Bayesian Microphone Array Calibration Without Reference Source
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Solution Overview
Problem
Existing microphone array calibration methods require a calibrated source or reference sensor, which is not feasible for on-site calibration without expensive laboratory equipment, and they fail to correct both gain and phase deviations simultaneously.
Innovation Solution
A Bayesian algorithm that estimates gain and phase differences in a microphone array using probabilistic methods, allowing calibration without a calibrated source and addressing phase-wrapping ambiguity through a novel approach, enabling calibration with uncertain acoustic sources and waveguides.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional calibration methods using a calibrated source are used, then measurement precision is improved, but device complexity and cost increase due to requiring expensive calibrated acoustic laboratory equipment
Solution Approach 1:
The system performs self-calibration by having each microphone in the array measure the sound pressure level at its own location and comparing it with the average level across all microphones. This eliminates the need for external calibrated sources or reference microphones, as the array calibrates itself using its own measurements and the known geometric relationships between microphones.
Solution Approach 2:
The calibration method creates a virtual reference by having each microphone act as both a measurement device and a reference source for other microphones. The sound pressure level measured by one microphone is used as a reference for calibrating other microphones, eliminating the need for a physical calibrated reference source.
2Reliability
If conventional calibration methods are used, then gain and phase deviations are corrected, but the method fails when the source is unknown or uncalibrated
Solution Approach 1:
The system determines the relative positions and orientations of microphones through self-measurement, using the sound pressure levels measured by each microphone and the known geometric relationships. This allows the system to adapt to any unknown source position without requiring pre-calibration or knowledge of source characteristics.
Solution Approach 2:
The calibration method changes from relying on fixed source characteristics to using variable geometric relationships between microphones. By using the known positions and orientations of microphones in the array, the system can calculate expected sound pressure levels and compare them with actual measurements to determine calibration factors, regardless of source characteristics.
3Measurement precision
If multiple microphones are used in an array, then measurement capability is improved, but phase-wrapping ambiguity arises that complicates calibration
Solution Approach 1:
Each microphone in the array performs measurements and contributes to the calibration of the entire system. By using the collective measurements from all microphones and their known geometric relationships, the system can resolve phase ambiguities through mutual reference rather than requiring external phase reference information.
Solution Approach 2:
The known geometric relationships between microphones serve as an intermediary that connects the phase measurements from different microphones. By using the predetermined positions and orientations, the system can unwrap phase ambiguities through geometric constraints rather than requiring complex external phase reference systems.
Data Source
AI summary
Microphone array calibration that does not require a calibrated source or calibrated reference microphone is provided. We provide a statistical (Bayesian) algorithm that (under condition of reasonable environment noise during calibration) can determine gain and phase differences of a whole array at once, even when the gain and/or phase of the source is unknown. More specifically, a Bayesian regression with complex log-normal prior and complex normal likelihood is employed. The inherent phase-wrapping ambiguity in this regression is resolved by exploiting the similarity of likelihood between a lattice point and its Euclidean Voronoi region.