Towards Hybrid Lunar PNT: Error Models, Lower Bounds and Algorithms

Abstract: Accurate positioning, navigation and timing (PNT) are crucial for upcoming lunar surface missions. Lunar satellite navigation systems are being developed, but lack coverage during early deployment phases. Hybrid lunar PNT combining cooperative navigation, satellite systems, and an optional reference station offers improved accuracy and availability. This study develops realistic error models that incorporate temporal correlations often ignored in existing works. We derive a cooperative navigation error model considering fading and pseudorange bias from multipath propagation, and compare three error models for lunar satellite pseudorange and pseudorange rate signal-in-space error. These temporal error correlation models integrate easily into Kalman filters and provide realistic performance predictions essential for robust navigation engines. We perform case studies to demonstrate that hybrid navigation significantly improves accuracy, particularly with static users present. Most notably, hybrid navigation enables optimal performance when using a lunar reference station, achieving sub-meter accuracy with only two visible satellites.