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.