## 4 Conclusions  
Addressing the high-precision positioning requirements for small-scale or indoor scenarios, this paper proposes a transition zone-based base station self-optimization method for high-precision acoustic ranging in robotic applications. Acoustic signals are susceptible to environmental factors such as temperature, humidity, and airflow, leading to significant absolute errors in both short-range and long-range transmission. To enhance the precision of the distance information obtained after preprocessing, this paper establishes a high-precision confidence interval for ranging information and introduces a novel method for assigning weights within the high-precision acoustic ranging confidence interval. Furthermore, to achieve positioning functionality, this paper presents a weighted average-based self-optimization positioning method based on the trilateration algorithm. This method selects ranging information with higher precision from the confidence interval as input for the positioning algorithm and calculates the weighted average based on the assigned weights, thereby improving the positioning accuracy of two-dimensional coordinates and facilitating the transition of base station selection modes across different areas. Experimen  
Figure 5: Comparison experiment results of cross-regional positioning accuracy.  
tal validation has confirmed that the acoustic signal positioning method realized by the aforementioned approach achieves centimeter-level precision, meeting the requirements for practical scenario applications.  
However, although this positioning method can improve positioning accuracy, it cannot meet the typical positioning update frequency (\(\geq\)10 Hz) of current real-time robot navigation and can only achieve an update frequency of 2-5 Hz. In the future, we will consider adding UWB positioning components to integrate the advantages of fast UWB positioning update frequency, high acoustic positioning accuracy, and IMU local supplementary positioning to develop a multi-sensor fusion positioning module. The UWB update frequency can easily reach 50 Hz, but due to its propagation at the speed of light, the measurement accuracy of propagation time is difficult to guarantee, resulting in difficulty in breaking through the positioning accuracy to within \(\pm\)10 cm. Therefore, the subsequent multi-sensor fusion methods consider UWB positioning as the main body and acoustic positioning with low-frequency correction assistance to achieve high-frequency and high-precision indoor positioning.  
Methodology, Z.Z., X.L. and L.G.; software, Z.L.; validation, Z.Z. and Z.L.; formal analysis, Z.Z. and J.C.; investigation, Y.S. and B.G.; data curation, Z.Z. and Z.L.; writing--original draft preparation, Z.Z.; writing--review and editing, Z.Z. and L.G.; supervision, L.G.; project administration, L.G. All authors have read and agreed to the published version of the manuscript.  
The work is supported by the Shanghai Agriculture Applied Technology Development Program, China (grant no. T2022-03-01).  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} TOF & Time of Flight \\ GPS & Global Positioning System \\ UWB & Ultra-Wide Band \\ SLAM & Simultaneous Localization and Mapping \\ GCC & Generalized Cross-Correlation \\ CC & Cross-Correlation \\ TDOA & Time Difference in Arrival \\ \end{tabular}