Improving positioning accuracy by enhanced ToA estimation for a narrow-bandwidth sound-based positioning system using FDMA in protected cropping systems

Robotics technology has advanced significantly, not only in industrial applications but also in agriculture. To meet the growing demand, a novel robotic system employing multiple small ground robots has been proposed for use in greenhouses. To localize robots in GPS-denied environments, we developed a Spread Spectrum Sound-based Local Positioning System (SSSLPS). Specifically, a Frequency Division Multiple Access (FDMA)-based positioning system was developed to simultaneously localize multiple robots. To minimize Time-of-Arrival (ToA) estimation errors and enhance positioning accuracy, we introduced a Modified Cross-Correlation (MCC) algorithm designed to reduce the number of peaks encountered during ToA estimation. Both 1-dimensional (1D) and 2-dimensional (2D) experiments were conducted to evaluate the ranging and positioning performance of the SSSLPS utilizing FDMA. The results demonstrated that the MCC algorithm effectively minimized cross-correlation peaks, thereby improving ToA accuracy for certain channels. In a quiet environment, FDMA signals achieved a measurement range of up to 39 m with an error of 12.8 ± 10.3 mm. In a greenhouse measuring 50 m × 10 m, the SSSLPS covered half of the area (22 m × 8.3 m). By combining standard cross-correlation and MCC algorithms, the system attained a 2D positioning error of 25.9 ± 9.1 mm in a noisy, windy environment, with a maximum measurable range of approximately 22 m. These findings confirm that employing the MCC algorithm significantly enhances the positioning accuracy of SSSLPS, making it a viable solution for precise robot localization in greenhouses.