1. The Doppler Shift of Satellite Radio Beacons

Introduction

This project extends the acoustic Doppler analysis I developed to the analysis of Doppler shifts in radio frequency beacons from earth orbiting satellites. It is a low key, collaborative effort with my older son who suggested that we try it when he and his wife visited us at Christmas 2009.

We captured two passes of an amateur radio microsatellite (VO-52, HAMSAT) operating in a near circular polar low earth orbit. On the evening of December 25th (Dec 26 UTC) there were two useful passes, one to the east and one to the west of our location. We used the first to find the beacon and set up our recording and monitoring equipment. The second pass we took our first serious data. Then on the evening of December 26th (Dec 27 UTC) we took our serious data on the first pass of the evening using a modified recording setup.

We compare the satellite’s range as calculated from the Doppler shift analysis to that predicted by satellite tracking software. We found that in this example, the linear path model for the Doppler shift that I developed predicts the range remarkably well.

Data Acquisition

The data acquisition system was very simple, consisting of a Kenwood TS-700 S 2-meter all mode transceiver, a four-element, 2-meter Yagi antenna, and one or two MacBook computers. The radio was operated using the upper sideband (USB) filter so the actual frequency was taken to be the sum of the carrier frequency readout on the radio plus the audio frequency we measured in the audio analysis. We found that the beacon signal on the VO-52 satellite was strong enough and the beam on the antenna wide enough that we did not have to actively track the satellite. The antenna was repositioned once or twice during the pass.

The Doppler shift of the signal was much greater than the USB passband so the receiver had to be tuned downward several times during each pass.

The audio from the radio headphone jack was connected to the line input of the MacBook(s). A shortcoming of the Raven Lite software is that it has a one minute limit on the length of the recording. Since the satellite pass is several minutes long this required multiple recordings. This was the method we used on the first night. On the next night we split the audio to two computers, using one to monitor and record the signal with Raven Lite and using the other to make a continuous recording using a program called Audacity. Raven Lite also required a sampling rate of 44100 samples per second. Since the USB passband was less than 3 kHz that sampling rate was mostly wasted. Audacity allowed sampling at 8000 samples per second that was much better suited to these data.

Data Analysis

As has been done previously with the audio Doppler projects, a number of time/frequency pairs were extracted from the Raven Lite spectrograms of the audio recordings. The audio frequency was added to the radio frequency that the receiver was tuned to at the time. Recall that the radio had to be retuned several times during each pass. The spectrogram for the recording made with Audacity shows the effect of the receiver retuning.

For the curve fit, the time was taken to be the number of seconds into the pass from some arbitrarily chosen point. When the range data were compared, we scaled the seconds data to real time based on the file creation time. This is not an accurate timing method as will be discussed below.

The linear path Doppler shift function that I derived for the audio shifts was then fit to the time/frequency data using the curve fitter in Igor Pro. The only change to the function was to replace the speed of sound with the speed of light, 299, 792.458 km/sec

The fit results are shown:

Because the curve fit gives the time of closest approach, the distance or range at that time, and the velocity, we can calculate the range at other times during the pass. We used a satellite tracking program called PREDICT to estimate the range of the satellite based on the orbital elements and compared the two predictions. The comparisons are shown graphically:

Discussion

The linear path Doppler function fit to the satellite data remarkably well and the range data derived from the fit was also remarkably close to the range predicted by the orbital elements.

The velocity estimates are reasonably close to each other, especially when the differences in recording methods between the two nights are considered. In retrospect, it would have been nice to have data from the second pass on the evening of the 27th UTC using the continuous recording method. The continuous recording is obviously the preferred method.

All of the passes we studied were relatively low in the sky with a maximum elevation of roughly 30 degrees so the distance at closest approach was not the altitude but rather the “slant range”. Those values cannot be compared from pass to pass.

The beacon frequency is listed at 145.936 MHz. The Igor Pro curve fitter estimated the frequency on the Dec 26 UTC pass as 145.93726 MHz and on Dec 27 UTC as 145.93744 Mhz.  During the week after we made these estimates, my son made a recording of a terrestrial GPS disciplined beacon located in the Blue Ridge Mountains which showed his receiver to read about 661 Hz too high which explains about half the difference.

The measurement timing is an obvious issue for the segmented recording made with Raven Lite with our real time estimates being fast by about 40 seconds. The range comparison to the orbit based range are shown below with the Doppler estimates shifted backward by that amount.

The timing of the continuous Dec 27 UTC recording was much better.  A general solution would be to inject an accurate timing pulse based on GPS or WWV into the audio signal at every minute.

This project was done as an experiment. As with most experiments it raises more questions. With accurate timing, can data from two or more stations spaced a hundred miles or more apart be used to plot the actual orbit?  I was surprised by how well the linear model fit to the data.  On close examination though, the range estimates are only to within 10s of kilometers.  At least two factors would contribute to an improved model, definition of the orbital path and consideration of the observer motion due to the Earth’s rotation.