Doppler-Based GNSS Variometry for Velocity Estimation in High-Dynamic Sounding Rocket Missions

Imagine you are trying to track a hummingbird zooming through a storm. To know exactly where it is and how fast it's going, you might try to take a series of high-definition photos. If the bird moves too fast or the wind shakes the camera, the photos might come out blurry or missing entirely. This is the challenge of tracking high-speed objects like rockets. Scientists use a system called GNSS (the same technology that guides your phone) to listen to signals from satellites. Usually, they try to measure the "phase" of the signal—think of it as counting the exact number of waves in a sound—to get incredibly precise speed data. However, when a rocket blasts off with massive force, the signal can get scrambled, and those precise wave counts get lost. This leaves scientists with a gap in their data right when they need it most: during the most exciting, high-speed part of the flight. The big question is: if the high-definition photos are gone, can we still figure out the speed using a simpler, more rugged method?

This research paper dives into that exact problem by testing a clever workaround on real sounding rockets. The authors, Carolina Ghini and Augusto Mazzoni from Sapienza University, decided to stop trying to count the waves and instead listen to the "pitch" of the signal, known as the Doppler shift. It's like how a siren sounds higher as an ambulance speeds toward you and lower as it speeds away. While this method isn't as perfectly precise as counting waves, it is much tougher and less likely to break when things get chaotic. The team launched two small rockets—one in Roccaraso, Italy, and another in Texas, USA—carrying a lightweight, off-the-shelf computer setup. They compared the "wave-counting" method against the "pitch-listening" method during the flights. The results suggest that while the wave-counting method is smoother when things are calm, it often fails to capture the rocket's speed peak during the intense boost phase. In contrast, the Doppler method kept working the whole time, successfully tracking the rocket's speed even when the other method gave up.

The Story of the Two Rockets

To understand what happened, let's look at the two missions the team flew. The first rocket, launched in Italy in May 2025, had a "normal" flight. It shot up, coasted to a peak height of about 1,200 meters, and then gently drifted down with a parachute. The second rocket, launched in Texas in June 2025, was a bit more dramatic. It had a stronger engine and flew higher (about 2,600 meters), but things went wrong. The airbrakes didn't work right, and the parachute failed to open. This meant the rocket didn't slow down gently; instead, it fell back to Earth in a fast, uncontrolled dive.

The team equipped both rockets with a simple payload: a Raspberry Pi computer and two small GPS chips. They set these chips to listen to satellites at different speeds—some listening once per second (1 Hz) and others listening faster (2 Hz or 5 Hz). Their goal was to see if they could calculate the rocket's speed just by looking at the raw data the chips collected, without needing a complex navigation system.

The Two Ways to Listen

The paper compares two main ways to figure out speed:

1. The "Wave Counter" (Carrier-Phase): This is the high-precision method. It tries to count the exact number of radio waves between the satellite and the rocket. It's like trying to measure a distance by counting every single step you take. It's super accurate, but if you trip or the ground shakes (like during a rocket launch), you lose your count.
2. The "Pitch Listener" (Doppler): This method looks at how fast the signal's frequency is changing. It's like listening to a train whistle change pitch as it zooms past. It's not as precise as counting steps, but it's very hard to lose track of. Even if the train is shaking, the whistle still changes pitch.

What They Found

The results were a clear lesson in "robustness over perfection."

The Italian Flight (Roccaraso):
During the smooth Italian flight, the "Wave Counter" method was indeed more precise when it worked. However, it had a major flaw: it stopped working during the most important part of the flight—the boost phase when the rocket was accelerating fastest. Because the rocket was shaking so hard, the signal got lost, and the data was full of holes. When the team tried to reconstruct the speed, the "Wave Counter" missed the peak speed entirely, only reaching about 120 m/s instead of the actual 150 m/s.

The "Pitch Listener" (Doppler), on the other hand, never stopped talking. It kept recording data the whole time. Because it didn't lose the signal, it successfully captured the rocket's peak speed of 150 m/s. While its numbers were a little "noisier" (less precise) than the wave counter, it gave a complete picture of the flight.

The Texas Flight:
The Texas mission was even more chaotic. Here, the "Wave Counter" method failed completely. The signal was so disrupted that the team couldn't get any usable speed data from it at all. The "Pitch Listener" was the only thing that worked. It managed to track the rocket all the way through the high-speed ascent and the wild, uncontrolled fall.

Interestingly, the team found that listening faster (2 Hz) actually helped capture the details of the flight better than listening slower (1 Hz). On the Texas flight, the 2 Hz setting did a superior job of approximating the rocket's peak speed, missing it by only a few meters per second, whereas the 1 Hz setting underestimated the speed by a huge margin (about 80 m/s). However, the team also noticed that the rocket's internal clock—the "metronome" keeping time for the data—behaved differently depending on the speed. At 1 Hz, the clock was surprisingly stable. But at 2 Hz, the clock started to wobble more, likely because the faster sampling rate was more sensitive to the violent vibrations and thermal changes of the chaotic flight. So, while the faster 2 Hz setting provided a more accurate speed reading, it also exposed the hardware to more stress, causing the clock to drift more.

The Takeaway

The paper suggests that for high-speed rockets, especially during the violent boost phase, the "Pitch Listener" (Doppler) is the more reliable tool. It might not be as perfectly precise as the "Wave Counter," but it doesn't quit when things get tough. The authors found that Doppler-based variometry is a robust way to estimate speed when the more precise methods are likely to fail due to signal loss.

They also looked at the rocket's internal clock, which acts like a metronome for the data. They found that on the chaotic Texas flight, the clock started to wobble more when listening at higher speeds (2 Hz) compared to lower speeds (1 Hz). This confirmed that the harsh environment of the flight was affecting the hardware, making the "Pitch Listener" even more valuable because it could handle that wobble better than the fragile "Wave Counter."

In short, if you want to track a rocket that might shake itself apart, don't rely on the method that requires perfect silence. Listen to the pitch, and you'll hear the whole story.