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Session F3a: Lunar Positioning, Navigation, and Timing

Orbit Determination of Lunar Radio Navigation Satellites Using MEMS Accelerometers and Microwave Tracking
Luciano Iess and Andrea Sesta, Sapienza University of Rome
Alternate Number 1

The performances of a lunar radio navigation system depend on a precise orbit determination and time synchronization (ODTS) system. In a prior work (Iess et al., 2023), we introduced a system architecture built on the concept of Multiple Spacecraft per Aperture (MSPA). In this framework, a constellation of small satellites (smallsats) is tracked in two-way coherent mode from a single ground antenna, yielding highly accurate range, range rate, and single-beam interferometry (SBI) measurements crucial for orbit determination. The preferred frequency of the link is in K band (22.5-26.5 GHz) to reduce ionospheric effects and use larger modulation bandwidths enabling more accurate ranging measurements.
While the proposed system is able to meet the positioning and time synchronization requirements being considered by the space agencies, the orbit determination analysis found that the ageing of the navigation message, in particular the ageing of the ephemerides, is relatively fast. This is a consequence of the large area-to-mass ratio of the satellites of the constellation, based on smallsats. The satellites are therefore subject to quite significant non-gravitational accelerations (NGA), with solar radiation pressure dominating over thermal recoil and other weaker effects.
In this work we assess the benefits and limitations of a direct measurement of NGA by means of low mass, low power, MEMS-based accelerometers under development in Europe. Although the technology readiness level (TRL) of these units is still low, we use the predicted performances, at two levels of their development stages, to improve the orbit determination and the propagation of the spacecraft state. In the first stage, the target for the acceleration noise floor is 3 10-8 m/s2 /sqrt(Hz) at 10-4 Hz, and 3 10-7 m/s2 /sqrt(Hz) at 10-5 Hz. In a further development, the target acceleration noise floor is one order of magnitude lower. At 10-4 Hz the noise floor is about 1% and 0.1% of the total expected solar radiation pressure acceleration (using an area-to-mass ratio typical of smallsats), respectively for stage 1 and 2 of the MEMS accelerometer development. Given that the orbital period of the satellites is about 24 h, the performances at low frequency are especially relevant.
Numerical simulations indicate that even a low-rate transmission to ground of the three components of the measured acceleration (one vectorial acceleration every 60 s) may improve the accuracy of orbit determination if the advanced version of the accelerometer is used. However, only a further improvement by a factor of 10 in the noise floor of the accelerometer at low frequencies (10-5 – 10-3 Hz) would result in a major advantage over mathematical modelling of non-gravitational accelerations.
While accelerometers may contribute to a better orbit reconstruction, therefore extending the validity period of the navigation message, the main factor causing the ageing of the ephemerides, i.e. the inaccurate modelling of the NGA in the orbit propagation, still persists. We propose two methods to tackle this problem, by means of a combination of accelerometer data, radio-metric measurements and mathematical modelling or by adopting physics-informed machine learning methods, trained on the measured accelerations and housekeeping data.

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