Pseudo-orthogonal chirp-based multiple ultrasonic transducer positioning

Distance-based ultrasonic positioning systems (UPSs) using the trilateration algorithm have been adopted in various types of applications across a wide variety of fields. Recently, the use of a chirp signal in conjunction with cross-correlation has drawn a considerable amount of attention for UPSs. However, when they use a chirp signal for positioning, they suffer from the multiple-access problem due to signal interference. In this paper, to solve this problem, we propose two sets of pseudo-orthogonal chirp waveforms. The basic idea behind the first one is to exploit the orthogonality of the sub-carriers of a chirp waveform, i.e., the discrete frequency components of a chirp waveform, whereas the second one not only exploits the orthogonality of the sub-carriers of a chirp waveform but also chirp rates as a mechanism for assigning uniquely modulated chirp signals to the transmitters. All the waveforms contained in each set have good orthogonality and all the advantages of a classic chirp waveform. First, the performances of the waveforms are investigated through correlation analysis and then, in an indoor environment, evaluated through simulations and experiments for ultrasonic positioning.