Given:

• Satellite positions for the 28 GPS satellites visible on January 1, 2001.(This is a Matlab file)
• Your software to compute latitude/longitude/height.
• Your software to compute elevation angle.
• Your software to compute PDOP(position dilution of precision)

Description

As engineers, you are often asked to solve a problem given financial or other practical constraints. GPS surveyors have similar concerns. For example, you may need to pay a field crew to operate a GPS receiver, and you'd like to send them to the field for the shortest period of time in order to achieve the most accurate results.

In class we have talked about how one would go about building a satellite constellation - in general terms of course. One of the issues that needs to be taken into account is the quality of your position value. If you needed greater accuracy, you might need to launch more satellites, etc. The accuracy of your position value could also depend on where you are on the Earth, and this is something you would want to know before you build the satellite constellation. In this lab, you will be asked to assess the quality of a potential GPS position solution at two currently operating GPS sites:

• Table Mountain (north of Boulder)
    X= -1283388.8693 Y = -4713016.9053 Z = 4090191.0471
• McMurdo (Antarctica)
    X= -1310695.2483 Y = 310468.9347 Z = -6213363.4927

You will use a quantity called PDOP (position dilution of precision) to define goodness. Since the mathematics and models needed to understand this quantity won't be covered until later in the course, we won't spend a lot of time discussing the definition of PDOP. You can think of it is as being an average position uncertainty for a GPS receiver, i.e. if I turned on my GPS receiver right now, and it gave me an answer, how big would the error bar be (or in two dimensions, we usually say the error ellipse)?

Your main code should:

• Define the given receiver locations.
• Calculate local up for each.
• Read in the satellite coordinates. The data are defined as SatPos(145, 3, 28). The first column defines the time epoch; the second column stores the X, Y, and Z coordinates of the satellite; the third column defines the satellite number, from 1-28. The time indices correspond to 24 hours on January 1, 2001, at increments of 10 minutes.
• For each site, calculate the elevation angle for the 12th satellite. Plot the elevation angle (degrees) of this satellite as a function of time (hours). Only plot elevation angles above 10 degrees. Why are the elevation angles different at the two sites?
• For each site, loop through the time indices and the satellite indices and determine how many satellites are above an elevation angle of 10 degrees. When you have found all the visible satellites at a given time epoch, store the value of PDOP at that epoch.
• Make two plots - one for Boulder and McMurdo. The plot should show both time vs. number of visible satellites and time vs. PDOP, using lines rather than symbols. On the same plot, show with a symbol the times at which PDOP is less than 2 (the find function is a good way to do this).

Turn in: plots and your code.