Directional Sensitivity-Based DOA Estimation Using a Fourier Series Model

Direction of arrival (DOA) estimation is a fundamental problem in signal processing and has applications in various fields such as radar, sonar, and acoustics. In this article, we propose a method for DOA estimation using the received power at each sensor. The method is based on the directional sensitivity of the sensor elements at various frequencies. We model the directional sensitivity using a Fourier series (FS) model, where the parametric model enables Cramér–Rao lower-bound (CRLB) computations. The FS model is estimated from measurements of a wideband noise signal. To estimate the DOA, the measured power profile is compared to the FS model using the least-squares (LS) method. The proposed power-based method offers several advantages over classical time-delay methods, particularly in allowing arbitrarily small arrays and still handling broadband signals. Additionally, it enables low-rate sampling, which simplifies hardware requirements and significantly reduces processor load. In numerical evaluations with a microphone array and natural sound sources, we still benchmark our method against state-of-the-art time-delay methods. Real-world experiments show promising results, performing on par with the best of the other evaluated methods for all natural signals, despite relying on significantly less information. A key benefit is robustness against array size limitations. By utilizing the received signal power instead of time delays or phase information, the method enables small arrays with great DOA resolution. Furthermore, outdoor data collected a year after calibration confirms its robustness, demonstrating consistent performance over time.