Asymptotic Gradient Clock Synchronization in Wireless Sensor Networks for UWB Localization

Time-of-flight-based localization requires high-accurate synchronization among the nodes in a network. Gradient clock synchronization (GCS) is a class of distributed algorithms capable of providing the demanded accuracy. Global clock rates defined by GCS algorithms are susceptible to drift relative to the individual hardware clock rates. This is due to the lack of a hard tie to a physical clock rate and is identified as the chaotic clock rate phenomenon. This scales range of measurements and can lead to stability issues in the network. This article presents a novel GCS algorithm for ultrawideband (UWB) ranging networks, addressing the chaotic global clock rate phenomenon. A correction term is introduced in the generic GCS algorithm so that the global clock rate is guaranteed to be converging into the average of individual clock rates. This also achieves asymptotic stability in the clock rate error state. The stability of the generic GCS and the proposed method for time-invariant hardware clock rates are compared using eigenvalue analysis in the clock error state space. A Kalman filter-based technique is used to precisely estimate the interanchor clock dynamics and ranges, which are then used in the asymptotic GCS (AGCS) update rule to calculate synchronization parameters. Simulations and experiments are conducted to evaluate the stability and synchronization accuracy of the proposed algorithm. The localization accuracy is evaluated for an indoor quadcopter localization task, which uses a range-assisted inertial navigation system (INS), resulting in rms position errors in the order of 0.2 m.