A Closed-form Estimator for Target Position and Propagation Speed Using TOA Measurement

The underwater acoustics propagation speed varies with changes in water temperature, salinity, and depth. Existing studies frequently treat the propagation speed as an unknown constant, which requires the simultaneous estimation of both the target position and the propagation speed. This paper presents a closed-form estimator for jointly estimating the target position and propagation speed using time of arrival (TOA) measurements. The proposed method begins with an initial estimate obtained through the null space projection (NSP) method, followed by refinement via error compensation to yield a more accurate estimate. Additionally, we derive the cramér-rao lower bound (CRLB) considering sensor position errors. Simulation results demonstrate that the proposed method outperforms previous closed-form method in localization performance, while exhibiting lower complexity compared to the semidefinite relaxation (SDR) method, yet achieving performance close to that of SDR. Furthermore, the proposed method approaches the CRLB at low noise levels.