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Friday, 27 April 2012

Trip to the Algonquin Radio Observatory to track GPS Satellites!

The task sounded simple enough: develop software to be used to direct an antenna, specifically the Algonquin Radio Observatory, in tracking a GPS satellite. Observe the radio frequency sent by said satellite to confirm successful tracking. Well, however easy or difficult the task sounds to you, I can assure you that it was quite a lot of work.

It was actually kind of nice working on this project because it was one that required planning, division of work, and development over a long period of time. Often, work catches up with me, and some of my best work comes through toward the end of a project. As difficult as it can be to work on something piece by piece, it was nice to work on this project in stages.

Using Matlab, a programming language frequently used by engineers and physicists for data analysis, algorithm development, and numerical computation, the class paired off, starting with the simple, but necessary functions, and working toward the final, complicated project.

After reviewing the specifications document, it seemed that a lot of the code to be developed was in simply converting things into the proper format. For example, dates and times, readily accessible on Matlab, had to be converted to Julian Dates, or epochs (Julian dates since a specific event). For anyone unfamiliar, Julian Dates represent the interval of time in days and fractions of a day since January 1st, 4713 B.C. For example, today's date, Friday, April 27th = 2456045 in the Julian date system.

Kind of sounds like star dates used in Star Trek, right? Yes, so we needed functions to compute that, and some to calculate specific things based on that. There was a lot of formatting involved with this project.

The real substance of this project was in determining a satellite's position, velocity, and the angles the antenna would need to use to look at a satellite for any given time. How do we determine a satellite's position, you ask?

Well, the first thing we need is an ephemeris file. Simply put, this is a list, or table, with the positions of the satellites in question at a specific time. The information concerning the whereabouts of GPS satellites isn't exactly secret, so we were able to get an ephemeris file of the satellites in question from not too long ago.

It is important to have a fairly recent ephemeris file because everything is in constant movement and nothing stays the same from one cycle to the next. The rotation and revolution of the Earth is not constant, the revolution of satellites is not constant, even the direction of axes, the directions we use to make measurements, changes over time, allow David Tennant, as Dr. Who, to partially explain: Timey Wimey. While he's talking about time, the same thing holds true for space. Simply put, the Earth doesn't stand still and so our measurements have to keep up.

So, ephemeris file gives us an idea of where satellites are at a specific time, say a couple of months ago. Then, we have to calculate where the satellites are now and where they will be in the future. This involves a lot of math. And I mean a lot.

First, we pick a time in which to observe the satellites. Say, a half hour interval, 1pm to 2pm on a specific day, say yesterday. Whatever. Now that you have that time frame in mind, you have to calculate the positions and velocities of the satellites as they travel in their orbit around Earth. The information from the ephemeris file helps us out, but from this we get the values in Keplerian coordinates.

Whoa...what? Alright, so most people imagine a satellite going around the Earth, and the Earth going around the Sun, to be in a circular orbit, as seen below where the black dot is Earth, and the red is the satellite. The distance between the two is the radius, R, and the speed of the satellite in its orbit is its velocity, v.

But, Johannes Kepler, German astronomer, observed and realized that orbits in space are more like the above right, where instead of the more massive object sitting at the centre, the orbit was more of an ellipse with the massive object off to the side (this position is known as a focus, or one of the foci, by the way). The model and way of understanding an object in a Keplerian orbit is to use Keplerian coordinates.

So, we determine the orbital characteristics of our satellites in Keplerian coordinates. Then we want to change to something called ECI, or Earth-Centred Inerial. This system, as you can gather from the name, places the Earth at the centre, and has the directional axes pointing in very specific directions.

Because I feel like showing off, here is a review of said directions. The z-zxis points along Earth's rotational axis, remember though it's changing all the time due to a wobbling, rotating Earth. But, more or less, north to south. The x axis points toward the vernal equinox.

Okay, so as the Earth goes around the Sun, the path it makes looks similar to the above diagram. The vernal equinox, besides being the longest day of the year, is the point where the Earth's path seems to rise above the plane on which the Sun and most of the solar system sits.
So, long side note. Basically, you have to determine the satellites positions as they will be when you want to look at them, using the ephemeris file. Then, you change it from Keplerian, with its crazy ellipses, into ECI, Earth-Centred, to make it a little easier. But you're not done!
Oh no, you have to then determine the position of the station you're viewing from in the ECI coordinate system AND it might be a good idea to change from ECI to ECF, where the F stands for fixed. Basically, the ECF coordinate frame fixes the x-axis at the Prime Meridian, 0° in Longitude, that vertical line on maps running through Greenwich, England. The reason you might want to switch is simply to make things a little more straightforward.

