Future lunar surface missions require reliable positioning for autonomous rover operations. Lunar navigation satellite systems may provide limited vertical positioning accuracy due to satellite availability and observation geometry, particularly during early deployment. This study investigates a radiometric navigation architecture in which a lunar surface station (SS) improves rover positioning through double-differenced satellite observations and additional surface-to-surface ranging. Pseudorange and Doppler measurements from lunar navigation satellites are used for relative positioning between the SS and rover, while dual one-way ranging (DOWR) provides an additional range observable. The radiometric solution is integrated with rover dead-reckoning information. Monte Carlo simulations were conducted using five satellites representative of NASA's Lunar Communications Relay and Navigation Systems (LCRNS) constellation and a rover trajectory near Connecting Ridge at the lunar south pole. The results show that the SS improves horizontal and vertical relative positioning, with further gains from DOWR. In the simulated scenario, the mean 99.7% vertical positioning error decreased from 29.9 m without the SS to 5.5 m with double-differenced pseudorange and Doppler processing, and to 4.8 m with DOWR. An uncorrected DOWR hardware bias significantly degraded positioning, whereas the proposed bias-estimation method achieved a final estimation error of 0.058 +/- 0.057 m. The benefit of DOWR also depended on observation geometry. These results demonstrate the potential of a lunar surface station to improve vertical relative positioning through direct radiometric ranging, complementing its communication and navigation support roles.
Figures & tables
Figure 1: Overview of the radiometric architecture. (The figure was generated using the image generation feature in ChatGPT GPT-5.6 Sol and subsequently edited by the author.)
Figure 2: Sensor Fusion Architecture. (The figure was generated using the image generation feature in ChatGPT GPT-5.6 Sol and subsequently edited by the author.)
Figure 3: Simulated lunar navigation satellite orbits in the MCMF frame: three-dimensional view (left) and polar view (right).
Figure 4: Simulated SS location, rover trajectory, and SS–rover LOS conditions. Each line-of-sight grid represents 100 m × 100 m.
Parameter
Value
Unit
Epoch interval
0.5
min
Radiometric observation interval
1
epoch
Total simulation period
7200
epochs
Evaluation period
3601–7200
epochs
Doppler weighting factor
1
–
PDOP-like metric threshold for DOWR-bias update
3
–
Table 1: Simulation parameters.
Figure 5: Terrain horizon elevation along the rover trajectory for eight azimuth directions.
Figure 6: Received-power histories at the rover for lunar navigation satellites S1–S5.
Satellite
68%
95%
99.7%
Satellite clock range error [m]
S1
2.0±0.39
2.9±0.31
3.4±0.32
S2
2.0±0.33
2.9±0.24
3.4±0.26
S3
2.0±0.34
2.9±0.28
3.4±0.28
S4
2.2±0.34
3.0±0.23
3.5±0.23
S5
2.0±0.35
3.0±0.17
3.5±0.19
Table 2: Statistics of the simulated error sources.
Figure 7: User positioning errors for the three navigation cases: pseudorange (PR) and Doppler without SS, DD PR/Doppler, and DD PR/Doppler with SS–rover DOWR. The upper panels show the radiometric position error δxR obtained from the radiometric positioning without sensor fusion. The lower panels show the corresponding user positioning errors after integration with the navigation-sensor measurements through the sensor-fusion filter. The shaded regions indicate epochs in which radiometric position updates were unavailable. Each line represents one Monte Carlo run.
Figure 8: Visualization of the horizontal and vertical positioning accuracy for the three navigation cases summarized in Table 3 . Bars show the mean accuracy over the Monte Carlo runs, and error bars indicate the corresponding standard deviation.
Metric
PR/Doppler (Without SS)
DD PR/Doppler (Without SS–rover ranging)
DD PR/Doppler + DOWR (With SS–rover ranging)
Horizontal accuracy, 68% [m]
10.6±2.9
2.8±0.7
1.8±0.3
Horizontal accuracy, 95% [m]
26.1±13.1
10.8±4.7
8.7±3.9
Horizontal accuracy, 99.7% [m]
33.1±15.6
16.2±6.7
14.1±5.7
Vertical accuracy, 68% [m]
14.2±4.6
1.3±0.2
1.1±0.2
Vertical accuracy, 95% [m]
25.1±7.9
3.4±1.1
2.7±0.7
Vertical accuracy, 99.7% [m]
29.9±8.0
5.5±1.8
4.8±1.6
Table 3: Comparison of the user positioning performance after integration with the navigation-sensor measurements. Positioning errors are shown as mean ± standard deviation.
Figure 9: DOWR-bias estimation error during the calibration period. Each line represents one Monte Carlo run. The stepwise behavior of the DOWR-bias estimation error was caused by the geometry screening based on the PDOP-like metric DP,k .
