Multiple access chirp-based ultrasonic positioning

Distance-based ultrasonic positioning systems (UPSs) using trilateration 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 a chirp signal is used for positioning, these algorithms suffer from problems due to signal interference. In this paper, to solve this problem, we propose using four sets of orthogonal chirps, each of which contains three waveforms. The first three sets use chirp rates as a mechanism for assigning uniquely modulated chirp signals to transmitters while the basic idea behind the last one is to exploit the orthogonality of the subcarriers of a chirp waveform, i.e., the discrete frequency components of a chirp waveform. All the waveforms contained in each set have good orthogonality (i.e., the waveforms contained in sets 1 to 3 and set 4 are, respectively, quasi-orthogonal and perfectly orthogonal) and also have all the advantages of a classic chirp waveform. First, the performance of the waveforms is investigated through correlation analysis and then, in an indoor environment, evaluated through simulations and experiments for ultrasonic positioning. For sets 1 to 4, for an operational range of approximately 1000 mm, the positioning root-mean-square-errors 90% error were 6.20 9.13 mm, 6.05 8.90 mm, 7.38 10.85 mm, and 4.54 6.68 mm, respectively.