Lab Assignment #3 ASE 272N/172G Satellite Navigation Prof. G. Lightsey Assigned: October 28, 2003 Due: November 11, 2003 in class

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1 The University of Texas at Austin Department of Aerospace Engineering and Engineering Mechanics Lab Assignment #3 ASE 272N/172G Satellite Navigation Prof. G. Lightsey Assigned: October 28, 2003 Due: November 11, 2003 in class 1 Objectives We have previously studied the determination of the transmitter locations using the broadcast ephemerides, and the pseudorange measurements made from the receiver code generation/correlation process. We have also discussed the algorithm required to take this information and solve for the receiver s position (called a position fix). In this lab, we put it all together to actually determine the location of the receiver based on its own measurements. We will use results from previous labs to analyze the data that we collect. We will also look at the effect of geometry on the solution, known as Dilution of Precision (DOP). Procedure The data collection portion of this lab is actually very simple. We will collect 10 minutes of raw data using the Rhino Rover GPS Backpacks. We will download the broadcast ephemeris using the CORS website for station TXAU and process the satellite positions and pseudorange measurements simultaneously to compute position fixes. 1

2 2 Data Collection Collect 10 minutes of Garmin pseudorange data. (a) On a day of your choice, check out one of the Backpacks from either my office, or from WRW 412D. Make sure the batteries are charged and then take the Backpack to a nearby open area. (b) Place the Backpack in a fixed location so that it has as clear a view of the sky as possible. Extend the antenna mast and make sure the mast is positioned in such a way that the antenna does no shift excessively during data collection. Plug the receiver into the battery pack, power on the TDS Recon and open Rhino Rover as explained in the Backpack User s Manual. Do not start recording observation data yet. (c) Wait until the receiver is tracking at least 4 satellites and computing position fixes to begin collecting data. This is very important, as the receiver may appear to be computing position fixes even when it has less than 4 satellites (this is not actually the case, it may be computing a 2-dimensional fix constrained to the surface of the Earth). You may easily check to see how many satellites the receiver is tracking by noting the number of bars displayed on the Rhino Rover screen. When there are at least 4 green bars (more is better), you may begin recording data per the instructions given in the Backpack User s Manual. If you stop collection for any reason and need to begin again, you must close Rino Rover with the exit button and re-establish the connection to the receiver. If this is not done subsequent data files will have missing information from the file header that may cause your load obs program you are about to write to run incorrectly. (d) Collect data continuously for 10 minutes. During this time manually record the Latitude, Longitude, and Height solution displayed on the TDS Recon several times during the 10 minute data collection. Try to record the exact solution at least 5 times during the data collection. Your team members may share the same data file (this may make it easier to check your results). Include your observations in each person s individual lab report under the heading Data collection. 2

3 (e) Move your observation file off of the TDS Recon so that you can use it on other computers and remove it from the Pocket PC to prevent file clutter. Return the GPS Backpack to my office or if I m not there you may return it to one of the students in WRW 412D. Plug in the battery chargers if its practical to do so. (f) After you have collected your data and verified that it is a reasonable data set (i.e., at least 10 minutes in length, at least 4 satellites all the time), go to the CORS web site and download the corresponding navigation file for the TXAU reference station. 3 Analysis Tasks In this assignment, you will have 2 shorter analysis tasks and 1 longer analysis task. You will want to get the first two analysis tasks done quickly (say in the first week) to give yourself more time to work on the position fix analysis task. A sample raw data file has been provided with results, so that you may check your work as you go. 3.1 Write a Matlab Function to Decode the Observation file Earlier in the course, you received and edited a function of the form nav record = load nav(measf ile) where measfile was a RINEX navigation file name (in quotes) and nav record was the output of a K by 37 array, where K is the number of GPS satellites (nominally 32). For this lab you will write your own function of the form: [meastime, P R record] = load obs(obsf ile) from scratch, where obsfile is the observation file name (in quotes) that you created in the previous section, and PR record is an N by K array of pseudorange measurements. K is the same number of GPS satellites defined in load nav (nominally 32), and N is the number of measurement epochs in the observation file. Initially this quantity will be unknown until the file has 3

4 been read. At each epoch, if there is a measurement for a PRN code, that measurement goes in the column number of the PRN code (e.g. PRN code 7 measurements go in column 7). If there is no measurement from that PRN for that measurement epoch, a value of zero goes in the column. meastime is an N by 2 array. The first column of the array is the time of each measurement epoch as reported in the observation file in seconds of the GPS week. The second column of the array is the GPS week number. This is somewhat wasteful since the GPS week is unlikely to change during the data collection, but we will not worry about that here. You will need to refer to the rinex v2.txt to decode the observation file. Table A2 will be particularly helpful in this task. You will have to handle the fact that the number of measurements may vary from epoch to epoch, and the fact that you don t intially know the number of measurement epochs in the observation file. Try to follow the same coding standards that were introduced in the load nav function. Turn in a printout of your function. Your code will be graded as part of the assignment. You may want to inspect the output of your function for the first few measurement epochs manually to make sure that it is working correctly. 3.2 Satellite Clock Corrections As has been discussed in class, even though the GPS satellites have very accurate clocks, they are not perfect and they still drift relative to GPS system time. If uncorrected, this timing error manifests itself as an error in the predicted pseudorange, since the satellite says the time is one value when in fact it is slightly different, and in that amount of time the satellite s position has moved. Even on the scale of nanoseconds, this timing error can have a noticeable effect on the quality of the GPS position fix. The receiver is able to remove the majority of this error through the GPS satellite clock correction coefficients, which are broadcast in the navigation message (see the Navigation Message handout posted with Homework 2) which is transmitted with the broadcast ephemeris. The coefficients provide a curve fit which removes most of the satellite clock drift over the four hour validity time of the broadcast ephemeris. The formula for the curve fit is as follows: clksv = a 0 + a 1 (t t 0 ) + a 2 (t t 0 ) 2 4

