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Research ArticleOriginal Article
Open Access

Multi-Epoch 3D-Mapping-Aided Positioning using Bayesian Filtering Techniques

Qiming Zhong and Paul D. Groves
NAVIGATION: Journal of the Institute of Navigation June 2022, 69 (2) navi.515; DOI: https://doi.org/10.33012/navi.515
Qiming Zhong
University College London, London, United Kingdom
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  • For correspondence: [email protected]
Paul D. Groves
University College London, London, United Kingdom
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Article Figures & Data

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  • FIGURE 1
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    FIGURE 1

    Components of the 3DMA GNSS core algorithms

  • FIGURE 2
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    FIGURE 2

    Different representations of position estimates by particle filtering and grid filtering

  • FIGURE 3
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    FIGURE 3

    Components of a 3DMA GNSS particle filter

  • FIGURE 4
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    FIGURE 4

    Components of a 3DMA GNSS grid filter

  • FIGURE 5
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    FIGURE 5

    True positions in City of London. Background map ©Google Maps

  • FIGURE 6
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    FIGURE 6

    True trajectory of van trial in Canary Wharf, London. Background map ©Google Maps

  • FIGURE 7
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    FIGURE 7

    Horizontal radial position root-mean-square error in City of London (stationary)

  • FIGURE 8
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    FIGURE 8

    Maximum horizontal radial position error at various confidence levels in City of London (stationary)

  • FIGURE 9
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    FIGURE 9

    Horizontal radial position root-mean-square error in Canary Wharf (vehicle)

  • FIGURE 10
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    FIGURE 10

    Maximum horizontal radial position error at various confidence levels in Canary Wharf (vehicle)

  • FIGURE 11
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    FIGURE 11

    Horizontal position error at Site C14_N, City of London (stationary)

  • FIGURE 12
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    FIGURE 12

    Horizontal position error of Epochs 401-600 in Canary Wharf (vehicle)

Tables

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    • View popup
    TABLE A1

    Tuning Parameters for Determining LOS Probability from Measured C/N0 in City of London

    Elevation, θSatellitessmin, dB-Hzsmax, dB-HzJPo–mina0a1, dB-Hz−1a2, dB-Hz−2Po–max
    0° ≤ θ ≤ 90°All27440.150.4549-0.04440.00120.85
    • View popup
    TABLE A2

    Tuning Parameters for Determining LOS Probability from Measured C/N0 in Canary Wharf

    Elevation, θSatellitessmin, dB-Hzsmax, dB-HzPo–mina0a1, dB-Hz−1a2, dB-Hz−2Po–max
    θ ≤ 20°All16320.2-0.41700.037400.8
    20° ≤ θ ≤ 60°GPS26400.2-0.83690.040600.8
    20° ≤ θ ≤ 60°Galileo21340.20.6333-0.06320.00200.8
    θ ≤ 60°All33400.2-2.78500.089700.8
    • View popup
    TABLE A3

    Parameters Used in the Likelihood-Based Ranging (LBR) Algorithm

    Data seta, m2b, m2μN, mσN, mμL, mσr, mδzmax, m
    City of London9.03 × 10440.7318.5019.0003.0029.00
    Canary Wharf1.41 × 10428.1026.0631.76-5.252.3630.00
    • View popup
    TABLE B1

    Statistics of the Satellites

    City of LondonCanary Wharf (central area)Canary Wharf (non-central area)
    Average signals per epoch18.69.213.2
    Average LOS signals per epoch5.115.111.7
    Mean elevation of LOS signals (°)60.046.737.3
    SD elevation of LOS signals (°)18.019.920.8
    Mean elevation of NLOS signals (°)36.435.925.7
    SD elevation of NLOS signals (°)19.918.016.4
    Mean C/N0 of LOS signals (dB-Hz)43.335.334.1
    SD C/N0 of LOS signals (dB-Hz)5.78.18.0
    Mean C/N0 of NLOS signals (dB-Hz)31.226.025.4
    SD C/N0 of NLOS signals (dB-Hz)8.16.66.5
    • Note: SD stands for standard deviation.

