Manual GPS Trilateration Blitz Mystery Cache

Puzzle cache guaranteed to make you learn more about GPS than you thought possible…

Have you ever wondered what’s going on inside of that GPSr you own when you turn it on? How does it work? What it is doing is quite amazing and this cache is all about giving you some appreciation for the complexity of it all. When you get down to the challenges involved what is amazing is that it works at all.

Most experienced geocachers know that their GPSr is a radio receiver, locking on to available signals from a constellation of 24 (+/- a few spare) US Military satellites. The carrier transmits from the satellites at 1575.42 MHz and within each signal pseudo random code is embedded at 10.23 MHz. This lower frequency code gives information about the satellite’s orbits (almanac data), their clock and orbit corrections and other system status (ephemeris data). Because the GPSr knows to look for the specific pseudo random codes of each satellite in the signal it can filter out a lot of noise and use a very low power signal negating the need for a big antenna like you would see on other satellite signal receivers.

So in this puzzle we are receiving signals from 4 satellites and the signals are travelling in more or less a straight line from the satellites through the ionosphere, troposphere and other layers of the atmosphere to the receiver at a little less than the speed of light (c = 299,792,458 metres per second).

In simple terms the GPS is a stopwatch that times the transmission delay from 3 or more satellites to the receiver. By measuring the lag in the pseudo random code between the signals received from the satellite and the GPSr clock the GPSr can figure out how far away the satellites are from the receiver.

But if the timing is off by even one thousandth of a second that translates into 300 km of error, and since atomic clocks used in the satellites cost between $50000 and $100000 the GPSr has to use a clever trick to synchronize it’s clock with GPS time. The GPSr uses a fourth satellite signal and looks for a single time correction to the GPSr clock that will allow the distances from all four satellites to intersect, thereby turning your inexpensive handheld GPSr into a synchronized clock that is nearly as accurate as an atomic clock.

In this case the satellite positions and difference in signals between the receiver and each satellite (SV – Space Vehicle) are:

The height is above the WGS84 ellipsoid. Can you be the GPSr and calculate the position of the cache and the offset in the GPSr clock? You can assume that all other factors that mess with the timing, like multipath signals, atmospheric delays, satellite timing errors and others have been accounted for already and do not factor into the equation.

Some wisdom from Dr. Carl Sagan:

“We live in a society exquisitely dependent on science and technology, in which hardly anyone knows anything about science and technology.”

“... the use of our intelligence quite properly gives us pleasure. In this respect the brain is like a muscle. When we think well, we feel good. Understanding is a kind of ecstasy.”

This cache was created to add to the number of QUALITY caches hidden in Manitoba. It is an official BLITZ cache for the May Madness event. Hope you enjoy the hunt!