TOA-based joint synchronization and source localization with random errors in sensor positions and sensor clock biases

This paper considers the problem of joint synchronization and source localization using time of arrival (TOA) when the known sensor positions and sensor clock biases are subject to random errors. We derive the Cramér-Rao lower bound (CRLB) of the source position and the source clock bias, and quantify the amount of estimation performance degradation due to sensor position errors and sensor clock bias errors. A mean square error (MSE) analysis is conducted and it shows that ignoring the errors in the known sensor positions and sensor clock biases would lead to an estimation accuracy worse than the CRLB. This paper then proceeds to develop a new joint synchronization and source localization algorithm. The new method takes into consideration the presence of sensor position errors and sensor clock bias errors, and has the advantage of being a closed-form solution. Theoretical performance analysis proves that the proposed algorithm can attain the CRLB accuracy under small noise condition. Computer simulations are used to corroborate the theoretical derivations and demonstrate the good performance of the newly developed algorithm.