Article Figures & Data
Figures
- FIGURE 1
Components of the 3DMA GNSS core algorithms
- FIGURE 2
Different representations of position estimates by particle filtering and grid filtering
- FIGURE 3
Components of a 3DMA GNSS particle filter
- FIGURE 4
Components of a 3DMA GNSS grid filter
- FIGURE 5
True positions in City of London. Background map ©Google Maps
- FIGURE 6
True trajectory of van trial in Canary Wharf, London. Background map ©Google Maps
- FIGURE 7
Horizontal radial position root-mean-square error in City of London (stationary)
- FIGURE 8
Maximum horizontal radial position error at various confidence levels in City of London (stationary)
- FIGURE 9
Horizontal radial position root-mean-square error in Canary Wharf (vehicle)
- FIGURE 10
Maximum horizontal radial position error at various confidence levels in Canary Wharf (vehicle)
- FIGURE 11
Horizontal position error at Site C14_N, City of London (stationary)
- FIGURE 12
Horizontal position error of Epochs 401-600 in Canary Wharf (vehicle)
Tables
- TABLE A1
Tuning Parameters for Determining LOS Probability from Measured C/N0 in City of London
Elevation, θ Satellites smin, dB-Hz smax, dB-HzJ Po–min a0 a1, dB-Hz−1 a2, dB-Hz−2 Po–max 0° ≤ θ ≤ 90° All 27 44 0.15 0.4549 -0.0444 0.0012 0.85 - TABLE A2
Tuning Parameters for Determining LOS Probability from Measured C/N0 in Canary Wharf
Elevation, θ Satellites smin, dB-Hz smax, dB-Hz Po–min a0 a1, dB-Hz−1 a2, dB-Hz−2 Po–max θ ≤ 20° All 16 32 0.2 -0.4170 0.0374 0 0.8 20° ≤ θ ≤ 60° GPS 26 40 0.2 -0.8369 0.0406 0 0.8 20° ≤ θ ≤ 60° Galileo 21 34 0.2 0.6333 -0.0632 0.0020 0.8 θ ≤ 60° All 33 40 0.2 -2.7850 0.0897 0 0.8 Data set a, m2 b, m2 μN, m σN, m μL, m σr, m δzmax, m City of London 9.03 × 104 40.73 18.50 19.00 0 3.00 29.00 Canary Wharf 1.41 × 104 28.10 26.06 31.76 -5.25 2.36 30.00 City of London Canary Wharf (central area) Canary Wharf (non-central area) Average signals per epoch 18.6 9.2 13.2 Average LOS signals per epoch 5.11 5.1 11.7 Mean elevation of LOS signals (°) 60.0 46.7 37.3 SD elevation of LOS signals (°) 18.0 19.9 20.8 Mean elevation of NLOS signals (°) 36.4 35.9 25.7 SD elevation of NLOS signals (°) 19.9 18.0 16.4 Mean C/N0 of LOS signals (dB-Hz) 43.3 35.3 34.1 SD C/N0 of LOS signals (dB-Hz) 5.7 8.1 8.0 Mean C/N0 of NLOS signals (dB-Hz) 31.2 26.0 25.4 SD C/N0 of NLOS signals (dB-Hz) 8.1 6.6 6.5 Note: SD stands for standard deviation.
