Multistatic Localization Aided by a Calibration Object in the Absence of Synchronization and Transmitter Position

In this paper, we address the multistatic localization problem when the transmitter position is not known and the synchronizations among the receivers and with the transmitter are not available. Aided by a calibration object, the problem is solvable where the unknown object position, the transmitter position and the synchronization errors can be estimated using the time delay measurements from the direct paths between the transmitter and receivers, and the indirect paths reflected by the calibration and unknown objects. To solve this challenging problem, we propose a three-step estimation method that obtains a different unknown in each step. Specifically, the transmitter position is estimated by formulating a constrained weighted least squares (CWLS) problem in the first step, and a linear weighted least squares estimator follows to determine the synchronization errors in the second step. Finally, the object position is estimated by formulating a different CWLS problem in the third step. The solutions are closed-form in all three steps, and thus, the proposed method is computationally efficient. Furthermore, the proposed method is extended to the more practical scenario in which the calibration object position error is present. The mean square error analysis validates that the object position estimate is able to achieve the Cramer-Rao lower bound performance under small Gaussian noise, which is further confirmed by numerical simulations.