A Two-Stage Coarse-to-Fine Cross Correlation Method for Chirp-Based Ultrasonic Positioning

A multiaccess ultrasonic positioning system (UPS) based on chirped signals needs to estimate the ultrasonic (US) time-of-flight (TOF) of at least three channels. If the cross correlation method is used to estimate the TOF, the calculations will be very extensive, making it difficult to meet the real-time requirements of the system. In this article, to solve this problem, a TOF estimation method based on the two-stage coarse-to-fine cross correlation approach is proposed for chirp-based UPS. The coarse cross correlation is achieved by decimating the transmitted and received data to obtain a rough TOF value with less sampled data. In the fine cross correlation, the rough TOF value is used to select data for further cross correlation and obtain the final TOF. Compared to the traditional cross correlation method for chirp US signals, the proposed two-stage cross correlation method requires fewer data to compute the cross correlation, resulting in lower computational costs and improved real-time performance. The simulation results for a US multiple-access positioning system show that the performance of the proposed method lags behind that of the cross correlation method at low signal-to-noise ratios (SNRs). However, with fewer transmitting chirps, the proposed method has a better performance at zero or higher SNR levels. In the experiments, compared to the traditional cross correlation method, the computational time of the proposed method is reduced by a factor of approximately 116. The results confirm that the proposed method exhibits superior real-time performance over the traditional cross correlation method and can meet the requirements for the US multiaccess location of chirp signals.