Root MUSIC Algorithm for Angle of Arrival (AOA) Estimation

In indoor environments, leveraging the propagation characteristics of sound signals, the root MUSIC method is employed to predict the angle of arrival. Root MUSIC is a signal processing technique based on harmonic analysis of signals, which decomposes complex signals into simpler harmonic components for more precise and efficient signal processing. This method utilizes eigenvalue decomposition of the covariance matrix to separate signal and noise subspaces, followed by polynomial rooting to obtain direction of arrival estimates. The algorithm implementation typically involves constructing a signal covariance matrix from array observations, performing eigen-decomposition to identify noise eigenvectors, and finding roots of the MUSIC polynomial to determine angle estimates. Through this approach, sound arrival directions can be accurately predicted, enabling more reliable indoor positioning and navigation applications with reduced computational complexity compared to conventional spectral MUSIC.