ECE 6390 Radiolocation Scavenger Hunt - 3
Late for Dinner
Georgia Institute of Technology
Solution - Main Equations
Solution - Notes
Maple Solution:
Maple is a powerful mathematical analysis tool that we used to compute the triangulated position of the GPS receiver. First, we defined constants like the speed of light, radius of the earth and the height of Atlanta above sea-level. Since we only had data from 3 satellites, we had to assume that the height of the GPS receiver would be about 308 meters above the sea-level, or 63800308 meters from the center of the earth. This simplification devolved the complex problem into a relatively easy to analyze 3-equation, 3-variable problem. We gave 3 equations to Maple, which are given below, and asked it to find points at which all three were identically zero.
Maple gave us a set of solutions (six solutions to be precise). Only one of these solutions made sense for the receiver to be in Atlanta.
A MATLAB verification script was used to verify our solution. The r.m.s error of our solution was less than 1 meter. To further drive the nail into the proverbial coffin of the problem, we used the concatenation of the street names as the password of the pdf file available on the ECE 6390 website and it magically got decrypted.
MATLAB Solution:
hw8.m and hw8_brute_force.m use brute force to search a defined box-shaped area around Atlanta for a given value of the unknown time constant u, which is given as a parameter to the function hw8_brute_force. It doesn't make sense to test our areas that are too far away from the surface of Atlanta, so we use matrices to transform coordinates into a perspective that has the z-axis pointing to the sky relative to Atlanta and y-axis pointing west. We transform the satellite coordinates to this coordinate system and try a large number of values of x, y and z within a certain range that can be specified and compute the r.m.s. error value. The granularity of the values can be varied.
Ambiguities:
Maple found several other solutions to this problem, but they were ignored due to the fact that we know the location is somewhere close to downtown Atlanta.
Source Code - Maple
Source Code - MATLAB
hw8.m
hw8_brute_force.m
hw8_test.m
Invitation
