Manipulation of GPS data

GPS observations are usually archived in an ASCII format called RINEX (for “Receiver INdependent EXchange” format. See http://www.ngs.noaa.gov/CORS/Rinex2.html for a complete explanation of the format.

There are RINEX observation files for storing phase and pseudorange observables, and RINEX navigation files for storing satellite ephemerides.

RINEX files for a number of permanent stations, in particular the ones that participate in the IGS, are freely available on data servers on the internet. Check out http://igscb.jpl.nasa.gov/ or http://sopac.ucsd.edu for various maps with all available stations and for station description (type of equipment, etc…).

The following anonymous ftp sites archive the IGS data:

Site	ftp address	directory
Scripps Institution of Oceanography, San Diego	lox.ucsd.edu	/pub/rinex/YEAR/DAY
Institut Géographique National, Paris	igs.ensg.ign.fr	/pub/igs/data/YEAR/DAY
Institüt für Angewändte Geodäsie, Frankfurt	igs.ifag.de	/IGS/obs/YEAR/DAY
CDDIS	128.183.204.168	/gps/gpsdata/YRDAY/YRo

(YEAR = civil year, DAY = day of year)

Get and read a RINEX data file

Þ Ftp the RINEX observation file from January 10, 2002, for station SJDV

Þ Read and interpret the RINEX header

Þ Get the site descrition file for that station and verify that the RINEX file header is correct

Assignment:

Read RINEX observation file and manipulate GPS observables.

1. Reading the RINEX observation file.

Matlab is not very efficient at reading ascii data files. We could write a function to read RINEX observation files, but it would be extremely slow. It is more efficient to write such a function in C (or Fortran?) and compile it in Matlab. We will use the C program readrinex.c. Copy it in your working directory and compile it using:

>> mex readrinex.c

This will create a Matlab executable file readrinex.mexgl. You use it as follows:

>> [Observables,epochs,sv,apcoords]=readrinex(rnx_file);

rnx_file is the name of your rinex file. Readrinex returns:

- apcoords = vector containing approximate X, Y, Z coordinates (ECEF, m) of GPS site, read from the rinex file header.

- sv = vector containing the list of all satellites recorded during the observation period, by their PRN number.

- epochs = n x 6 matrix. n = number of epochs (2880 for a 24 hour rinex files sampled at 30 sec). Columns are: year, month, day, hour, minute, second.

- Observables = structure containing phase and pseudorange observables. Think of it as a series of five n x m matrices with n = number of epochs (n=length(epochs)), m = total number of satellites visible over the observation period (m=length(sv)). Each of these 5 matrices correspond to: L1, L2, P1, P2, C1. To read a full P1 dataset from Observables, use: P1=Observables.P1; If there is no data for a particular sv and/or at a particular epoch, Observables contains NaN (= not a number, can be tested using Matlab’s function isnan).

2. Read ephemeris and convert to XYZ position in ECEF frame: use your read_rinexn.m and get_satpos.m functions.

3. Write a function to calculate theoretical satellite-receiver range R, given apcoords and the satellite ECEF positions computed in step 2 above.

4. Plot the following quantities as a function of time for PRN31:

- Plot 1: satellite elevation

- Plot 2:

o C1

o C2

o P1

- Plot 3:

o L1

o L2

- Plot 4:

o C1 – P1

o P1 – P2

- Plot 5:

o C1 – R

o P1 – R

- Plot 6:

o C1 – l₁ x L1

o P1 – l₁ x L1

o l₁ x L1 – l₂ x L2

5. Comment your results briefly

Use the following values:

f₁ = 1.57542 x 10⁹ Hz;

f₂ = 1.2276 x 10⁹ Hz;

c = 0.299792458 x 10⁹ m/s;

l₁ = c/f₁;

l₂ = c/f₂;