The Effects of Different Amounts of Satellites on the Efficiency and Accuracy of a GPS system

by Lyonel Dario

Takoma Park Middle School

Introduction

Lyonel Dario stands in front of his exhibit.This project will help one learn if more satellites are needed in calculating the location of any point on the ground surface will increase the accuracy.  The hypothesis is that the accuracy will increase when more satellites are utilized in calculating the position of any given point on the surface of the earth.

A Global Positioning System (GPS) is a worldwide radio-navigation system formed from twenty four satellites and ground stations.  These artificial satellites are used to calculate certain positions accurately in meters.  GPS systems are actually communicational satellites (they are used for the purpose of communication).

Calculating a certain place using a GPS system works in three steps.  The first step is called triangulating.  Triangulating is when different satellites are used as differential reference points to pinpoint a certain location.  

After triangulation, the data is calculated with the equation V+T= D, where V equals velocity, T equals time and D equals the distance used.  This is used because when the data is sent to the GPS, it doesn’t get the data at the exact same time, so some of the data could be faulty (since time is an important variable).  So the pseudo-random code is used to make sure that the GPS and the satellites are in sync.  The pseudo-random is basically a sequence of on and off pulses (like a heart monitor).

Atomic accuracy clocks are used to make sure the measurements are exactly perfect.  These clocks work by this common principal, if three perfect measurements can

 

 

 

 

 

 

 


 

 

locate a three-dimensional space then four imperfect measurements can locate a three dimensional space.  This also eliminates all possible errors.

Many people ask how satellites positions are known in space.  Well, their positions are known due to predictability (the satellites are programmed to move in a certain path).  Also, there is an almanac in each GPS that tells them were each satellite is every moment.  Errors may occur, but mathematics, modeling and the configuration of these satellites are used to correct these mistakes.

GPS provides data in the form of Latlong and elevation.  The Latlong is a series of imaginary lines that are used in order to measure points on the Earth.  These lines are called latitude and longitude, where longitude goes from north to south, and latitude goes from west to east.  Elevations are based on any given vertical datum such as the North American Vertical Datum (NAVD) of 1983.  The elevation is calculated as the vertical distance from the zero mean sea level.

There are three types of GPS grades currently available.  They are recreational grade, GIS grade and Survey grade.  They differ based on their accuracy.  The recreational grade is at approximately ten meter accuracy, the GIS grade is at about meter accuracy and Survey grade is about sub-meter accuracy according to industry practice or product literature.

A program from NOAA is used in order to translate these points from latlong to Maryland State Plane Coordinate System, which just makes it easier to graph.

After translating the data, then one must put it on an Excel file as a table.  Then the data is graphed to plot data points on a coordinate plane.

Experimental Design

Title: The Effects of Different Amounts of Satellites on the Efficiency and Accuracy of a Global Positioning System (GPS)

Hypothesis: If different amounts of satellites varying from five to ten are used, then the more amount of satellites used, the more accurate and efficient reading is calculated.

IV: The Amount of Satellites

IV levels:        3 sat.    4 sat.    5 sat.    6 sat.    7 sat.    8 sat.    9 sat.    10 sat.

Trials:               5          5          5          5          5          5          5          5

DV: The DV is the efficiency and accuracy of the GPS system, this is calculated by the machine itself

Constants: GPS system, Points (object points)

Materials

Procedures

  1. Locate at least three permanent points in an open area.
  2. Obtain positional reading (Number of satellites, Latlong, elevations & accuracy) using a recreational GPS unit over each point.  Collect numerous amounts of readings with varying numbers of satellites.
  3. Then convert the latlong data into Maryland State Plane Coordinate System using NOAA’s Geodetic Latlong to SPC program.
  4. Then plot the data on Microsoft Excel program.
  5. Analyze the points.

