Abstract
The increasing focus on the development of positioning techniques reflects the growing interest in applications and services based on indoor positioning. Many applications necessitate precise indoor positioning or tracking of individuals and assets, leading to rapid growth in products based on these technologies in certain market sectors. Ultrasonic systems have already proven effective in achieving the desired positioning accuracy and refresh rates. The typical signal used in ultrasonic positioning systems for estimating the range between the target and reference points is the linear chirp. Unfortunately, it can undergo shape aberration due to the effects of acoustic diffraction when the aperture exceeds a certain limit. The extent of the aberration is influenced by the shape and size of the transducer, as well as the angle at which the transducer is observed by the receiver. This aberration also affects the shape of the cross-correlation, causing it to lose its easily detectable characteristic of a single global peak, which typically corresponds to the correct lag associated with the signal's time of arrival. In such instances, cross-correlation techniques yield results with a significantly higher error than anticipated. In fact, the correct lag no longer corresponds to the peak of the cross-correlation. In this study, an alternative technique to global peak detection is proposed, leveraging the inherent symmetry observed in the shape of the aberrated cross-correlation. The numerical simulations, performed using the academic acoustic simulation software Field II, conducted using a typical ultrasonic chirp and ultrasonic emitter, compare the classical and the proposed range techniques in a standard office room. The analysis includes the effects of acoustical reflection in the room and of the acoustic noise at different levels of power. The results demonstrate that the proposed technique enables accurate range estimation even in the presence of severe cross-correlation shape aberrations and for signal-to-noise ratio levels common in office and room environments, even in presence of typical reflections. This allows the use of emitting transducers with a much larger aperture than that allowed by the classical cross-correlation technique. Consequently, it becomes possible to have greater acoustic power available, leading to improved signal-to-noise ratio (SNR).