The abstract of this pre-print paper is: Robot localization in buried pipes presents a number of challenges, including the unavailability of methods such as a global positioning system, and the limited perspective of sensors such as vision. This paper addresses these challenges by using acoustic sensing, where signals sent by robots propagate long distances and around corners in the pipe environment, and can be used to estimate the distance to reflective features. It is shown that the reverberant environment causes a number of echoes which contain useful information. A novel algorithm for using this information in pose-graph optimization is proposed, and is shown to be necessary in comparison to a naive approach. The algorithm is demonstrated to be accurate and robust by measuring the error rate, which is the proportion of estimate error that was greater than a target threshold of 0.5 metres.  The median error rate was 0 for measurement uncertainty 2.5 times larger than that found experimentally, and for motion uncertainty 4 times that which could be tolerated by an idealised loop-closure approach used for comparison. This work is the foundation for new data fusion methods for robot localization in buried pipes.