Where Am I?

Well, to answer the question in the title, I am currently in a lab at the University of Arizona. But if I didn't tell you that, how would you know where I am without a search party? This week I am going to rant about the three different tracking systems that I've learned about. While the systems themselves are relatively easy to understand, I still have to take into account a whole bunch of considerations in order to figure out what system might be best for tracking sea otters.
I will warn you that I made some of the diagrams myself, so I apologize in advance if they only confuse you.

Triangulation is probably the simplest and the cheapest way to track via radio telemetry, and many of you are already familiar with how it works. The most commonly used antenna to receive the signals from the tracking device is a hand-held Yagi-Uda antenna, which is extremely directive, as some may remember from last week's post. Here's a picture of one, which may look familiar because it is commonly found on the roofs of houses. To start the triangulation a person will use their highly directive antenna to determine the direction where the signal from the transmitter is the strongest, creating a vector of possible places where the tracking device may be. Since the tracking device may be anywhere on that vector, at least one more person in a different position must go through the same process, and the transmitter will be located where the vectors from the different people meet. Only two different vectors are necessary, but having three or more vectors can make the estimated location more accurate. Here's a diagram!

Triangulation at its best

Another method for locating a tracking device is something that all of you are somewhat familiar with: the Global Positioning System. There are 24 GPS satellites orbiting the earth, each working constantly to give countless systems in the world updated information about their location. The GPS satellites do not use triangulation vectors. Instead, they measure how much time it takes for a signal to get to the satellite, which means that the satellite has a sphere of infinitely many location possibilities that are each the same distance from the given satellite. When a GPS transmitting device is able to lock on to a signal from three or more GPS satellites, then it is able to formulate a position. Interestingly enough, if a GPS device locks on to only three GPS satellites, then it is only able to calculate 2-dimensional coordinates on the earth, which is enough if you're using a car GPS. However, if you need to know the 3-dimensional coordinates of the tracking device, i.e. the coordinates and the depth, the device must lock on to four or more GPS satellites. Probably the most important consideration for GPS systems is that they can be much more expensive than triangulation systems. Here's another diagram!

Since he only has a lock on three satellites, he doesn't know how far above sea level he is.

The last system that I would like to consider is called multilateration, and is most commonly used with cell phones because this system requires cell towers. At least three different cell towers need to be involved in order to get a working location on a device, because the cell towers rely on communication with each other. Each pair of cell towers will calculate a TDOA (time-difference of arrival), which essentially is the difference in the distances of the device to both towers. Geometrically, this creates a hyperbola of possible locations for the transmitter (think y² – x² = C). Since this is incomplete, at least one more tower is needed to calculate two more hyperbolas so that the intersection of the three hyperbolas can be found, and a location on the device can be found. Multilateration can be cheap and effective if the infrastructure for the system is already there, but if you want to start building cell towers, the project gets really expensive. Again, here's another diagram!

Is he confused because he's lost, or because he can see an elephant? Who knows.

As always, thanks for reading, and please leave a comment if you feel compelled to ask me a question or tell me how much you like or hate this post!

Picture:
http://www.antenna-theory.com/antennas/travelling/yagi1.jpg