In the previous article we introduced the system that revolutionized the way to sea or GPS.
Let’s then analyze the User Segment.
The GPS user segment is the receivers that are able to receive and decode signals transmitted by satellites.
Each receiver is able to provide the coordinates (referred to the installation point of the antenna even if it is usually in use to speak of receiver coordinates) expressed in Latitude, Longitude and Dimension (the latter uninfluential for the purposes of the maritime navigation); In addition, the system also provides UT- Universal Time, which is the average Greenwich time on which clocks are adjusted relative to the time zone they belong to; time has absolute precision being that held by the atomic clock on board the satellites.
The equation at the base of the calculation process is that of the distance between receiver and satellite, that distance, will be equal to the rate at which electromagnetic waves propagate for the time it takes the signal to reach the receiver.
All other data provided by the system as a route and speed is the result of the processing of position data by the individual receivers.
Now the distance in space between satellite and receiver will be given by the sum of the square differences of the antenna and satellite coordinates in space.
It may seem complex, but the success of the system lies precisely in the formula below, which we will try to explain even to those who do not get along very well with mathematics.
In the equation we have the following elements:
- Ri – Satellite Receiver Distance
- X,Y,Z – receiver coordinates
- Xi,Yi,Z, satellite coordinates
- “T” shift of time
- c – electromagnetic wave propagation speed
At this point all the elements are clear, but why do we find an additional amount of Tc? If you have read the article on the Space Segment you will remember that on board each satellite time is marked by a very expensive atomic clock whose expense can not be incurred in the construction of a receiver for commercial use (we speak of millions of dollars).
For this reason, the cheap quartz clock of the receiver (digital clock at very low cost) can never be synchronized with the atomic one of the satellite and this difference is called a time shift that at the same time is not can be calculated on the individual satellite.
At this point we have as unknowns in addition to the three coordinates of the receiver a fourth represented by the time shift.
The coordinates of the satellites are known because the receiver has the ephemerals of each satellite received by the latter (very similar to the astronomical ones allow to have the position of the satellite at the time the signal was transmitted).
Now even if we are not mathematical experts we will have to know that a mathematical system of equations is solvable only if the number of unknowns is equal to that of equations: well we just have to write the previous equation for 4 different satellites to get a system of 4 equations and 4 unknowns and that’s it.
Now for the first receivers able to receive only 4 satellites at the same time, the problem did not arise since the reception of more than 4 satellites at the same time in the early 90s was difficult especially if you pushed at high altitudes.
Today a receiver has a high number of channels (going beyond 10) this allows you to receive all the satellites transmitted to the geographical area in which you are located greatly increasing the calculation accuracy with a resolution to the minimum squares of a system of multiple equations to 4 unknowns, but this is another story.
Most of these receivers, given the large number of satellites visible at the same time mainly in the open sea, are also able to choose the most appropriate number of satellites (excluding, for example, the lowest ones on the horizon whose signal may suffer from multiple reflections).
Last the article giving some recommendations:
- The position provided by a GPS receiver refers to its antenna, if integrated will be the position of the receiver itself, if external as a result; this should be kept in mind when looking for accurate positioning on large vessels or ships (from 20-30m being the precision now below 10m)
- Always use a good external antenna and place it at the highest possible point so that signals from the satellite reach directly to the antenna and are not reflected first by other objects (in order to avoid multipath errors).
- Remember that the system is based on the proper operation of the on-board electronics and that of the space segment: venture into high-water navigations only if you also know how to go “back” using the methods of traditional navigation.
To conclude the topic read GPS – Control Segment