A Novel Timestamp-Conversion-Based Localization and Synchronization Method for Moving Users Using Sequential Measurements

Localization and synchronization of moving users in a time-division scheme have attracted considerable attention. Currently, closed-form methods are more prevalent than iterative methods due to their advantages, including not requiring initialization and avoiding divergence issues. However, existing closed-form methods are primarily effective for low-speed users and are associated with a substantial computational burden. High-speed users, such as unmanned aerial vehicles, satellites, and spacecraft, can experience significant errors when using these existing methods. Therefore, this study presents a novel two-step localization and synchronization method. In the initial step, we convert the sequential measurements from each anchor node into time-of-arrival measurements at a single reference instant. Commonly employed conversion methods can introduce errors due to the time-varying measurement period caused by timestamp uncertainty. To resolve this challenge, this study introduces a computationally efficient piecewise osculating interpolation algorithm. In the second step of our proposed method, the measurement equations are linearized through squaring and differencing operations. The unification of timestamps allows for the elimination of many common terms through difference operations. Consequently, closed-form results are obtained by applying the least-squares method without introducing intermediate variables. The proposed method is validated through theoretical analysis and numerical simulations, showing improved precision and reduced computational complexity compared to existing methods. It is thus well-suited for applications with strict precision requirements and limited computational resource.