Metric
Bias est. OFF
Bias est. ON
Horizontal accuracy, 68% [m]
4.6±1.0
1.8±0.3
Horizontal accuracy, 95% [m]
10.7±3.3
8.7±3.9
Horizontal accuracy, 99.7% [m]
18.9±6.8
14.1±5.7
Vertical accuracy, 68% [m]
8.6±2.3
1.1±0.2
Vertical accuracy, 95% [m]
16.7±4.8
2.7±0.7
Vertical accuracy, 99.7% [m]
19.7±5.7
4.8±1.6
Table 4: Effect of DOWR-bias estimation on user positioning accuracy for two SS–rover ranging cases. Values are shown as mean ± standard deviation.
Figure 10: Comparison of the VDOP-like vertical geometry metric with and without SS–rover ranging. The upper and lower panels show the same data with different vertical-axis scales. The dashed line indicates the geometry threshold used for radiometric position updates.
Figure 11: DD pseudorange observation geometry and SS–rover DOWR observation vector at epochs 5000 and 5580.
Accurate position estimation is crucial for the successful implementation of future lunar landings using autonomous vehicles, especially in dangerous environments with sparse terrain features. In this paper, we propose a terrain relative navigation (TRN) algorithm combining our deep-learning crater detector, which was designed specifically for the NASA Crater Detection Challenge problem, and an Extended Kalman Filter (EKF). Our detector analyzes crater features from the monocular images acquired from orbit, and their matches with craters from a global database are identified via a Hungarian assignment approach followed by the consensus-based outliers removal method. The estimated measurements are then used to refine an EKF, where spacecraft pose estimation in the Lunar-Centered Lunar-Fixed (LCLF) frame of reference, augmented with altitude aiding information, constrains radial drift. The simulation results indicate that even if the spacecraft is off from its actual location up to 5 km, TRN could recover from this situation, achieving navigation error reduction to a few hundred meters. It should be noted that in order to maintain crater feature correspondences, it is important to match the image resolution and the scales within the scene to the detector training set distribution.
Batu Candan, Simone Servadio
Aerospace Engineering Department · Iowa State University · Ames, Iowa, USA
Future planetary surface missions are likely to involve multiple independently operated rovers sharing the same deployment region, raising the need to verify compliance with operational constraints such as Lunar Safety Zones. Because continuous in-situ observability is rarely available, such verification requires post-hoc reconstruction of rover trajectories from sparse telemetry, including odometry, pose priors, and relative inter-rover detections. We introduce the problem of forensic trajectory analysis for non-cooperative planetary rovers in the presence of Byzantine agents: rovers that provide miscalibrated or deliberately falsified measurements to support an incorrect trajectory. We show that standard outlier-robust pose graph optimisation methods are vulnerable in this setting, because Byzantine rovers can generate measurements that are internally consistent and numerous enough to make truthful incriminating measurements appear as outliers. To address this, we propose an attribution-aware trajectory estimation method that reasons over rover credibility rather than individual measurement validity. The method evaluates candidate credible rover subsets by comparing the statistical consistency of their internal and boundary relative detections against provided priors, and then estimates trajectories using only measurements attributed to credible agents. Across synthetic simulations and real planetary-analogue trajectory data, the proposed method identifies Byzantine rovers and produces significantly more accurate trajectory estimates than existing robust pose graph optimisation baselines.
Lachlan Holden, Feras Dayoub, Melissa de Zwart +2
AI for Space Group · Andy Thomas Centre for Space Resources, Adelaide University, Australia.
Future lunar missions will require autonomous rovers capable of traversing tens of kilometers across challenging terrain while maintaining accurate localization and producing globally consistent maps. However, the absence of global positioning systems, extreme illumination, and low-texture regolith make long-range navigation on the Moon particularly difficult, as visual-inertial odometry pipelines accumulate drift over extended traverses. To address this challenge, we present a stereo visual simultaneous localization and mapping (SLAM) system that integrates learned feature detection and matching with global constraints from digital elevation models (DEMs). Our front-end employs learning-based feature extraction and matching to achieve robustness to illumination extremes and repetitive terrain, while the back-end incorporates DEM-derived height and surface-normal factors into a pose graph, providing absolute surface constraints that mitigate long-term drift. We validate our approach using both simulated lunar traverse data generated in Unreal Engine and real Moon/Mars analog data collected from Mt. Etna. Results demonstrate that DEM anchoring consistently reduces absolute trajectory error compared to baseline SLAM methods, lowering drift in long-range navigation even in repetitive or visually aliased terrain.
Adam Dai, Guillem Casadesus Vila, Grace Gao
Stanford University William F. Durand Building 496 Lomita Mall Stanford, CA 94305