- TABLE B2
Horizontal Radial Position RMS Errors (in Meters) for Different Algorithms in City of London
Single-epoch Conventional Filtering 3DMA Filtering Experiment ID Conventional 3DMA EKF PF PF GF C1_W 8.13 7.60 4.42 7.30 6.37 7.82 C1_E 5.37 2.70 3.62 5.26 2.05 1.72 C2_W 13.47 14.38 7.21 10.71 10.50 7.86 C2_E 10.07 11.91 9.76 9.64 10.05 6.98 C3 13.69 2.74 2.97 7.37 4.54 4.15 C4 5.36 2.43 5.33 5.54 2.41 1.76 C5 6.13 4.28 5.04 5.91 4.33 3.09 C6 2.91 3.41 2.19 2.46 2.43 1.52 C7 6.10 4.74 3.37 5.30 1.77 2.05 C8 16.25 21.67 14.40 18.39 14.56 7.97 C9_W 14.07 4.87 12.14 14.53 5.86 8.45 C9_E 12.86 8.53 9.25 8.58 4.14 3.23 C10_W 11.23 5.79 12.63 10.37 3.87 2.64 C10_E 17.56 12.88 14.02 16.66 15.98 9.53 C11 12.89 1.82 6.93 9.96 2.78 3.46 C12_N 9.15 5.16 7.14 9.28 6.89 6.12 C12_S 9.32 3.92 5.76 10.01 3.83 4.35 C13_N 12.37 28.15 8.24 10.13 38.84 42.83 C13_S 23.88 10.14 27.32 22.85 15.03 16.15 C14_W 15.75 5.51 7.90 20.01 7.70 10.37 C14_E 13.33 6.72 6.26 12.40 6.68 6.69 C15_W 13.75 18.80 12.58 12.50 12.66 14.63 C15_E 32.68 21.31 28.77 23.91 11.99 11.12 - TABLE B3
Horizontal Radial Position RMS Errors (in Meters) for Different Algorithms in Canary Wharf
Single-epoch Conventional Filtering 3DMA Filtering Epoch range Conventional 3DMA EKF PF PF GF 1–200(0) 21.52 19.89 5.87 8.38 9.16 7.97 201–400(0) 40.01 36.36 45.60 56.74 11.64 10.61 401–600(139) 66.83 26.58 29.80 16.91 16.27 15.74 601–800 (27) 14.86 18.34 26.93 19.22 15.60 16.88 801–1,000(144) 66.27 49.62 13.51 17.50 8.48 7.63 1,001–1,200(124) 84.52 68.28 39.95 33.60 9.35 8.59 1,201–1,400 (27) 12.48 15.14 24.20 18.08 13.29 13.84 1,401–1,602 (0) 4.79 5.71 5.77 7.68 4.72 4.43 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.
- TABLE B4
Maximum Horizontal Radial Position Error (in Meters) for Different Algorithms in City of London, 90% of Confidence
Single-epoch Conventional Filtering 3DMA Filtering Experiment ID Conventional 3DMA EKF PF PF GF C1_W 13.29 14.08 5.66 11.82 10.61 9.88 C1_E 8.91 3.88 4.81 7.76 3.00 2.31 C2_W 19.95 16.48 9.22 15.82 16.96 12.21 C2_E 14.06 14.82 12.04 12.76 14.54 7.75 C3 21.73 4.12 4.13 11.31 6.42 5.63 C4 8.93 3.03 6.29 9.00 3.29 2.49 C5 8.41 6.60 6.47 7.53 6.00 4.78 C6 4.07 4.15 3.64 3.94 3.02 1.71 C7 10.10 6.16 5.22 8.52 2.63 3.11 C8 25.47 33.49 18.03 27.83 19.61 11.16 C9_W 18.99 5.78 13.75 19.48 4.78 17.49 C9_E 19.56 10.19 10.80 12.34 5.86 5.65 C10_W 15.99 7.22 14.70 15.37 5.47 3.56 C10_E 24.04 25.71 14.47 23.50 40.26 16.11 C11 19.16 3.27 10.33 15.49 4.55 4.24 C12_N 12.58 6.91 9.25 12.84 7.89 7.70 C12_S 13.64 5.32 8.25 14.65 5.57 6.51 C13_N 21.05 32.40 10.77 17.52 47.96 47.95 C13_S 31.84 21.26 28.47 28.13 32.00 31.42 C14_W 25.26 7.23 8.87 32.12 10.09 12.84 C14_E 19.81 8.81 7.75 17.67 8.14 9.04 C15_W 19.29 32.48 15.70 16.67 24.59 30.58 C15 E 44.10 28.87 38.97 40.96 17.23 15.51 - TABLE B5
Maximum Horizontal Radial Position Error (in Meters) for Different Algorithms in Canary Wharf, 90% of Confidence
Single-epoch Conventional Filtering 3DMA Filtering Epoch range Conventional 3DMA EKF PF PF GF 1–200 (0) 22.26 22.85 9.47 13.99 13.49 12.09 201–400(0) 76.77 51.58 82.27 104.03 14.17 13.66 401–600(139) 147.54 55.27 53.46 27.60 22.67 19.05 601–800 (27) 20.71 24.01 58.46 17.13 24.24 24.36 801–1,000(144) 74.82 29.49 24.23 31.44 12.99 11.41 1,001–1,200(124) 151.18 79.45 82.97 64.04 15.05 14.56 1,201–1,400 (27) 21.17 12.46 55.76 22.57 9.04 12.11 1,401–1,602 (0) 5.90 8.51 10.23 12.82 6.81 7.00 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.
