Construction of a Single-Reference τ-Parametrized Time Scale and Its Application in Solar System Centimeter-Level Navigation

Abstract Research Background and Motivation: The current IAU post-Newtonian (PN) framework for solar system navigation suffers from core deficiencies including redundant reference frames and time scale chains, high risk of error accumulation, and poor engineering adaptability. Notably, a critical theoretical gap exists in the relativistic correction model for Mars navi gation, which fails to meet the high-precision requirements of Chang’e lunar missions, Mars exploration, and future solar system centimeter-level navigation. Theoretical Innovation and Methodology: Based on the author’s proposed Fuxi theory (a relativistic spacetime theory centered on the time flow rate ratio A), this study systematically explores its application in solar system high-precision navigation for the first time, establishing a new paradigm for τ-parametrized time effect calculation. This theory is equivalent to general relativity (GR) under both weak-field and strong-field conditions, fully matches the ten parameters of the parameterized post-Newtonian (PPN) formalism, and effectively resolves issues of strong-field compatibility and dimensional contradictions. Core Advantages and Performance: Method ologically, the ”single TCB reference + A direct mapping” mechanism reduces computa tional steps from ≥ 20 in traditional PN methods to ≤ 4. Combined with τ-parametrized dynamics, Bayesian fusion, and physics-constrained machine learning (ML), tests based on a simulated ARM Cortex-A53 CPU (1.2 GHz frequency, 256 KB cache) demonstrate that the theoretical computational efficiency is improved by 500 times compared with traditional PN methods, while accommodating non-Gaussian error distributions. From an engineering perspective, the framework exhibits forward compatibility with the IAU 2025 Resolution, with single-scenario computation time ≤ 0.92 ms and memory usage ≤ 38.7 KB, theoretically meeting the resource constraints of deep space probes. Application Value and Validation: This study fills the theoretical gap in relativistic corrections for Mars navigation, directly supporting high-precision time synchronization for the Chang’e series missions, orbit cor rections for Mars sample return, and accuracy enhancement for multi-body solar system navigation. It provides a concise and efficient relativistic solution for frontier tasks such as lunar base construction. Python code for Bayesian parameter estimation of lunar vLLO orbits based on Fuxi theory has been uploaded to Zenodo (DOI: 10.5281/zenodo.18264078), offering a reproducible tool for theoretical validation. Research Limitations and Collaboration Invitation: This is an independent theoretical research effort without aerospace practice or Construction of a Single-Reference τ-Parametrized Time Scale and Its Application in Solar System Centimeter-Level Navigation experimental conditions. Engineering adaptability is verified based on a simulated CPU, and strong-field scenarios as well as non-Gaussian error processing lack calibration with actual aerospace measurement data. We sincerely invite relevant institutions or funds to provide sponsorship, or teams with aerospace measurement capabilities to collaborate, jointly ad vancing the in-orbit validation and engineering implementation of the theory. Additionally, we kindly request senior scholars in the fields of general relativity, spacetime physics, and dark matter research to provide recommendations for this study on arXiv via the following link: https://arxiv.org/auth/endorse?x=G9TUIW.