Task
Localise the (x, y) position of a sound source from recordings of an 8-microphone outdoor sensor array across 5 independent scenarios. Each scenario provided:
(8, T)float32 waveform array — one row per sensor- Known sensor positions (x, y) in metres
- Sample rate, speed of sound
- Known calibration pulse template
- Per-sensor clock offset bound (magnitude only — actual offsets unknown)
Approach
1. Arrival Time Estimation
Cross-correlated each sensor's recording against the calibration pulse template to detect the arrival time. The pulse is a known reference waveform, so the cross-correlation peak corresponds to the sample at which the pulse arrived at each sensor.
2. TDOA Computation
Computed Time Differences of Arrival (TDOA) between sensor pairs using the estimated arrival times. Unknown clock offsets introduce additive bias per sensor — bounded but unknown in sign and magnitude.
3. Clock Offset Handling
With per-sensor offsets bounded by clock_offset_bound_sec, used robust TDOA estimation — preferring sensor-pair differences that minimise offset sensitivity, or fitting a source position that is maximally consistent with the TDOA measurements under the bounded offset uncertainty.
4. Source Position Estimation
Given TDOA measurements and known sensor positions, solved for (x, y) geometrically. Each TDOA constrains the source to a hyperbola; the intersection of hyperbolas from multiple sensor pairs localises the source. Used least-squares fitting to find the position minimising total TDOA residual.
Key Techniques
Cross-correlation based arrival time detection, TDOA-based hyperbolic localisation, bounded clock offset handling, least-squares geometric fitting, numpy signal processing
Environment
Isolated Docker environment. Output JSON per scenario validated against reference (x, y) coordinates within a positional accuracy threshold.