Summary of Results

The hypothesis of this project states that if different amounts of satellites varying from five to ten are used, then the more amount of satellites used, the more accurate and efficient reading is calculated.  Some of this data does support this hypothesis.  Point 1 supported the hypothesis because the calculated points with nine to ten satellites were all grouped closest to the real point.  The other points (2-4), which varied from six to eight satellites, were off, but close to the group of nine’s and ten’s.  Point four also supports my data, because it has a group of eights and nines grouped near the real point.  Point four though is unreliable, since some of the data points strayed far away from the real point.  This might be because of human error or the GPS system could’ve malfunctioned. 

 

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Explanation of graphs, tables and diagrams

The first graph “Accuracy of Satellites” states what the accuracy of the satellites was when they were calculated, according to the GPS.  It ended up that the accuracy according to the GPS unit is false and unreliable after the data was plotted.  The smaller the amount of feet is, the better the accuracy.  For example, one calculation had a satellite of six, and an accuracy of eight feet, that means that this was one of the calculations that were most accurate.  The “Site Map” diagram is just displaying where the points are located.  The site is at the Burtonsville Park off Old Columbia Pike Road in Burtonsville, Maryland.

The Point Graphs all show that a Recreational grade GPS isn’t reliable.  Although some of the data was clustered together near the real point, more than half of the other data was scattered almost randomly around the grid.  For example, the point with seven satellites in “Point 4” is approximately eight hundred feet apart from the real point, where 3’s, 10’s and 9’s are group together.  This data is also random because it does not have a pattern.  For example on point one, there is a group of nines and tens in one corner but in the other corner there exists a group of nines, eights, fives and sixs.

The purpose of this project was to find the Effects of Different Amounts of Satellites on the efficiency and Accuracy of a GPS system.  The hypothesis of this experiment was that if different amounts of satellites were used to test the efficiency and accuracy of a GPS system, then the more satellites used, the more accurate the data will be.

The data rarely supported the hypothesis.  Point one definitely supported some of the data because some of the data points were close to the real point, but the points nearest to the real point had nine to ten satellites, and those groups were close together.  Point four supported this hypothesis very little.  Only four of point four’s points were grouped together, and were closest to the real point, but then some of the other points are far away in many, different random places.  For example, one of the data points strayed near point one and another just strayed really far from any of the data.  The data point two definitely did not support the data.  All of point two’s points were scattered all around the coordinate plane.  One of the points is close, but then the others are far away, some with point one’s, some with point four’s and one even strayed really far from the actual point.

There were many problems that happened during this experiment.  One was that there were clouds on one of the days that the data was collected.  Since the satellites send their information to the GPS recipient, the clouds can deflect the data, which can mess it up.  Another problem was human error.  When translating data, it was very possible that some of the number were mixed up, or that a point was misplaced.  The final problem was that the data was scattered around.  On diagram one, one could see that the data points for point two is horribly scattered.  Also, some of point four’s data points are scattered around the diagram too.  The only reliable data is point one, which points all are near together.  This made it very hard to analyze the data because some of the data could be faulty and although it was checked a lot, the data was still untrusting.

Finally, the data somewhat supports the hypothesis.  Although some of the data was scattered around, some of the data was still accurate.  Also, the misleading data might have been caused for many reasons.  If satellites are used for the use of a GPS system, then more satellites will increase the accuracy.

Acknowledgements

Thanks a lot to my father because he’s the one who loaned me a GPS system from his work and helped every step of the way.

References

Brown, Charlie.  The Use of GPS in the Departments of Transportation North Carolina: Technology Implementation Group, Seminar

Dana, Peter “GPS”. Global Positioning System Overview 05/01/00, 11/20/03 www.colorado.edu.geography/gcraft/notes/GPS

“Education” GPS Primer.  Last updated May, 1999, The Aerospace Coorperation.  11/20/03, www.earo.org/publications/GPSprimer

“Satellites, Artificial” World Book Encyclopedia, 78th 2000 ed,

“Tremble, GPS” 10/27/03.  Tremble. 10/1/03 http://www.trimble.com