Lunar Laser Ranging (LLR) technology has evolved significantly over the past 55 years since its inception in the last century. During this period, both the theoretical framework of LLR and the associated hardware technologies have advanced rapidly. These advancements have substantially enhanced the detection capabilities of LLR systems, enabling the ranging uncertainty to improve from an initial meter-level accuracy to the current millimeter-level accuracy [1,2]. Furthermore, ongoing developments are pushing the boundaries towards achieving sub-millimeter level uncertainty.

The precise measurement of the Earth-Moon distance holds immense value for testing and refining fundamental theories of gravity [[3], [4], [5], [6], [7], [8], [9]]. For instance, high-accuracy LLR data have been instrumental in the following areas:

• 1.
  Strong Equivalence Principle (SEP): Precision of approximately 3 × 10^-5.
• 2.
  Weak Equivalence Principle (WEP): Precision of approximately 10^-14.
• 3.
  Temporal Variation of the ≈ 10^-14 per year.
• 4.
  Inverse-Square Law at Large Distances: Precision of approximately 5 × 10^-12.

To further enhance the precision of fundamental physics research, obtaining high-accuracy LLR data is currently a critical bottleneck. A significant obstacle to improving LLR accuracy is the phenomenon of echo broadening associated with corner reflector arrays. Specifically, the A15 corner reflector array exhibits echo broadening in the range of 0–350 ps, while the A11 and A14 arrays demonstrate echo broadening of 0–150 ps [10]. One of the primary causes of this echo broadening is the Moon’s “libration” motion as it orbits the Earth [11]. This libration causes the plane of the corner reflector arrays to tilt relative to the Earth, contributing to the observed broadening effect.

Yang et al. developed a methodology aimed at deriving precise modes of free lunar librations, achieving results that are currently recognized as the most accurate lunar ephemeris. This was accomplished utilizing data from the Gravity Recovery and Interior Laboratory (GRAIL) mission [12]. In a separate study, Dmitry A. Pavlov et al. analyzed lunar physical libration by employing LLR normal point (NP) data spanning from 1970 to 2013 [13]. N. Rambaux et al. utilized LLR data in conjunction with the DE421 ephemeris to identify and estimate approximately 130–140 terms in the angular series of latitude librations and polar coordinates, along with 89 terms in the longitude angle [14]. Additionally, J. Chapront et al. investigated four distinct libration models: three numerical models developed by JPL and an analytical model enhanced with numerical complements fitted to recent LLR observations. Their study focused on the differences between these models, which are influenced by the Moon’s gravitational and tidal parameters, as well as the amplitudes and frequencies of free librations [15].

To mitigate the impact of echo broadening from corner reflectors on the uncertainty of Lunar Laser Ranging (LLR), the development of next-generation LLR corner reflectors [[16], [17], [18], [19], [20]] has emerged as a key research focus in the field. Among these advancements, the design and fabrication of single large-aperture corner reflectors have garnered significant scientific interest. Yun He et al. developed a hollow retroreflector with a 100 mm aperture, employing silicate bonding and an innovative manufacturing technique, achieving dihedral angle shifts of 0.5″, 0.8″, and 1.9″ [21]. Similarly, M. Martini et al. designed a solid corner reflector with a 100 mm aperture, conducting simulations and experimental studies on its optical far-field diffraction pattern. They established a relationship between far-field energy distribution and temperature variations and simulated the energy changes of the reflector under fluctuating lunar surface temperatures [22]. Additionally, Slava G. Turyshev et al. performed preliminary thermal, mechanical, and optical design and analysis for a novel single-corner reflector. Their research demonstrates that this new instrument can achieve an Earth-Moon distance measurement uncertainty of 1 mm in a single pulse, endure the extreme thermal variations on the lunar surface, and maintain a low mass suitable for robotic deployment [23].

Even though the echo broadening effect induced by the corner reflector array may increase ranging uncertainty, this phenomenon can be scientifically exploited based on the information it carries. This study presents a comprehensive analysis of the ranging accuracy for multiple corner reflector arrays during simultaneous observations on the same night and under similar temporal conditions, enabling the inversion of lunar libration parameters. The findings of this research are expected to contribute significantly to the refinement of lunar ephemeris.

The manuscript is organized as follows: Section 2 introduces the methodological framework and establishes the inversion model for lunar libration based on the ranging uncertainty analysis of multi-corner cube reflector arrays. Section 3 presents a comprehensive analysis of lunar laser ranging (LLR) data obtained from the International Laser Ranging Service (ILRS), specifically from the Grasse station, including uncertainty assessment and subsequent lunar libration calculations. Section 4 details the error analysis and quantification of the derived lunar libration parameters. Finally, Section 5 provides a comprehensive summary and discussion of the study’s findings.