# Acoustic Simulation for Performance Evaluation of Ultrasonic Ranging Systems
## 1 Introduction  
Position-based applications are attracting increasing market interest for the development of related products and systems that could lead to accurate mall navigation, path finding in large indoor buildings (e.g., conference centers, airports or hospitals) [1, 2], unmanned guidance, surveillance systems [3, 4], monitoring systems [5, 6], and other systems able to operate indoors with high positioning accuracy. The trilateration technique has been shown to provide interesting results in indoor positioning systems, requiring at least three measurements of the distance between the reference emitters and a sensor to be positioned [7, 8]. Ultrasonic signals represent a solution that combines both the requested degree of precision [9] and the low-cost implementation [10, 11]. The estimation of the time of arrival (_TOA_) of a suitable transmitted ultrasonic signal is the building block of the commonly used ranging techniques. The analysis of the received and post-processed signal leads to the identification of a peculiar characteristic of the signal through which it ispossible to estimate the _TOA_. For example, the maximum peak of the envelope of an ultrasonic pulse is a feature suitable for estimating the _TOA_. Nevertheless, this technique could be affected by acoustic disturbances, with errors in the order of wavelengths (centimeters), even in the presence of a high signal-to-noise ratio (SNR) [12; 13]. Instead, the use of cross-correlation [14] allows the high accuracy estimation of the TOA [15], while showing a good immunity to acoustic disturbances [16; 17]. In fact, the TOA estimation through the cross-correlation peak provides an accuracy, regarding the distance measurement, of the order of the distance covered by the ultrasound during the time sample interval, namely the current space sampling, which is much smaller than the ultrasonic wavelength. From an implementation perspective, the use of a chirp signal facilitates the detection of the cross-correlation peak, leading to a range resolution up to the order of one tenth of the wavelength used in practical systems. In [17], a range resolution of \(\pm\)1.2 mm was experimentally achieved by using a 15-40 kHz chirp, with a wavelength range of 22.86-8.57 mm and a sampling frequency of 1 MHz, achieving a space sampling of 0.343 mm with a sound speed of 343 m/s. As an additional benefit of using cross-correlation, a significant increase in SNR can be achieved, provided that the signal and noise are not correlated. Usually, the design of the acoustic section of ranging systems is carried out, adopting the approximation of the near-field and far-field acoustic field. In real systems, however, this approximation does not provide sufficiently accurate a priori information for a realistic design of ranging systems, especially when the signal shape is much more complex than pulses or sinusoidal continuous waves. For example, the linear chirp may suffer an aberration of its shape, due to acoustic diffraction, depending on the shape and size of the transducer and the angle under which the emitter is viewed by the receiver. In the presence of such aberrations of shape, even the most robust cross correlation ranging technique provides results affected by a much larger error than expected. Therefore, great attention must be paid to the design and evaluation of the acoustic section of ultrasonic positioning systems, considering together the shape and size of the ultrasonic emitters, the shape of the acoustic signal and the specific ranging technique used. The acoustic effects, including absorption and diffraction, along with the performance of different ranging techniques, can be analyzed in detail using the renowned academic acoustic simulation software Field II [18; 19]. Indeed, Field II was designed to simulate ultrasound imaging systems in the human body, mostly composed of water.