Comparison calibration system for digital-output infrasound sensors

This paper presents a comparison calibration system that achieves phase synchronization between analog reference standards and digital-output MEMS infrasound sensors, demonstrating its effectiveness by characterizing the sensitivity and phase delay of a specific module to enable more reliable high-density monitoring networks.

The Gist

The Big Picture: Listening to the Earth's "Hum"

Imagine the Earth is constantly humming a very low, deep song. This "song" is called infrasound. It's the sound of volcanoes rumbling, tsunamis rolling in, or even nuclear tests happening far away. The frequencies are so low that human ears can't hear them, but special sensors can.

For a long time, scientists have used expensive, high-tech microphones to listen to this hum. But these sensors are like luxury sports cars: they are accurate, but they cost a fortune and are heavy. You can only afford to park a few of them in a city.

Recently, engineers invented a new kind of sensor using MEMS (Micro-Electro-Mechanical Systems). Think of these as the Toyota Corollas of the sensor world. They are tiny, cheap, and digital. Because they are so affordable, we could potentially build a massive network of them—thousands of sensors spread out everywhere—to get a much clearer picture of the Earth's hum.

The Problem:
While these "Corolla" sensors are cheap and easy to set up, nobody knew exactly how well they performed. Specifically, we didn't know if they were "in tune" with the real world. If one sensor hears a sound a split-second later than another, it throws off the math used to find out where the sound came from. It's like trying to figure out where a thunderstorm is by listening to your friends, but one friend is wearing headphones that delay the sound by 10 seconds. You'd think the storm is miles away when it's actually right next door.

The Solution: The "Time-Travel" Calibration Lab

The authors of this paper built a special testing lab to fix this problem. Their goal was to create a system that could compare the cheap digital sensors against a "Gold Standard" (a super-expensive, highly accurate reference microphone) and, crucially, synchronize their clocks perfectly.

Here is how they did it, using a few metaphors:

1. The Sound Chamber (The "Quiet Room")

They built a small, sealed box. Inside, they played a pure, low-frequency tone (like a single note on a piano, but very deep).

• The Setup: They put the "Gold Standard" microphone and the cheap digital sensor right next to each other in this box.
• The Goal: Both sensors hear the exact same sound at the exact same time.

2. The Synchronization Problem (The "Two Watch" Dilemma)

This is the tricky part.

• The Gold Standard outputs an analog signal (a continuous wave of electricity).
• The Digital Sensor outputs a list of numbers with timestamps (e.g., "At 12:00:01, pressure was 50").

Usually, when you compare two things, you look at them at the same time. But here, the digital sensor is writing its own diary, and the Gold Standard is being recorded by a computer. How do you make sure the diary entry "12:00:01" matches the computer's recording of "12:00:01"?

If the digital sensor's internal clock is slightly slow or fast, the whole comparison falls apart.

3. The Magic Trick: The "Pulse Per Second" (PPS)

To solve this, the researchers used a Pulse Per Second (PPS) signal.

• The Analogy: Imagine a giant, atomic clock tower in the sky that drops a giant ball exactly every second, hitting a bell. Ding!
• The Execution:
  1. They connected this "Ding" signal to both the computer recording the Gold Standard and the digital sensor.
  2. When the "Ding" happened, the computer knew, "Okay, I am starting my recording right now."
  3. The digital sensor also knew, "Okay, I am starting my diary right now."
  4. Because both started at the exact same "Ding," their timelines were perfectly aligned, even though they were using different internal clocks.

What They Found

They tested a specific digital sensor (a DPS310 chip paired with an ESP32 computer) and found two main things:

1. The Volume (Sensitivity) was Good: The cheap sensor was almost as good at measuring how loud the sound was as the expensive one. It was within a few percent of accuracy.
2. The Timing (Phase) was Delayed: The cheap sensor was consistently 10 milliseconds late.
   • The Metaphor: Imagine you and a friend are clapping your hands to a beat. Your friend claps exactly on the beat. You clap, but you are always a tiny fraction of a second late. You aren't clapping at the wrong volume; you're just slightly out of sync.
   • Why it matters: In infrasound, a 10-millisecond delay can make a volcano look like it's in a different country. But now that the scientists know about this delay, they can add a "correction factor" to the data. It's like telling your friend, "Just clap 10ms earlier next time," and suddenly you are perfectly in sync.

The "Clock Drift" Issue

They also discovered that the cheap sensors have "wobbly" internal clocks. Over time, the sensor's clock might drift, getting slightly faster or slower.

• The Fix: They found that if you reset the sensor's clock every 10 minutes using the "Ding" signal (PPS), the error stays small enough to be manageable.

The Conclusion: Why This Matters

This paper is a roadmap for the future. It proves that we can use these cheap, tiny sensors to build massive networks to monitor natural disasters.

• Before: We had a few expensive sensors, and we weren't sure if the cheap ones could be trusted.
• After: We have a method to calibrate the cheap ones. We know exactly how to fix their timing errors.

The Takeaway:
Just because a sensor is cheap and digital doesn't mean it's useless. With the right "tuning" (calibration) and a way to sync the clocks (the PPS signal), these little sensors can become a powerful, global ear for listening to the Earth's most dangerous secrets. We can now build a "coral reef" of sensors instead of just a few "whales," giving us a much better view of the world.

Technical Summary

1. Problem Statement

Infrasound monitoring is critical for detecting natural disasters (e.g., volcanic eruptions, tsunamis) and anthropogenic events (e.g., nuclear tests). While the International Monitoring System (IMS) relies on high-precision analog sensors, these are expensive and bulky, limiting the density of measurement networks.

