Constructing a 3-D Virtual Map Utilizing GPS Coordinates. Jonathan McGinnis. Hickory High School Hickory, NC

Transcription

1 Constructing a 3-D Virtual Map Utilizing GPS Coordinates Jonathan McGinnis Hickory High School Hickory, NC Summer Ventures in Science and Mathematics 2007 Visual and Image Processing Dr. Rahman Tashakkori, Mr. Jere Miles Appalachian State University, NC July 28, 2007

2 Abstract This research involved collecting GPS coordinates based on latitude, longitude, and elevation, to create images based on three quantitative categories. These images can resemble three-dimensional plots that allow further analysis. Using GPS devices, we collected the data in a specified area. With these points, we analyzed the comparison between latitude, longitude, and altitude.

3 Introduction Global Positioning System (GPS) is a satellite navigation system that was designed for military purposes that would replace the Transit Navy Navigation Satellite System and funded by the U. S. Department of Defense. However, GPS became available to civilians and thousands of people are civil users today. On June 26, 1993, the U.S. Air Force launched the 24 th NAVSTAR satellite into orbit, completing a network of 24 satellites that forms the Global Positioning System. [1] Each one of the satellites transmits precise microwave signals. With a GPS receiver that costs less than a few hundred dollars you can instantly learn your location on the planet--your latitude, longitude, and even elevation--to within a few hundred feet by measuring the distance between itself and three or more GPS satellites. Measuring the time delay between transmission and reception of each GPS microwave signal gives the distance to each satellite, since the signal travels at a known speed. [2] The signals also carry information about the satellites' location. By determining the position of, and distance to, at least three satellites, the receiver can compute its position using trilateration. Receivers typically do not have perfectly accurate clocks and therefore track one or more additional satellites to correct the receiver's clock error. [3] MATLAB (Matrix Laboratory) is an interactive system for numerical computations. This program is excellent for developing algorithms and problem solving environments. It can also be used to create 3-D visualizations and maps from data points in a matrix. You can use MATLAB s functions to create a grid of uniformly sampled data points, which MATLAB then constructs a surface plot by connecting neighboring matrix elements to form a mesh of quadrilaterals.

4 Figure 1 Shows a 3-D surface plot with color texturing. By plotting data points into a matrix in MATLAB, one can create different images depending on how many categories of data available. Figure 1 shows an image based on three quantitative categories. We intend to explore the concept that by using GPS coordinates based on latitude, longitude, and elevation, one could create an image based on three quantitative categories. This image could be produced to visualize a 3-D map of a specified area as a surface plot in MATLAB. Methods To begin this research, we decided which desired area of the Appalachian State University campus we wanted to collect data from. We wanted a relatively small plot of area to limit time and labor consumed, and an area that was easily accessible. To do so,

5 we consulted an Appalachian State University campus map and found an area that resembles our theoretical area. Figure 2 Map of Appalachian State University campus. The red rectangle in Figure 2 best fit our parameters, so we decided to pursue this area. To further increase the accuracy of our selected area, we zoomed in and selected an accessible boundary from which we will collect our data. Figure 3 represents the border we opted for with a red line.

6 Figure 3 Zoomed in image of plot. We decided to scout our original projected area, and found out that boundary line located behind Welborn Cafeteria (Blue line in Figure 3) was blocked by a construction site. Therefore, we had to alter our original course by going around the Welborn Cafeteria to avoid the construction site. With the new plot boundary, we created a grid of projected paths that we will take to collect our data. For data points easier to collect and measure, one would want easy, accessible paths to follow. So, we tried to choose paths that follow actual pathways or roads. This creates a type of mesh-grid that can be plotted on the map. Figure 4 shows the mesh-grid that we followed. Once this grid was completed, we could continue on our project. We have our projected paths, so now we can commence collecting data. To get a good collection of data from our plot, we wanted to get a data point from approximately every intersection in the mesh of Figure 4.

7 Figure 4- Image of projected. We determined that 30 data points was a sensible number of points for our project. With 30 points, we could work from left to right across the plot and gather data for approximately every intersection. To collect the data, we received two GPS handheld devices to calculate the latitude, longitude, and altitude of each point. We needed two to retrieve the average latitude, longitude, and altitude because each individual GPS device does not measure each category perfectly. So at each point, we recorded data from both devices and calculated the mean. Once we had 30 points from across the plot, we could interpret and analyze the data with computer software. We then imported the data into a Microsoft Excel worksheet in three columns based on the quantitative variables latitude, longitude, and altitude. Since each latitude and longitude point had a constant degree and minute measurement, we decided it would be easier to analyze the seconds of a degree. By placing the data into Microsoft Excel, we could then import it into MATLAB to produce three-dimensional images. This could be done by inserting the saved data into a matrix and using the MATLAB commands

8 Num=xlsread( data ) Plot3(num(:,1),num(:,2),num(:,3)) with data being the Microsoft Excel file name. To mark each individual data point with a marker, we used the command plot3(num(:,1),num(:,2),num(:,3),'.','markersize',15) This produced an image that could be rotated and viewed by the three quantitative variables. We also thought it would be intriguing to compare the scale given on the map to the actual walking distance of our route. We did this by first calculating the actual distance we walked between two points on our mesh-grid. Then, using ImageJ, another program that can be used to analyze and process images, we could compare the pixel lengths of the scale given on our map. According to the map and ImageJ length analysis, the ratio between distance in feet and pixels is approximately 300:43. So, by measuring the pixel lengths of our paths, we can verify the accuracy of this scale. Utilizing the line selection tool, we calculated the distance in pixels between our first data point and second data point. This number turned out to be 31 pixels. With an actual distance of 231 ft, we compared the ratio. 300:43 = st Data Point 231:31 = nd Data Point 195:24 = rd Data Point 240:34= 7.05 Results After collecting our data and importing to the computer for analysis, we created various images that represent the latitude, longitude, and altitude of our data compilation.

9 Figure 5- Shows comparison between data points collected and actual route taken based on latitude and longitude. Figure 6- Altitude difference can be observed between southern-most point and Plemmons Student Union.

10 Figure 7- Shows the comparison between highest and lowest altitudes recorded. Exact difference is 210 ft between 3340 ft and 3130 ft. These images could be rotated in a 3-D form and analyzed according to position of latitude and longitude against altitude in an arrangement that resembles the original map. The scale on the map seemed to be skewed according to our actual distance calculations. According to our calculations, a distance of 300 feet on the map should be greater than 43 pixels. Conclusion We were somewhat disappointed with our image renderings based on our GPS coordinates. We were unable to investigate into the creation of a surface plot using data points in matrices. However, we were able to recognize the position of our data compared to the Appalachian State University campus map and the elevation of the points. Of course, our GPS figures could not be 100% accurate, so there was some distortion between each individual data point location. Our projected paths on our mesh-grid were easily accessible, as planned. Overall, we thought that our experiment was successful

11 based on the fact that we collected data from GPS devices and analyzed them in computer software to compare latitude and longitude versus altitude utilizing threedimensional images.

12 References [1] "Global Positioning System." Wikipedia. 21 July Wikipedia. 26 July 2007 < [2] Parkinson, B.W. (1996), Global Positioning System: Theory and Applications, chap. 1: Introduction and Heritage of NAVSTAR, the Global Positioning System. pp. 3-28, American Institute of Aeronautics and Astronautics, Washington, D.C. [3] Brain, Marshall. "How GPS Receivers Work." How Stuff Works. How Stuff Works. 26 July 2007 <