Objectives Underwater acoustic navigation predominantly employs active positioning models due to the inherent challenge of achieving precise time synchronization among seafloor navigation beacons. A fundamental limitation of this model is its ill‑posed nature, where each observation corresponds to two unknown states of the carrier vehicle. A common simplification assumes the carrier is stationary during the signal's round‑trip travel time, allowing the use of half this duration for positioning via spatial intersection. However, this assumption inevitably introduces model errors, which become significant in deep‑sea environments or during high‑speed carrier motion. Alternative approaches integrate external information from sensors such as Doppler velocity logger (DVL) or inertial navigation system (INS) to resolve the ambiguity, but it compromises the independence of system and introduces complexities related to cross‑sensor error contamination. The primary objective is to develop a self‑contained navigation and positioning model that effectively resolves the inherent ill‑posedness of active sonar systems without relying on external aiding information, thereby enhancing both accuracy and autonomy in underwater navigation.

Methods To address the aforementioned challenge, a novel time‑window navigation and positioning model for active sonar is proposed. The core innovation lies in the incorporation of the carrier's kinematic parameters directly into the observation model. Instead of estimating only a single position per epoch, the proposed model treats the carrier's trajectory over a short, sliding time window as a polynomial. This allows for the joint estimation of key motion states, including position, velocity, and acceleration, using only the accumulated two‑way travel time measurements from multiple pings within the window. The proposed method leverages the principle of windowed estimation, analogous to techniques used in satellite orbit determination, to overcome the rank deficiency of single‑epoch solutions. Furthermore, to quantitatively assess the geometric strength and reliability of the positioning configuration within the time‑window framework, a new metric termed the trajectory dilution of precision (TRDOP) is introduced.

Results The performance of the proposed time‑window model and the effectiveness of TRDOP are rigorously validated through both simulation and real data experiments. The simulation results demonstrate a strong positive correlation between the calculated position dilution of precision and acceleration dilution of precision values and the corresponding root mean square errors in estimated position and velocity, confirming that TRDOP is a reliable indicator of navigation configuration quality. The comparative analysis reveal that the traditional spatial intersection model, which ignores carrier motion, produces substantial errors in simulated scenarios with moving carriers. In contrast, the proposed time-window model can achieve positioning accuracy at the meter level. A key finding is that the positioning accuracy at the mid-point of the time window is consistently higher than that at the current epoch. The tests conducted on a publicly available Japanese global navigation satellite system‑acoustic dataset show that the time‑window navigation model successfully achieves positioning accuracy better than 5 m. The constant‑velocity model generally yield slightly better and more stable results for the tested trajectories, which could be effectively approximated as piecewise linear.

Conclusions We present a significant advancement in active sonar‑based underwater navigation by introducing a time‑window positioning model that intrinsically resolves the system's ill‐posedness. The proposed model successfully eliminates the dependency on external sensors like DVL or INS for fundamental disambiguation, enabling the generation of independent, high‑rate estimates of the carrier's full kinematic state solely from acoustic ranging observations. The proposed TRDOP metric provides a valuable tool for designing and evaluating the geometric strength of such time‑window navigation scenarios. The experimental results conclusively demonstrate the superiority of the proposed model over the conventional spatial intersection approach, particularly under dynamic carrier motion. The achieved sub‑5‑meter accuracy on real data highlights its practical potential.