• The Shift to MEMS: Micro Electro-Mechanical Systems (MEMS) offer a cost-effective, compact alternative for creating high-density sensor networks. These modules typically combine a MEMS pressure sensor with a microcontroller to output timestamped digital data.
• The Calibration Gap: Manufacturers provide specifications for static pressure but lack data on dynamic frequency response (sensitivity modulus and phase).
• The Core Challenge: Calibrating digital-output sensors is difficult because:
  1. Primary calibration methods for frequencies below a few Hz are still developing.
  2. Phase Synchronization: Unlike analog sensors where signals are digitized simultaneously by a single converter, digital sensors output data with internal timestamps. Comparing these against an analog reference requires precise time synchronization to ensure phase alignment, which is non-trivial due to communication latency and clock drift.

2. Methodology

The authors developed a comparison calibration system designed to synchronize analog reference signals with digital sensor outputs.

A. System Design & Requirements

• Acoustic Environment: A sealed chamber (220 mm × 300 mm × 250 mm) was constructed to ensure uniform sound pressure (<0.6% modulus variation, <0.1° phase variation) in the 0.2 Hz to 20 Hz range. A loudspeaker generated sinusoidal waves up to 2 Pa.
• Reference Standard: A Brüel & Kjær (BK) Type 4160 laboratory microphone, pre-calibrated via laser pistonphone, served as the reference.
• Synchronization Strategy (The Key Innovation):
  • Instead of trying to synchronize the start of data acquisition (which is difficult due to variable communication times), the system assigns absolute timestamps to the analog reference signal.
  • PPS Signal: A Pulse Per Second (PPS) signal, synchronized with the national time standard UTC(NMIJ), was fed into the data acquisition system.
  • Timestamping: The system monitored the rising edge of the PPS signal to determine the exact fractional start time of the analog acquisition. This allowed the analog voltage data to be mapped to an absolute time axis, enabling direct comparison with the digital sensor's timestamped data.

B. Device Under Test (DUT)

• Hardware: A custom MEMS module consisting of a DPS310 pressure sensor and an ESP32 microcontroller.
• Operation: The sensor measures pressure at fixed intervals (70 ms). The ESP32 retrieves time from an external NTP server (for seconds) and uses a PPS-corrected system clock (for sub-second precision) to attach timestamps to the pressure data.
• Signal Processing:
  • Sine Fitting: Both the analog voltage and digital pressure data were fitted to sinusoidal waveforms using a least-squares algorithm (IEEE 1057:2017) to extract amplitude and phase.
  • Calculation: Sensitivity modulus ratio ($s_d$) and phase shift ($\Delta\phi_d$) were calculated by comparing the fitted parameters of the DUT against the reference microphone, correcting for the time difference between acquisition starts ($\Delta t_{d-a}$).

3. Key Contributions

1. Novel Calibration System: Developed the first comparison calibration system specifically for digital-output infrasound sensors that solves the phase synchronization problem by timestamping the analog reference signal using a PPS signal.
2. Uncertainty Analysis of Digital Clocks: Quantified the impact of microcontroller clock drift (ppm level) on calibration accuracy. The study demonstrated that while clock drift causes phase errors, periodic resetting (e.g., every 10 minutes) and correction mechanisms can mitigate this.
3. Validation of MEMS Modules: Successfully calibrated the sensitivity and phase of MEMS modules in the 0.2 Hz to 4 Hz range, a range previously unassessed for digital infrasound sensors.

4. Results

The system was tested on two identical MEMS modules (Module1 and Module2) in the 0.2 Hz to 4 Hz range.

• Sensitivity Modulus:
  • The measured sensitivity matched the reference standard within 2% for Module1 and 5% for Module2.
  • Variations were attributed to the intrinsic self-noise of the MEMS sensors.
• Phase Response:
  • A consistent time delay of 10 ms to 20 ms was observed between the acoustic event and the digital output.
  • This delay represents the processing time from pressure detection to timestamped output.
  • Correction: The study confirms that applying a phase correction based on these calibration results is essential for accurate source localization.
• Uncertainty Budget:
  • Expanded Uncertainty (k=2): 0.07 for sensitivity modulus and 6.5° for phase.
  • Dominant Sources: Repeatability (due to MEMS sensor noise) and microcomputer clock drift. Below 1 Hz, the reference standard's uncertainty became more significant.
  • Clock Drift Impact: A drift of ~4.1 ppm was observed in the ESP32 clock, leading to a phase lead of ~4.1 ms per 1000 seconds.

5. Significance and Conclusion

• Enabling High-Density Networks: This work validates that affordable MEMS modules can be used for infrasound monitoring if their dynamic characteristics are properly calibrated. This paves the way for dense sensor networks that were previously cost-prohibitive.
• Phase Accuracy: The study highlights that without phase calibration, the time delays inherent in digital processing (10–20 ms) would severely degrade the accuracy of infrasound source localization algorithms.
• Scalability: The proposed calibration methodology is not limited to the specific DPS310/ESP32 module tested; it is applicable to any digital-output infrasound sensor, provided the synchronization strategy (PPS timestamping of the reference) is implemented.
• Future Outlook: The authors suggest that applying the reported corrections will significantly enhance the reliability of infrasound measurements using digital sensors, making them viable for scientific and monitoring applications alongside traditional analog systems.