Session P5: GNSS Systems Timing Architectures and Capabilities

Convergence and Accuracy Assessment for Simultaneous Range Measurement and Clock Synchronization in Transceiver-Based Mutual One-Way Range Exchange Scheme
Junichiro Kawaguchi and Shingo Nishimoto, Australian National University
Location: Seaview A/B
Date/Time: Thursday, Jan. 30, 4:11 p.m.

Introduction:
The authors have recently investigated a novel method for simultaneous range measurement and clock synchronization. This method is known as the Asynchronous One-Way Range (AOWR) scheme, which operates using a transceiver-based approach. The authors have reported the results, including findings from field radio tests.
The AOWR method is characterized by its 'asynchrony' and involves iteratively synchronizing one clock to another. This allows for simultaneous ranging, even during high-speed motion, such as in space flight. The method does not require initial clock synchronization, which is why it emphasizes the concept of asynchrony.
The AOWR scheme differs significantly from conventional transponders, which measure round-trip time rather than direct range. In typical spacecraft operations, the ascent and descent ranges are different, necessitating the processing of transponder data in conjunction with flight dynamics for practical application. In contrast, the AOWR scheme involves the reception of the signals at the same instances at both the ground station and the spacecraft, ensuring that the range measured at both ends is uniquely and readily accessible. Iterative synchronization enables the reception instances identical.
For the purpose of clock synchronization, the range or position properties must be uniquely determined simultaneously. For instance, the Global Navigation Satellite System (GNSS) uniquely determines three-dimensional (3D) positions. However, in distant regions such as cis-lunar space, GNSS fails to synchronize clocks due to the poor geometry associated with short baseline lengths. In contrast, the AOWR system can synchronize clocks regardless of the distance from the ground station, as it only needs to determine a scalar property—the range—which is independent of baseline length. Despite numerous studies, an effective positioning method for cis-lunar space has yet to be established. The AOWR, when supported by three or more ground stations, can facilitate positioning in cis-lunar space. When combined with GNSS, which receives signals through the side lobes of the GNSS satellites, the method requires only one AOWR ground station for positioning. This presents a highly practical solution for positioning in cis-lunar space.
Besides, the AOWR scheme has the advantage of operating solely through a pair of entities: a ground station and a spacecraft. Additionally, it inherently possesses the remarkable property of providing pseudo-range measurements that are free from both range uncertainty and clock uncertainty, which facilitates immediate carrier-phase synchronization.

Objectives:
The reports published by the authors have primarily focused on the theoretical fundamentals. However, they have not provided detailed information on how the iterative synchronization is performed. This paper aims to concentrate on the practical properties, the convergence process, and the residual errors associated with the AOWR scheme. In the absence of range-rate and clock drift, resetting the clock in a straightforward manner seems to effectively synchronizes it. However, this approach does not perform as expected when range-rate and clock drift are present. This paper derives the convergence process and examines the practical convergence speed, along with the residual differences observed during the iterative AOWR process.

Methodology:
This paper primarily examines the synchronization mechanism and successfully articulates the pseudorange data, including range rate and clock drift, for both the ground station and the spacecraft. As presented in the paper, this analysis is used to derive the convergence conditions along with the convergence properties—specifically, the speed and the residuals. These aspects are detailed concretely within the paper.

Analytical Results and Numerically Simulated Results:
The paper concludes the convergence ratio observed during measurements. At short distances, when the Measurement Interval (MI) is sufficiently long relative to the One-way Propagation Time (OPT), the synchronization error decreases rapidly with the ratio of OPT to MI with each measurement. When MI is close to OPT, the ratio reduces to one-half. At longer distances, when MI is significantly shorter than OPT, the convergence ratio decreases to one-third. The properties are expressed concretely in the paper.
For demonstration purposes, this paper presents numerical simulations that examine the convergence properties. These simulations are conducted for cases in cis-lunar space and the near-Earth interplanetary field. The results of these simulations are reported in this presentation.

What is New and/or Innovative / Conclusions and Significance:
The AOWR scheme synchronizes clocks regardless of their distance from Earth, as it does not rely on baseline length and is independent of three-dimensional positioning. Previous studies have assumed that simply resetting the clock directly achieves synchronization. However, this study investigates the synchronization process and derives the convergence properties associated with it.
The AOWR scheme is a method that does not require specific transponders. It allows non-agency entities to operate their spacecraft autonomously. However, the iterative process has not been thoroughly examined, and the relevant indices have been expected.
The properties examined in this paper, including the characteristics of concrete, the duration of synchronization, and the residual amount of synchronization, are articulated and elucidated. This study demonstrates and proves, for the first time, the stability of iterative synchronization within the AOWR scheme.
The practical applications for cis-lunar and near-Earth deep space navigation are being envisioned.