Article Figures & Data
Figures
- FIGURE 1
Population increase of the 35 largest cities in the United States (USCB 2019)
- FIGURE 2
Sky plot of the buildings surrounding Denver’s Union Station in 2014 (left) and the sky plot for the same location in 2019 (right)
- FIGURE 3
Diagram of regions that are shadowed and visible to a GNSS satellite in an urban canyon
- FIGURE 4
Map of the locations of the three experiments (top) and the sky plot generated from Google maps imagery for the center of the three experiments (bottom).
- FIGURE 5
Receiver positions in three experiments, Exp1 (left), Exp2 (center), and Exp3 (right). Images obtained from Google Maps
- FIGURE 6
Framework for software created for analyzing GPS signals in Denver urban environment using Qt and C++. Building model is rendered from software written using OpenGL for visualization. Building model is interrogated from software written using PBRT library of ray-tracing methods. Inputs to software include data from DRCOG, USGS, GNSS_Logger Android app, and GPS broadcast messages.
- FIGURE 7
Three-dimensional model of Denver rendered with software framework (left) and the satellite imagery of Denver from Google maps (right). Right image obtained from Google maps
- FIGURE 8
Visibility-boundary sky plot of a location in downtown Denver generated using ray tracing and 3D building model (left) and the corresponding imagery of Denver from Google maps as a sky plot (right)
- ALGORITHM 1.
Assigning a specularity value to each direction in the sky
- FIGURE 9
Diagram of reflection geometry related to the Fresnel zone and specularity metric.
- FIGURE 10
Diagram of 3D model illustrating the intersection locations within the first Fresnel zones for GPS PRN 31 at 8:32 UTC for receiver location in experiment E1 (left). The intersections are shown in red, and the receiver location is shown as a green sphere. The Google imagery of the experiment location is shown to the right
- FIGURE 11
Diagram of 3D model illustrating the intersection locations within the first Fresnel zones for GPS PRN 31 at 3:58 UTC for receiver R3 in experiment E2 (left). The intersections are shown in red, and the receiver location is shown as a green sphere. The Google imagery of the experiment location is shown to the right.
- FIGURE 12
SNR (top) and specularity value (bottom) time histories for GPS PRN 31 for all four receivers for the entire duration of experiment E2
- FIGURE 13
Specularity value sky plot (left, middle) and the sky plot of the boundaries for the specularity sky plot with the solid line defining the higher elevation boundary and the dotted line defining the lower elevation boundary (right)
- FIGURE 14
Visibility sky plots (top) showing directions obstructed by buildings (white) for receiver locations (R1-R4) and GPS (G) and GLONASS (R) satellite locations for duration of experiment Exp2 indicated from starting location (•) and ending location (×). Colors correspond to receiver markers shown in Figure 5. The specularity sky plots (bottom) showing directions with regions predicted to have strong specular reflections (shaded) and areas where specularity is weak and reflections are not predicted (white)
- FIGURE 15
Satellite SNR values for receivers (left) and the predicted specularity values (right) in experiments Exp1, Exp2, and Exp3
- FIGURE 16
SNR vs specularity value for all tracked satellites expected to be invisible. Gray is all observed data points (∼280,000 data points) and red is the average SNR value for each tenth of a predicted specularity integer value
- FIGURE 17
Average distance errors for Exp1, Exp2, and Exp3 for the single receiver and the collaborative receiver for the SM and SPM scoring scheme
- FIGURE 18
Average distance errors for Exp1, Exp2, and Exp3 for a single receiver and the collaborative receiver for the SM+i and SPM+i scoring schemes
- FIGURE 19
Scores for candidate locations in Exp1 for receiver R1 at 21:46 (top), Exp 2 for receiver R3 at 3:46 UTC (middle), and Exp3 for receiver R3 and 6:27 UTC (bottom) for scoring schemes SM, SPM, SM+i, and SPM+i(left to right). The correct location for the receiver (red X) and the estimated location (black O) based on the scoring scheme are depicted on each plot
- FIGURE 20
Geometries for PRN 31 in Exp2. a. Buildings surrounding receivers in Exp2 obtained from Google Maps. b. 3D rendered building model with DLOS (blue line) to GPS satellite PRN 31 obstructed by building at 3:47 UTC for receiver R4 (green dot). Specular reflections intersection points reaching the receiver from PRN 31 indicated by red spheres. c. Specularity value at each candidate location for PRN 31 at 3:47 UTC with true location indicated by red X
- FIGURE A.1
Reflector geometry used to find specular reflection point (R)
- FIGURE A.2
Reflector geometry used to determine whether a generic intersection point (G) is within the first Fresnel zone ellipse
Tables
Predictions: Invisible Visible Observations Not-tracked 1 0 Tracked 0 1 Predictions: Invisible Diffracted Visible Observations Not-tracked 1 1 0 Weak signal 0.5 2 0.5 Strong signal 0 1 1 Date & Time Receiver No. Latitude, Longitude (deg.) Distance from avg. location (m) Exp1 June 26, 2018 (brdc1770.18) R1–R4 39.74854, −104.99400 21:35 – 23:10 UTC Exp2 July 30, 2018 (brdc2110.18) R1 39.74879, −104.99290 14 3:45 – 4:15 UTC R2 39.74885, −104.99283 5 R3 39.74892, −104.99273 7 R4 39.74896, −104.99268 13 Exp3 March 2, 2019 (brdc0610.19) R1 39.74637, −104.99053 10 6:22 – 6:45 UTC R2 39.74641, −104.99049 5 R3 39.74645, −104.99044 3 R4 39.74651, −104.99035 12 Predictions: Invisible Low Specularity Invisible High Specularity Visible Observations Not-tracked 1 1 0 Tracked 0 1 1 Predictions: Invisible Visible Observations Not-tracked 1 0 Tracked DLOS 0 1 Tracked NLOS 1 0 Predictions: Invisible Low Specularity Invisible High Specularity Visible Observations Not-tracked 1 1 0 Tracked DLOS 0 0 1 Tracked NLOS 0 1 0
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