Semidefinite Programming Methods for Alleviating Clock Synchronization Bias and Sensor Position Errors in TDOA Localization

This paper investigates the problem of source localization using signal time-difference-of-arrival (TDOA) measurements in the presence of clock synchronization bias and sensor position errors. Our existing work has developed a unified solution for TDOA localization in the presence of sensor position errors but clock synchronization bias was not considered. Clock synchronization bias is a more complex problem often encountered in practical localization networks. This paper further generalizes this framework to include clock synchronization bias. The proposed technique employs multiple calibration emitters to simultaneously alleviate both the sensor position errors and clock synchronization bias. The maximum likelihood estimator (MLE) for this problem is optimal, but too complex to be applied in practice. We develop a semidefinite programming (SDP) based localization algorithm to effectively solve the MLE problem. This SDP algorithm can reach the Cram$\acute{\text{e}}$r-Rao lower bound when sensor position errors are not unrealistically large.