As far as I can tell, my GPS unit doesn't have a transmitter, so how do those satellites know where I am?

When I was a freshman engineering student at the University of Southern California in 1982, I got to go on a tour of TRW’s Space Division where I saw one of the first GPS satellites being assembled.  We were told that this technology was going to revolutionize navigation.  Yet I couldn’t help but wonder how the satellites would know where I was.    Today that thought reminds me of a trip to the mall when my children were very young.  We looked at the mall map and found the label saying, “You are here” and my son asked me how the mall people knew where we were.

So goes the world of GPS.  GPS technology has evolved over the past 27 years and become much more accurate.  Nonetheless, the basic principle remains the same and you don’t have to be an RF expert or a math wizard to understand it.   With GPS, most of the satellites know very little except the exact time.  The GPS unit you hold in your hand or in your car has all the smarts.    The simple version of GPS, without any of the fancy corrections follows basic geometry.

It goes like this.  Say you know that you are a distance of 100 miles from a point of known location, even if you know nothing about direction, then you know you are someplace on a sphere with a radius of 100 miles from that point.  Now, let’s say you know that you are 100 miles from one point and 50 miles from a different known point.  In this case your location is a point which is common among two spheres of radios 100 miles and 50 miles respectively.  Since the intersection of two spheres is a circle, you know you are some place on that circle.  Finally, let’s add a third point.  Using the same logic you know your location is the intersection of three spheres.  Geometrically speaking, the intersection of three spheres is exactly one point.    So all your GPS receiver does is calculate the distance from satellites of known location by measuring the delay in the time-stamped signals from the satellites, then calculating your point location by intersecting spheres.  Now because this measurement is not perfect, we add extra satellites to reduce the error and provide a time reference.  All you really need to know is basic geometry.