Precise underwater positioning remains a fundamental challenge for underwater robotics since global navigation satellite system (GNSS) signals cannot penetrate the sea surface. This paper presents Raspi$^2$USBL, an open-source, Raspberry Pi-based passive inverted ultra-short baseline (piUSBL) positioning system designed to provide a low-cost and accessible solution for underwater robotic research. The system comprises a passive acoustic receiver and an active beacon. The receiver adopts a modular hardware architecture that integrates a hydrophone array, a multichannel preamplifier, an oven-controlled crystal oscillator (OCXO), a Raspberry Pi 5, and an MCC-series data acquisition (DAQ) board. Apart from the Pi 5, OCXO, and MCC board, the beacon comprises an impedance-matching network, a power amplifier, and a transmitting transducer. An open-source C++ software framework provides high-precision clock synchronization and triggering for one-way travel-time (OWTT) messaging, while performing real-time signal processing, including matched filtering, array beamforming, and adaptive gain control, to estimate the time of flight (TOF) and direction of arrival (DOA) of received signals. The Raspi$^2$USBL system was experimentally validated in an anechoic tank, freshwater lake, and open-sea trials. Results demonstrate a slant-range accuracy better than 0.1%, a bearing accuracy within 0.1$^\circ$, and stable performance over operational distances up to 1.3 km. These findings confirm that low-cost, reproducible hardware can deliver research-grade underwater positioning accuracy. By releasing both the hardware and software as open-source, Raspi$^2$USBL provides a unified reference platform that lowers the entry barrier for underwater robotics laboratories, fosters reproducibility, and promotes collaborative innovation in underwater acoustic navigation and swarm robotics.

翻译：精确的水下定位仍然是水下机器人领域的一项基本挑战，因为全球导航卫星系统（GNSS）信号无法穿透海面。本文介绍了Raspi$^2$USBL，一种基于树莓派的开源被动式倒置超短基线（piUSBL）定位系统，旨在为水下机器人研究提供低成本且易于获取的解决方案。该系统包括一个被动声学接收器和一个主动信标。接收器采用模块化硬件架构，集成了水听器阵列、多通道前置放大器、恒温晶体振荡器（OCXO）、树莓派5以及MCC系列数据采集（DAQ）板。除树莓派5、OCXO和MCC板外，信标还包括阻抗匹配网络、功率放大器和发射换能器。一个开源的C++软件框架提供高精度时钟同步和单程传播时间（OWTT）消息触发，同时执行实时信号处理，包括匹配滤波、阵列波束成形和自适应增益控制，以估计接收信号的飞行时间（TOF）和到达方向（DOA）。Raspi$^2$USBL系统在消声池、淡水湖和开放海域试验中进行了实验验证。结果表明，其斜距精度优于0.1%，方位精度在0.1$^\circ$以内，并在长达1.3公里的工作距离上保持稳定性能。这些发现证实，低成本、可复制的硬件能够提供研究级的水下定位精度。通过将硬件和软件作为开源项目发布，Raspi$^2$USBL提供了一个统一的参考平台，降低了水下机器人实验室的入门门槛，促进了可重复性，并推动了水声导航和群体机器人领域的协作创新。