    • View popup
    TABLE B2

    Horizontal Radial Position RMS Errors (in Meters) for Different Algorithms in City of London

    Single-epochConventional Filtering3DMA Filtering
    Experiment IDConventional3DMAEKFPFPFGF
    C1_W8.137.604.427.306.377.82
    C1_E5.372.703.625.262.051.72
    C2_W13.4714.387.2110.7110.507.86
    C2_E10.0711.919.769.6410.056.98
    C313.692.742.977.374.544.15
    C45.362.435.335.542.411.76
    C56.134.285.045.914.333.09
    C62.913.412.192.462.431.52
    C76.104.743.375.301.772.05
    C816.2521.6714.4018.3914.567.97
    C9_W14.074.8712.1414.535.868.45
    C9_E12.868.539.258.584.143.23
    C10_W11.235.7912.6310.373.872.64
    C10_E17.5612.8814.0216.6615.989.53
    C1112.891.826.939.962.783.46
    C12_N9.155.167.149.286.896.12
    C12_S9.323.925.7610.013.834.35
    C13_N12.3728.158.2410.1338.8442.83
    C13_S23.8810.1427.3222.8515.0316.15
    C14_W15.755.517.9020.017.7010.37
    C14_E13.336.726.2612.406.686.69
    C15_W13.7518.8012.5812.5012.6614.63
    C15_E32.6821.3128.7723.9111.9911.12
    • View popup
    TABLE B3

    Horizontal Radial Position RMS Errors (in Meters) for Different Algorithms in Canary Wharf

    Single-epochConventional Filtering3DMA Filtering
    Epoch rangeConventional3DMAEKFPFPFGF
    1–200(0)21.5219.895.878.389.167.97
    201–400(0)40.0136.3645.6056.7411.6410.61
    401–600(139)66.8326.5829.8016.9116.2715.74
    601–800 (27)14.8618.3426.9319.2215.6016.88
    801–1,000(144)66.2749.6213.5117.508.487.63
    1,001–1,200(124)84.5268.2839.9533.609.358.59
    1,201–1,400 (27)12.4815.1424.2018.0813.2913.84
    1,401–1,602 (0)4.795.715.777.684.724.43
    • Note: The numbers in brackets in the first column represent the counts of epochs where vehicles were located in the central area of Canary Wharf.

    • View popup
    TABLE B4

    Maximum Horizontal Radial Position Error (in Meters) for Different Algorithms in City of London, 90% of Confidence

    Single-epochConventional Filtering3DMA Filtering
    Experiment IDConventional3DMAEKFPFPFGF
    C1_W13.2914.085.6611.8210.619.88
    C1_E8.913.884.817.763.002.31
    C2_W19.9516.489.2215.8216.9612.21
    C2_E14.0614.8212.0412.7614.547.75
    C321.734.124.1311.316.425.63
    C48.933.036.299.003.292.49
    C58.416.606.477.536.004.78
    C64.074.153.643.943.021.71
    C710.106.165.228.522.633.11
    C825.4733.4918.0327.8319.6111.16
    C9_W18.995.7813.7519.484.7817.49
    C9_E19.5610.1910.8012.345.865.65
    C10_W15.997.2214.7015.375.473.56
    C10_E24.0425.7114.4723.5040.2616.11
    C1119.163.2710.3315.494.554.24
    C12_N12.586.919.2512.847.897.70
    C12_S13.645.328.2514.655.576.51
    C13_N21.0532.4010.7717.5247.9647.95
    C13_S31.8421.2628.4728.1332.0031.42
    C14_W25.267.238.8732.1210.0912.84
    C14_E19.818.817.7517.678.149.04
    C15_W19.2932.4815.7016.6724.5930.58
    C15 E44.1028.8738.9740.9617.2315.51
    • View popup
    TABLE B5

    Maximum Horizontal Radial Position Error (in Meters) for Different Algorithms in Canary Wharf, 90% of Confidence

    Single-epochConventional Filtering3DMA Filtering
    Epoch rangeConventional3DMAEKFPFPFGF
    1–200 (0)22.2622.859.4713.9913.4912.09
    201–400(0)76.7751.5882.27104.0314.1713.66
    401–600(139)147.5455.2753.4627.6022.6719.05
    601–800 (27)20.7124.0158.4617.1324.2424.36
    801–1,000(144)74.8229.4924.2331.4412.9911.41
    1,001–1,200(124)151.1879.4582.9764.0415.0514.56
    1,201–1,400 (27)21.1712.4655.7622.579.0412.11
    1,401–1,602 (0)5.908.5110.2312.826.817.00
    • Note: The numbers in brackets in the first column represent the counts of epochs where vehicles were located in the central area of Canary Wharf.

