Given:

• Satellite positions for the 28 GPS satellites visible on January 1, 2001. (This is a Matlab file)
• elevation angle software

• Table Mountain Coordinates (north of Boulder)
    X= -1283388.8693 Y = -4713016.9053 Z = 4090191.0471

Write a function that calculates a quantity called PDOP (position dilution of precision). This will be used in Lab 3 to define goodness of the constellation geometry.

PDOP function

• Input:
  • Cartesian receiver coordinates (meters)
  • The number of satellites with an elevation angle above 10 degrees
  • Cartesian coordinates for those satellites
• Output:
  • PDOP (dimensionless)

• Derivation of PDOP
  • Define the A Matrix. Below is an example for 6 satellites. Superscripts are satellites, i.e. 1-6; subscript ro refers to the receiver coordinates given above

    

  • Where:
    

  • Compute Q = inverse of (A^T*A)

  • PDOP = sqrt(Q(1,1) + Q(2,2) + Q(3,3))

• Define the location of Table Mountain.

• Calculate local up.

• 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 the first time only, calculate the elevation angle for each satellite. Use all satellites with an elevation angle above 0 degrees to calculate PDOP.