned with 500 MHz signals.

More on navigational uses of Phase Shift soon.