- TABLE B6
Maximum Horizontal Radial Position Error (in Meters) for Different Algorithms in City of London, 50% of Confidence
Single-epoch Conventional Filtering 3DMA Filtering Experiment ID Conventional 3DMA EKF PF PF GF C1_W 6.35 5.78 4.20 5.83 5.32 7.18 C1_E 3.86 2.42 4.05 4.75 1.76 1.56 C2_W 12.88 15.25 7.19 9.44 7.99 5.92 C2_E 9.52 11.87 8.50 9.86 9.84 6.90 C3 10.38 2.32 3.01 6.02 4.28 3.57 C4 4.68 2.33 5.69 4.45 2.28 1.15 C5 5.75 3.99 4.82 5.97 4.05 2.54 C6 2.63 3.51 1.64 2.11 2.40 1.50 C7 4.12 3.16 3.03 3.42 1.34 2.07 C8 13.64 18.18 14.59 15.34 13.53 8.53 C9_W 13.28 1.53 13.16 13.98 2.25 5.62 C9_E 10.90 8.62 8.95 8.77 4.04 2.40 C10_W 10.64 5.62 12.51 9.52 3.72 3.00 C10_E 16.76 6.03 14.15 15.31 7.77 5.82 C11 9.73 0.84 5.54 7.81 1.67 3.73 C12_N 8.53 5.16 7.26 8.29 6.46 6.87 C12_S 9.13 4.32 4.89 9.50 3.15 4.92 C13_N 8.44 30.74 8.98 7.65 34.58 47.38 C13_S 23.52 2.93 27.70 22.92 3.92 3.35 C14_W 11.57 5.30 7.84 16.09 7.48 9.69 C14_E 10.48 6.32 5.84 8.68 6.46 5.87 C15_W 10.82 12.94 10.97 9.44 7.87 10.47 C15 E 34.92 21.33 29.88 16.05 10.56 10.58 - TABLE B7
Maximum Horizontal Radial Position Error (in Meters) for Different Algorithms in Canary Wharf, 50% of Confidence
Single-epoch Conventional Filtering 3DMA Filtering Epoch range Conventional 3DMA EKF PF PF GF 1–200 (0) 5.26 4.14 4.76 5.68 3.74 3.62 201–400 (0) 5.86 6.17 26.63 29.17 5.29 5.32 401–600(139) 12.45 9.85 6.99 10.99 6.78 6.68 601–800 (27) 3.85 3.38 10.80 5.12 2.48 3.02 801–1,000(144) 9.93 5.78 6.89 9.81 4.72 4.23 1,001–1,200(124) 15.34 7.58 7.04 8.26 6.50 6.42 1,201–1,400 (27) 3.01 4.28 9.70 9.03 4.03 4.79 1,401–1,602 (0) 2.55 3.71 4.86 5.57 3.08 3.24 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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