5 where t is the current time and t 0 is the epoch time of the clock ephemeris. The clock ephemeris is different from the broadcast ephemeris time known as t 0e (which is defined as element number 18 in Table 3 of the Navigation Message Handout). The clock ephemeris is built from the Year, Month, Day, Minute, Hour, Second format of the first 6 elements listed in Table 3 of the Navigation Message Handout. This will generally be close to t 0e but they are not the same argument! The units for t t 0 should be in seconds, so both t and t 0 should be converted to seconds of the current GPS week (if there is no possibility of week rollovers between t and t 0 ). Write a function: clksv = clk corr(t, sv, nav record) that takes a time (t, you specify the format, for example, I use MJD format), a satellite id (sv) and an input array (nav record), and calculates the satellite s associated clock offset at that time using the broadcast ephemeris given in nav record. Turn in a printout of your commented function with your lab report. 5

6 3.3 Compute position fixes for your data (a) Using your Garmin RINEX navigation and observation files that are valid for your 10 minute data collection, calculate position fixes using the linearization technique discussed in class. To initialize your position fix loop, use the average latitude, longitude, and altitude measurements that you made while recording your measurements. Convert these values to ECEF coordinates. (b) Taking the initialized XYZ position from part (a) as the true ECEF XYZ coordinates, make a plot of x, y, and z error versus time (use the subplot command to put 3 plots on a page). (c) On another page, plot 3-axis error ( δx 2 + δy 2 + δz 2 ) versus time and PDOP versus time (use the subplot command to put 2 plots on a page). Notes: (a) Now is where your earlier hard work pays off! Use the functions you have developed to parse and load the data that you will need. You will need to load up only the measurements that are valid at each measurement sample. In other words, do not process zero entries in your measurement array. (b) Coding tip: even though you will eventually loop over all the measurements in your file, don t start trying to do this. Just work with one measurement time epoch and try to get a single position fix for it. Once you have that working, it will be a lot easier to loop over the set of all measurements. (c) Important: Rhino Rover version does not reference WAAS satellite data correctly. As a result PRN 122 corresponding to Inmarsat AOR-W may appear in the obsfile as PRN 22. Since this satellite is in geostationary orbit it will almost always be present in your data. Your program will then associate the ephemeris for the real PRN 22 with the geostationary satellite. Until this problem is fixed it is probably safest to find a way to skip over PRN 22 in your program. You may want to make this feature easily removable as the problem will be fixed in the future. 6

7 (d) A road map for your Matlab code might look something like this: (1) use load nav to read the navigation file. (2) use load obs to read the pseudorange measuremets from the observation file. (3) Compute the XYZ ECEF values as an initial guess for the position fix loop (may be entered manually). (4) begin loop to read over all observation times. (5) begin loop to iterate on a measurement sample. (6) begin loop to read over all available satellites at that sample (nsat). (7) compute satellite position at transmission time as given by bcast. (see item (c) below for additional notes!) (8) compute H(nsat) and ρ(nsat) matrix components for this observation. (9) Correct ρ measurements for GPS satellite clock correction (from clk corr). (10) end satellite loop. (11) compute the least squares estimate of receiver position and clock correction. (12) adjust position solution by x. (13) test for convergence ( x small). (14) end measurement epoch loop. (15) compute the P DOP. (16) store the values of time, x, clock bias, and P DOP. (17) end observation loop (18) make plots 7

8 (e) When you use your working bcast function in this problem, you will need to incorporate a concept that we discussed in class. We need to compute the locations of the GPS satellites at the signal Transmission Time, but the times given in the RINEX observation file are for the signal Reception Time at the GPS receiver. Thus, we need to back up the satellites in time to account for the time it takes for the signal to leave the satellites and arrive at the receiver. Thus, you will want a loop in your Matlab script that looks something like this: % Iterate 3 times % Tr= time of signal reception (days) % Tt=Tr-dt = time of signal transmission (days) Tr=time(t); % MJD format dt=0; % initialize [xs,clksv] = bcast(tr-dt,b,eph,toc,sv); range = norm(xs-x 0); % x 0 is initial position guess for q = 1:3 % Earth rotation during the signal propagation delt = range/c; theta = e-11 * delt; ct = cos(theta); st = sin(theta); rot = [ct -st 0; st ct 0; 0 0 1]; % correct for transmission time due to sv velocity dt = delt/86400; % dt calculated in days [xs,clksv] = bcast(tr-dt,b,eph,toc,sv); % correct for satellite position due to the Earth s rotation xs = xs *rot ; range = norm(xs-x 0); end Notice how both the effects of satellite motion and Earth rotation are removed during the signal travel time. 8

9 3.4 Discuss plots Make comments about the position error plots you obtained for your Garmin data collection. (a) Based on what you have learned about the pseudorange UERE (User Equivalent Range Error) and Dilution of Precision (DOP), what 3-axis error would you normally expect for your position fixes? (b) If the error in the Garmin data collection is larger than expected, can you explain why this might be the case? (Hint: error is listed in quotes for a reason.) 9