Uncertainty quantification of deep learning based direction-of-arrival estimation with conformal prediction

Direction-of-arrival (DOA) estimation is an important task in array signal processing with applications in underwater acoustics, biomedicine, geophysics, and robotics. The signals recorded on a spatially distributed array along with an analytical model of wave propagation, are used to estimate the unknown DOA. Recently, end-to-end deep learning-based methods have been proposed for improving DOA estimation performance. Yet, real-time DOA estimation has a number of challenges such as sensor noise, reverberant surroundings, uncertainty in sensor locations and environment. In this work, we propose to use conformal prediction for uncertainty quantification in DOA estimation. Conformal prediction is a statistically rigorous method to provide confidence intervals for an estimated quantity without making distributional assumptions. With conformal prediction, confidence intervals are computed via quantiles of user-defined score values. This easy-to-use method can be applied to any trained classification/regression model as long as an appropriate score function is chosen. The proposed approach shows potential to enhance the real-time applicability of deep learning methods for DOA estimation. We illustrate the advantages of conformal prediction for different deep-learning methods for DOA estimation. To the best of our knowledge, this is the first analysis of using conformal prediction for uncertainty quantification of deep learning methods for acoustic estimation.