Sure it is, you're thinking, but really, once you do the above steps, switching from ECI to ECF is actually as easy as subtracting one number from another., we finally have a list of the satellites we want to look at, and where they'll be and when. Now, we need to determine how to point the antenna in order to look at one of them. We first have to convert the station's position (more math!?) into something called topocentric. Basically, it means the antenna is at the centre of the system, makes pointing easier. So, once we've done that, we determine the azimuth and elevation angles.

As might be discerned from the above diagram (I looked for a better one, but didn't feel like drawing it myself), the azimuth angle is the "horizontal" angle, rotated from due north, eastward to the object. And the elevation is from the horizon straight up to the satellite. Basically, say you're facing north, but you want to face the Moon. The amount you turn on the spot is your azimuth, the amount you have to look up is your elevation. 

Once you've done that, there's one little step left to do. Because of the limits of the scope, namely that it cannot look through the horizon, you cannot simply track all satellites at a given time. So, once you know where the satellites are, you determine which ones might be easier to track based on which ones will be visible for the longest portion of time during the time you've chosen to track them. 

Now that you know where they'll be, this is easy, and once you see which satellites are visible, you simply choose the one visible the most and track it by telling the computer to rotate the antenna according to the angles and positions you have calculated.

Well...that was a lot of work just explaining that. Trust me, it was a lot of work in general, and everyone one of us lost a lot of sleep making sure things worked perfectly. To make this post a little more exciting, let me tell you more about the Algonquin Radio Observatory, to be referred to as here as the ARO.

Weighing over 1200 tons, with a diameter of 150 ft, or 46 m, it is the largest antenna in Canada.

Built in 1966, the ARO has been used for countless scientific experiments over the years. In the world of science, it was famous for the first very long baseline interferometry experiment in the world. Basically, using this antenna, and a smaller one in British Columbia, scientists were able to focus on the same very distant objects and use that data to actually establish the distance between the two antennas very accurately. It was a breakthrough which is still used to this day and is one of the ways we are able to determine our position on Earth with such a high degree of accuracy. Additionally, the facility features an atomic clock, hydrogen maser for anyone interested, and due to the precise readings taken over the years, the facility is actually the most accurately known position on the entire planet. In fact, surveyors used this location, branching out, in order to update and increase the accuracy of maps used all over Canada. It's an amazing facility, and while I have some pictures of it, none could quite capture the sheer size and impressive nature of it.

One thing that was really cool was that we were allowed to go up and walk on the dish! Moving the dish to an upright position, we climbed the spiral staircase in the centre of the base, leading all the way to the top.
Once there, we were allowed to walk around, and see the dish for ourselves. As you can see from the photos below, half of the dish is painted white and the other half is not. The unpainted side will be finished this summer, and the white paint helps make the antenna more accurate. 

 Sadly, we were unable to see the horizon, due to the fact that the antenna had to be pointed upright, but I managed to get a couple of nice photos in. The mesh on the outside is because the antenna's dimensions were expanded some time after it was built. It all works the same way, just looks different.

This is what we used to track the GPS satellites. Our code, its working components described above, was fed to the facility and instructed the antenna as to where to point and when. It was amazing to  watch the antenna swivel and point, while watching the controls light up as it worked.

The control panel, seen below, is old, and is not what they use currently, but was part of the original design. I thought it looked pretty neat.


In the end, it was an amazing project, and an amazing opportunity. I was looking forward to this trip for some time, and it was really a nice way to culminate this year. It brought so many ideas and techniques together and really gave me a sense that I had learned something, and that what I had learned could be exciting and truly applicable. I deal in the theoretical so much that sometimes I need to be reminded of the applications of my knowledge. Additionally, the facility was in the middle of Algonquin park, so when I wasn't stressing over my work, I was enjoying the serene wilderness.

Another year over, this one better than the rest, in terms of what I've learned. I now strike out to get ready for the summer, and to get ready to move and live in Edmonton for awhile. I hope to find employment quickly, and I look forward to keeping you up to date on my adventures.

Thanks for reading!

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