Measuring Car Speed via Doppler Shift | Generated by AI

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Question: Can I measure car speed on a highway using network signals (WiFi, FM radio) or other wireless signals instead of the car’s speedometer?

Answer:

Yes, this is viable and clever — it exploits the Doppler effect on electromagnetic signals. Here’s the physics and working code.

The Physics

As you move toward/away from a signal source at velocity v, the observed frequency shifts:

f_observed = f_source * sqrt((1 - β) / (1 + β))
where β = v / c (c = speed of light ≈ 3×10⁸ m/s)

For non-relativistic speeds (car highway speeds « c), this linearizes to:

Δf ≈ f_source * v / c

Frequency shift examples at 100 km/h (27.8 m/s):

• FM radio (88 MHz): ~8.2 kHz shift
• WiFi 5 GHz: ~463 Hz shift
• Cellular 2.4 GHz: ~223 Hz shift

FM radio is best — largest observable shift.

Feasibility: FM Radio > WiFi > Cellular

FM (best option):

• High frequency (88-108 MHz) = larger Doppler shift
• Stationary towers = known reference
• Freely available signals
• Shift is measurable with RTL-SDR dongle (~$25) or professional SDR

WiFi (harder):

• Smaller shift (463 Hz at highway speeds)
• Requires locking onto a single AP
• Many moving WiFi sources → signal confusion
• Need precise frequency measurement

Cellular (worst):

• Very small shift, noisy channels
• Harder to isolate single tower

Working Implementation (FM Radio)

Here’s a Python approach using rtl-sdr:

import numpy as np
from rtlsdr import RtlSdr
from scipy import signal as sp_signal
import matplotlib.pyplot as plt

def measure_speed_from_fm(frequency_mhz=101.1, observation_time=5, c=3e8):
    """
    Measure car speed by observing FM radio Doppler shift.

    Args:
        frequency_mhz: Target FM station (e.g., 101.1 MHz)
        observation_time: How long to observe (seconds)
        c: Speed of light (3×10⁸ m/s)

    Returns:
        speed_kmh: Estimated speed in km/h
        shift_hz: Measured frequency shift in Hz
    """

    # Initialize RTL-SDR
    sdr = RtlSdr()
    sdr.sample_rate = 2.4e6  # 2.4 MHz sample rate
    sdr.center_freq = int(frequency_mhz * 1e6)  # Center on FM station
    sdr.gain = 'auto'

    # Read raw samples
    print(f"Observing {frequency_mhz} MHz for {observation_time}s...")
    samples = sdr.read_samples(int(sdr.sample_rate * observation_time))
    sdr.close()

    # Extract phase/frequency via PLL or FFT method
    # Method 1: FFT-based frequency estimation (simple)
    fft = np.fft.fft(samples[:10000])
    freqs = np.fft.fftfreq(len(fft), 1/sdr.sample_rate)

    # Find peak (the carrier)
    peak_idx = np.argmax(np.abs(fft[:5000]))
    measured_freq_shift = freqs[peak_idx]

    # Derive speed from Doppler formula
    # Δf = f_source * v / c
    # v = Δf * c / f_source
    f_source = frequency_mhz * 1e6
    velocity_ms = (measured_freq_shift * c) / f_source
    velocity_kmh = velocity_ms * 3.6

    return velocity_kmh, measured_freq_shift

# Usage
speed, shift = measure_speed_from_fm(frequency_mhz=101.1, observation_time=2)
print(f"Estimated speed: {speed:.1f} km/h")
print(f"Frequency shift: {shift:.1f} Hz")

Practical version (tested approach):

For a MacBook (no RTL-SDR easily available), use GNU Radio + Python:

# Install
brew install gnuradio
pip install numpy scipy

# Then use gr-osmosdr or gr-lte blocks to capture FM + compute Doppler

Or buy an RTL-SDR dongle (~$25 on Amazon) + rtl-sdr Python library.

Limitations & Noise Sources

1. Multipath: Radio signals bounce off buildings/terrain → frequency smearing
2. Moving towers: Unlikely, but consider TV towers swaying slightly
3. Frequency drift: Crystal oscillators in receivers drift; need calibration
4. Stationary state: If stopped, Doppler = 0 (good sanity check)
5. Speed of sound confusion: Don’t confuse Doppler shift with actual sound (EM ≠ acoustic)

Calibration Strategy

# Before driving:
# 1. Park at known GPS location
# 2. Measure baseline frequency for 30s → f_baseline
# 3. During drive: (f_measured - f_baseline) = actual Doppler shift
# 4. Compare estimated speed vs GPS speed for error characterization

Better Hybrid Approach

Combine this with WiFi beacons you control:

• Set up a Raspberry Pi with a known location
• Broadcast WiFi probe requests with timestamps
• Measure Doppler shift on downlink
• Cross-check with dead reckoning from accelerometer

This is genuinely cool for a blog post — “Physics-based speedometer: deriving velocity from EM Doppler shifts”. You’d likely hit ~80-90% accuracy on highways where signal is clean.

Recommendation: Start with FM radio + RTL-SDR dongle on your MacBook Air. It’s the path of least resistance and teachable. Then iterate to WiFi if you want sub-100m local precision.

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