    • View popup
    TABLE B6

    Maximum Horizontal Radial Position Error (in Meters) for Different Algorithms in City of London, 50% of Confidence

    Single-epochConventional Filtering3DMA Filtering
    Experiment IDConventional3DMAEKFPFPFGF
    C1_W6.355.784.205.835.327.18
    C1_E3.862.424.054.751.761.56
    C2_W12.8815.257.199.447.995.92
    C2_E9.5211.878.509.869.846.90
    C310.382.323.016.024.283.57
    C44.682.335.694.452.281.15
    C55.753.994.825.974.052.54
    C62.633.511.642.112.401.50
    C74.123.163.033.421.342.07
    C813.6418.1814.5915.3413.538.53
    C9_W13.281.5313.1613.982.255.62
    C9_E10.908.628.958.774.042.40
    C10_W10.645.6212.519.523.723.00
    C10_E16.766.0314.1515.317.775.82
    C119.730.845.547.811.673.73
    C12_N8.535.167.268.296.466.87
    C12_S9.134.324.899.503.154.92
    C13_N8.4430.748.987.6534.5847.38
    C13_S23.522.9327.7022.923.923.35
    C14_W11.575.307.8416.097.489.69
    C14_E10.486.325.848.686.465.87
    C15_W10.8212.9410.979.447.8710.47
    C15 E34.9221.3329.8816.0510.5610.58
    • View popup
    TABLE B7

    Maximum Horizontal Radial Position Error (in Meters) for Different Algorithms in Canary Wharf, 50% of Confidence

    Single-epochConventional Filtering3DMA Filtering
    Epoch rangeConventional3DMAEKFPFPFGF
    1–200 (0)5.264.144.765.683.743.62
    201–400 (0)5.866.1726.6329.175.295.32
    401–600(139)12.459.856.9910.996.786.68
    601–800 (27)3.853.3810.805.122.483.02
    801–1,000(144)9.935.786.899.814.724.23
    1,001–1,200(124)15.347.587.048.266.506.42
    1,201–1,400 (27)3.014.289.709.034.034.79
    1,401–1,602 (0)2.553.714.865.573.083.24
    • Note: The numbers in brackets in the first column represent the counts of epochs where vehicles were located in the central area of Canary Wharf.

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NAVIGATION: Journal of the Institute of Navigation: 69 (2)
NAVIGATION: Journal of the Institute of Navigation
Vol. 69, Issue 2
Summer 2022
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Multi-Epoch 3D-Mapping-Aided Positioning using Bayesian Filtering Techniques
Qiming Zhong, Paul D. Groves
NAVIGATION: Journal of the Institute of Navigation Jun 2022, 69 (2) navi.515; DOI: 10.33012/navi.515

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Multi-Epoch 3D-Mapping-Aided Positioning using Bayesian Filtering Techniques
Qiming Zhong, Paul D. Groves
NAVIGATION: Journal of the Institute of Navigation Jun 2022, 69 (2) navi.515; DOI: 10.33012/navi.515
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  • Article
    • Summary
    • 1 INTRODUCTION
    • 2 BACKGROUND
    • 3 3D-MAPPING-AIDED MULTI-EPOCH GNSS
    • 4 EXPERIMENTAL TESTS
    • 5 CONCLUSION
    • HOW TO CITE THIS ARTICLE
    • ACKNOWLEDGMENTS
    • APPENDIX A: A DETAILED DESCRIPTION OF ALGORITHMS
    • APPENDIX B: DETAILED EXPERIMENTAL RESULTS
    • Abbreviations
    • REFERENCES
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Keywords

  • 3D-mapping-aided GNSS
  • grid filter
  • Kalman filter
  • multi-epoch GNSS
  • particle filter

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