Calibration Method for Planar Array Acoustic Cameras Based on Physical Topology Constraints

During the calibration process of planar array acoustic cameras, the Time Difference of Arrival (TDOA) is susceptible to background noise, which can cause geometric distortion in the estimated array coordinates and lead to unstable parameter estimation. To address these issues, we propose a calibration method that incorporates physical topology constraints. This method integrates spring-topology modeling, planar geometric constraints, and centroid-anchoring prior constraints. It constructs an optimization model that synergistically combines TDOA residuals with physically grounded geometric constraints. The geometric rigidity inherent in the array design is incorporated as a regularization term to constrain the inverse calibration process based on acoustic observation data. Consequently, this approach corrects the topological distortion in the calibrated coordinates induced by measurement noise. Numerical simulation results show that the Root Mean Square Error (RMSE) of the calibration stabilizes at the level of 10^-3 to 10^-2 meters under observation noise. The results confirm that the proposed physical topology constraints strategy effectively mitigates large calibration errors in array self-calibration methods relying solely on acoustic observations under low Signal-to-Noise Ratio (SNR). It achieves high-precision parameter estimation that balances data fidelity with physical consistency.