GPS System

The GPS (Global Positioning System) system is a worldwide radio-navigation system formed from a constellation of 24 satellites and their ground stations. GPS uses these "man-made stars" as reference points to calculate positions accurate to a matter of meters. In these days the GPS receivers have evolved so much and used various applications.

The GPS system is the unit which can locate the location of the 3-D point (x, y, z) on the earth with the help of 24 GPS satellites. The GPS(Global Positioning System) uses usually 3 to 4 satellites to determine its location.

Figure 1. GPS satellites
(a) actuall satelite

(b) 3 or 4 GPS satellites are used to determine the location of the receiver.

The basic idea of the GPS system is to use satellites in space as reference points. By measuring the distances from each reference satellites, we can calculate our location. This is so called triangular method in geometry. The distance between the reference satellite and GPS receiver can be calculated by measuring the flying time of the GPS R/F signal from the satellite to GPS antenna. The GPS signal is radio frequency signal, so the speed of the signal is same as the speed of light 30,000 km/sec. The flying time of the GPS signal can be calculated with the atomic clock which is installed on the GPS satellites. The following figure shows the range of points which are same distance from the satellite. You can easily think that it will become circle if we think only 2 dimensions.

Figure 2. GPS R/F signal ranges in 2D

If we think about the 3 dimension where we live in space, the range forms a sphere.

If there are 2 satellites, and we know the distances from the satellites then we can find the intersectional range. The intersection of the 2 circles will be 2 points as shown in next figure.

Figure 3. Intersection of the 2 circles of GPS signal range

In case of 2 dimensional space, from 2 of GPS signals we can determin the location of 2 points.

In case of 3 dimensional space, the intersection of 2 sphere will form a circle. To determine the point location, we need one more satellite. The intersection of 3 spheres in 3D space will form 2 points. If we use the 4-th satellite, then we can determine which is the correct solution among 2 candidates. Even though we can't use the 4-th satellite, one of the 2 candidates will be very unusual solution, i.e. hundread miles deep in the ground or up in the sky. So, if we can assume that the receiver or car is on the ground, the we can find which is correct one.

Mathematically we can determine the exact location of the receiver in the 3D space with 4 signals from known 4 satellites. However there are lots of effect which will make an unavoidable error;

To overcome the error limit of the conventional GPS, a new concept of DGPS (Differential GPS) was appeared. The DPGS is more accurate than the normal GPS with the help of correction signal generated from the correction station which is fixed at the known location. The basic concept is like this

The amount of the GPS error will be same to the all GPS in the same area on the earth. Therefore if we can measure the error of the GPS-calculated location to the exactly known location (i.e. the correction station), then we can find how much the error is in the GPS location data. The difference between the reference value and GPS received value is the correction value and it will be sent to the moving GPS near around. So, at the moving GPS system, by subtracting the error from the measured location we can calculate the correct values.

The following table is the specifications of the DGPS of the Novatel.

Figure 4. GPS antenna

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