Robotic swarms are becoming increasingly complex on the surface and in air due to highspeed and reliable communication links, Global Positioning Satellites (GPS), and visual support to relative navigation. However, the limited propagation of these signals in the ocean has impacted similar advances in undersea robotics. Autonomous underwater vehicles (AUVs) often rely on acoustics to inform navigation solutions; however, this approach presents challenges for scalable robotic swarms. Acoustic navigation is a means to inform range and bearing to a target. Many methods for range and bearing estimation, including current low-cost solutions, rely on precision time synchronization or two-way communication to compute ranges as part of a full navigation solution. The high cost of reliable Chip-scale atomic clocks (CSACs) and acoustic modems relative to other vehicle components limits large-scale swarms due to the associated cost-per-vehicle and communications infrastructure. We propose a single, high-cost vehicle with a reliable navigation solution as a "leader" for a scalable swarm of lower-cost vehicles that receive acoustic signals from a source onboard the lead vehicle using a single hydrophone. These lower-cost "followers" navigate relative to the leader according to the preferred behavioral pattern, but for simplicity, we will refer to a simple following behavior in this work. This thesis outlines a method to obtain range estimates to sound sources in which the signal content, including frequency and power at its origin, can be reasonably approximated. Total transmission loss is calculated based on empirical equations for the absorption of sound in seawater and combined with geometric spreading loss from environmental models to estimate range to a source based on the loss at differential frequencies. We refer to this calculation as the signal absorption-based range estimator (SABRE). This method for obtaining range combines with Doppler-shift methods for target bearing based on the maximum frequency detected within a banded limit around a known source frequency. A primary objective for SABRE is to address techniques that support low-cost options for undersea swarming. This thesis's contributions include a novel method for range estimation onboard underwater autonomous vehicles that supports navigation relative to a known source when combined with Doppler-shift methods for target bearing. This thesis seeks to develop the theory, algorithms, and analytical tools required and apply those tools to real-world data sets to investigate the feasibility, sources of error, and accuracy of this new approach to range estimation for underwater swarms.