Computationally Efficient and Noise Robust DOA and Pitch Estimation

Many natural signals, such as voiced speech and some musical instruments, are approximately periodic over short intervals. These signals are often described in mathematics by the sum of sinusoids (harmonics) with frequencies that are proportional to the fundamental frequency, or pitch. In sensor (microphone) array signal processing, the periodic signals are estimated from spatio-temporal samples regarding to the direction of arrival (DOA) of the signal of interest. In this paper, we consider the problem of pitch and DOA estimation of quasi-periodic audio signals. In real life scenarios, recorded signals are often contaminated by different types of noise, which challenges the assumption of white Gaussian noise in most state-of-the-art methods. We establish filtering methods based on noise statistics to apply to nonparametric spectral and spatial parameter estimates of the harmonics. We design minimum variance solutions with distortionless constraints to estimate the pitch from the frequency estimates, and to estimate the DOA from multichannel phase estimates of the harmonics. Applying this filtering method as the sum of weighted frequency and DOA estimates of the harmonics, we also design a joint DOA and pitch estimator. In white Gaussian noise, we derive even more computationally efficient solutions which are designed using the narrowband power spectrum of the harmonics. Numerical results reveal the performance of the estimators in colored noise compared with the Cram\'{e}r-Rao lower bound. Experiments on real-life signals indicate the applicability of the methods in practical low local signal-to-noise ratios.