Kalman filter based integrity for Lunar applications - Engwerda, H.J.A.; Swinden, R.; Uijt de Haag, M.; Melman, F. (ESA, 2024)
Outside the Earth's atmosphere, the traditional means of navigation is to perform tracking of the satellite by means of doppler ranging or other ground-based measurements. For most of these activities, the deep space network is utilized, which is approaching its limit in available bandwidth. Furthermore, for real-time navigation which is required for many forecasted operations outside Earth's atmosphere, this is not a viable solution. An alternative means of navigation is therefore required. For terrestrial applications, the use of GNSS as primary means of navigation is well developed. In space however, the implementation of this technology is still developing, but the potential for application far away from Earth's atmosphere is great. [1,2] By design, GNSS satellites transmit their signals in a (narrow) beam toward the Earth, for optimal use of its signal power. However, some of the power is also transmitted (mostly in side-lobes) into deep space and can therefore be used by orbiting satellites or Lunar receivers. When using these signals, it should be taken into account that the received power is significantly reduced, the geometric dilution of precision is poor, and a number of other factors such as doppler shift and availability of the signals is significantly different from terrestrial use. To this end, key players such as ESA and NASA are developing receivers and a Lunar PNT architecture including a lunar satellite constellation to support navigation on the Moon [3,4]. While some accuracy requirements could be met with these developments, the impact on navigation integrity is unclear. In previous work, the integrity of the navigation solution based on satellite navigation positioning at the Lunar surface was evaluated through the Advanced Receiver Autonomous Integrity Monitoring (ARAIM) algorithm [5]. This approach leveraged existing snapshot based positioning integrity monitoring, which is impacted by the poor geometry of GNSS-LCNS based navigation. To overcome poor observability and geometry, a Kalman filter based navigation approach is more likely to be expected for Lunar navigation applications. A filter design and implementation is presented, leveraging the ranging and range rate measurements coming from both GNSS and LCNS. A fault detection and exclusion approach based on [6] is implemented. Due to observability conditions, the filter design is evaluated to cope with correct error over bounding and protection level computations. As solution separation based integrity monitors such as ARAIM are severely hurt by poor satellite geometries and observability, the integrity monitor is a residual based monitor, which is affected less by such conditions and potentially is more computationally efficient. Such monitors rely on measurement residuals and the covariance associated with the state estimation, which means that incorrect state representation or poor filter design through the process noise and measurement noise matrices have a direct impact on the correctness of the integrity metrics. This work addresses some of these issues for expected Lunar applications. By means of service volume simulations, these integrity metrics are evaluated for regions on the lunar surface. As the moon is tidally locked, the far side will not have a direct line of sight towards the Earth and its orbiting satellites. The direct line-of-sight and dilution of precision is further determined in the simulations by considering the relative orbit and orientation towards Earth. The distance between the two celestial bodies varies over time, but also the orientation and regions which have a direct line of sight towards Earth and its orbiting satellites vary. Typical link budgets based on measured GNSS antenna radiation patterns are implemented, which together with forecasted receiver sensitivity and measurement noise allow for availability calculations. When taking into account performance expectations for lunar operations such as final descent or surface positioning, the integrity service availability can be determined from these simulations. Based on this work, recommendations can be made for potential applications and service levels for future Lunar missions.