TDOA Localization With Unknown Signal Propagation Speed and Sensor Position Errors

In time-difference-of-arrival (TDOA) localization systems, the TDOA measurements and range-difference-of-arrival (RDOA) values can be used interchangeably if the signal propagation speed is known. In some scenarios like underwater acoustic localization, the signal propagation speed is often unknown. This letter addresses joint source location and propagation speed (unknown) estimation using signal TDOA measurements in the presence of sensor position errors. The maximum likelihood estimator (MLE) for this problem is optimal, but it requires a suitable initial value to obtain the global solution or needs exhaustive grid search. We develop a semidefinite programming (SDP) based localization algorithm to effectively solve the MLE problem. The accuracy of the proposed algorithm is close to the Cramér-Rao lower bound and has a superior performance than existing solutions.