Introduction to Satelite Positioning
The Tralateration algorithm relies on the following information, three known points, and the distance between those known points and the point of intrest you wish to locate.
What the diagram shows is that you can conceptualize this process as finding the intersecting point between three circles. The point of intersection will coincide with the point of interest you wish to locate.
The diagram above is a 2-dimensional example however the same process is also applicable in 3 dimensions! This is what a GPS module uses to calculate its position in lat, lon, altitude. The trick is to visualize the point of intrest as coindicing with the intersection of several spheres
Satelite positioning systems such as the USA's GPS system is based around a global network of satelites that transmit radio signals from medium earth orbit.
The basic GPS service provides users with approximately 7.8 meter accuracy, 95% of the time, anywhere on or near the surface of the earth. To accomplish this, each of the 31 satellites emits signals to receivers that determine their location by computing the difference between the time that a signal is sent and the time it is received. GPS satellites carry atomic clocks that provide extremely accurate time. The time information is placed in the codes broadcast by the satellite so that a receiver can continuously determine the time the signal was broadcast. The signal contains data that a receiver uses to compute the locations of the satellites and to make other adjustments needed for accurate positioning. The receiver uses the time difference between the time of signal reception and the broadcast time to compute the distance, or range, from the receiver to the satellite. The receiver must account for propagation delays, or decreases in the signal's speed caused by the ionosphere and the troposphere. With information about the ranges to three satellites and the location of the satellite when the signal was sent, the receiver can compute its own three-dimensional position using Trilateration.
An atomic clock synchronized to GPS is required in order to compute ranges from these three signals. However, by taking a measurement from a fourth satellite, the receiver avoids the need for an atomic clock. Thus, the receiver uses four satellites to compute latitude, longitude, altitude, and time.
NMEA is the standard in which satelite positioning information can be efficiently shared in a human readable but still compact way. This is how our GPS modules output their data. The following image has some cursory information about the standard of which you can read more about here
Here at rover we will represent Latitude and Logitude degrees and minutes as a signed integer and signed floating point number pair following the East of North scheme meaning the Northernly and Easertnly directions will be considered positive and the Southernly and Westernly directions will be considered negative.
https://www.trimble.com/OEM_ReceiverHelp/V4.44/en/NMEA-0183messages_GGA.html