Joint Time Difference of Arrival and Frequency Difference of Arrival Based Localization and Sensor Trajectory Optimization in Presence of Time and Frequency Synchronization Errors

‍ ‍In recent years， passive location technology has been widely applied in multiple fields such as cognitive communication， spectrum management， and electronic warfare. Joint time difference of arrival （TDOA） and frequency difference of arrival （FDOA）-based localization has attracted widespread attention and application in China and internationally owing to its high measurement accuracy， low number of sensors required， unique solutions， and less susceptibility to localization ambiguity problems. Joint TDOA/FDOA-based localization typically requires precise time and frequency synchronization between sensors. However， when the sensor timing service cannot be used or is interfered with， time and frequency synchronization between sensors cannot be guaranteed and time and frequency offsets critically affect localization performance. The effects of time and frequency offsets on system performance are reflected by multiple aspects， including a decrease in location estimation accuracy， an uncertainty increase in target tracking， and a decrease in overall system reliability. These issues make it difficult to achieve high precision location. Therefore， accurate estimation and compensation methods are crucial to mitigate the effects of time and frequency synchronization errors. To improve localization accuracy under the condition of time and frequency synchronization errors， this study proposes joint TDOA/FDOA-based localization and sensor trajectory optimization considering time and frequency synchronization errors. The proposed method primarily includes two parts： alternating iterative localization and sensor trajectory optimization. The sensor trajectory optimization is based on the location results of alternating iterations. First， for alternating iterative localization， the high-dimensional parameter solving problem was transformed into two low-dimensional problems by alternating the estimation of the source location and time-frequency synchronization errors， which significantly reduced computational complexity. The initial value of the alternating iteration method was obtained using the difference method to avoid the impact of time and frequency synchronization errors. The second part involved the optimization of sensor trajectories. Based on the localization estimation results obtained from the first part， a cost function for optimizing sensor trajectories considering the uncertainty of source location estimation was constructed and efficient solutions were obtained using the particle filter method. Each particle represented the possible location of a randomly generated source， and the uncertainty of source estimation results was considered to optimize the sensor’s trajectory. The simulation results demonstrated that the alternate iteration method reduced computational complexity. Furthermore， when the measurement noise was minimal， the root mean square error of the location estimation algorithm proposed herein can approximate the lower bound of the Cramer-Rao Lower Bound. Compared to the situation where there is no track optimization at the sensor， the accuracy of localization estimation and that of the time and frequency offsets were effectively improved.