math june ia
GPS AND TRIANGULATION
GPS calculation works on the principle of the receiver (example the handheld GPS receiver on car or mobile) calculating the distance of that receiver from a set of known points.
1) The receiver needs to receive a straight line signal (also called line of sight) from the known point without reflection. The best things that can do that are satellites overhead.
2) To enable that, the US department of defence has setup 24 low earth orbit (LEO) satellites. They are called the GPS satellite constellation. The geostationary satellites (such as what are used for star TV, DD etc) will be too far to send a strong signal to your receiver, and also when you are lost in the wilderness, you will not know where to point the geostationary antenna. So there is a need for low earth orbit satellites. The problem with LEO satellites is that they cannot be geostationary, so they are constantly revolving around the earth, several revolutions per day.
2) A GPS signal originates at the broadcasting station in Colorado and is sent straight up to the satellites from multiple locations on the earth and from there beamed down to the ground. The GPS signal has a originating time stamp in it and a sinusoidal signal. On the receiving end, the receiver identifies the phase difference (phi) of the received signal, and based on the phase difference, the receiver can now tell accurately how far it is from the satellite.
3) The receiver now knows how far it is from the satellite, say r1, that means it can be anyway on the sphere of radius r1 away from the satellite. It needs to know the distance from many more satellites so it can calculate the intersection point of spheres.
4) If you take the intersection of two spheres, the intersection is a circle, so you can be anywhere on that circle. If you take the intersection of three spheres, you will get two possible points on that circle. One makes sense, and one will appear several km above or below sea level so the receiver
GPS calculation works on the principle of the receiver (example the handheld GPS receiver on car or mobile) calculating the distance of that receiver from a set of known points.
1) The receiver needs to receive a straight line signal (also called line of sight) from the known point without reflection. The best things that can do that are satellites overhead.
2) To enable that, the US department of defence has setup 24 low earth orbit (LEO) satellites. They are called the GPS satellite constellation. The geostationary satellites (such as what are used for star TV, DD etc) will be too far to send a strong signal to your receiver, and also when you are lost in the wilderness, you will not know where to point the geostationary antenna. So there is a need for low earth orbit satellites. The problem with LEO satellites is that they cannot be geostationary, so they are constantly revolving around the earth, several revolutions per day.
2) A GPS signal originates at the broadcasting station in Colorado and is sent straight up to the satellites from multiple locations on the earth and from there beamed down to the ground. The GPS signal has a originating time stamp in it and a sinusoidal signal. On the receiving end, the receiver identifies the phase difference (phi) of the received signal, and based on the phase difference, the receiver can now tell accurately how far it is from the satellite.
3) The receiver now knows how far it is from the satellite, say r1, that means it can be anyway on the sphere of radius r1 away from the satellite. It needs to know the distance from many more satellites so it can calculate the intersection point of spheres.
4) If you take the intersection of two spheres, the intersection is a circle, so you can be anywhere on that circle. If you take the intersection of three spheres, you will get two possible points on that circle. One makes sense, and one will appear several km above or below sea level so the receiver