Basic Positioning Principles of GPS


The basis of GPS is "triangulation" from satellites. A GPS receiver measures distance by measuring the transmission time of radio signals and determines the position of satellites with distance. It is a measurement of high orbit and precision positioning. Suppose we measure our distance from a satellite and find it to be 11,000 miles. First, we draw a circle with the satellite as the center, and we are on any point of the surface of a sphere that is centered on this satellite and has a radius of 11,000 miles

Next, say we measure our distance to a second satellite and find out that it is 12,000 miles away, and we're somewhere on the circle where these two spheres intersect. If we then make a measurement from a third satellite and find that we are 13,000 miles from that one. It narrows our position down even further, to the 2 points where the 13,000 mile sphere cuts through the circle that is the intersection of the first 2 spheres. So by ranging from 3 satellites we can narrow our position to just 2 points in space.

We need to measure the distance from a fourth satellite to decide on which one is our true location. From the viewpoint of Physics, the product of signal transmission time x speed will be the distance between the satellite and us. This distance is known as the virtual distance. In GPS measurement, we are measuring radio signals travel at quasi light speed, i.e. 186,000 miles/sec. It is too fast that sometimes it takes only 0.06 second. Therefore, we need 2 timers: one on the satellite to record the signal sending time, another one on the receiver to record the signal receiving time. Though the speed is fast, the signal sending/receiving time is not synchronous. Suppose both the satellite and receiver alarm us at the same time, we will hear 2 different sounds because there is time delay when signals are sending to us from 11,000 miles away. Therefore, we can calculate the distance: delay time x speed. The product will be the true distance between the satellite and the receiver. This is the basic theory of triangulation.

Well, what data does a GPS satellite send exactly? These data include the pseudo random code, ephemeris (pronounce as ee-fe-me-ris) and Almanac.

  1. Pseudo random code (see How does GPS distance measuring code works for details) can help us find out the source satellite of signals. Therefore, it is also the ID code of a satellite, from 1 through 32. Therefore, we can see the satellite code from the GPS receiver. Why there are 32 codes when there are only 24 satellites? Some codes are reserved for new satellites launched to the space when one is down. 
  2. Ephemeris data contain the status, current date and time of the satellite. These allow your receiver to understand the current time and so to determine your present location.
  3. Almanac transfers orbit data to inform the receiver the location of each satellite in the space.

Simply speaking, every satellite will tell your receiver 3 things: what satellite it is (pseudo random code), where the satellite is (almanac), and when the message is sent (ephemeris). After receiving these data, the receiver will save the almanac and ephemeris data as a reference for time correction on the GPS receiver.

After comparing the signal sending time of each satellite and the receiving time on the receiver, the receiver will calculate the distance between itself and each satellite. When receiving signals from more than one satellite, the receiver will triangulate the location. It needs 3 satellites to execute 2D positioning (latitude and longitude) and 4 or more satellites to execute 3D positioning (latitude, longitude and altitude). By continually updating your locations, the receiver can locate your moving direction and speed.

The satellite geometry will influence the accuracy of the GPS receiver. It refers to the relative position of individual satellites from the receiver. The angle of signal receiving will influence the accuracy of positioning. If the angle is too small, or that the satellites are located too close to one another, the accuracy of positioning will be influenced. When the angle among satellites is small, a bigger error will occur. Take 2 satellites for example as shown in the figure (Please wait…). Suppose satellites A and B are not moving in an instant, and that Satellite A is free from other interference and provides accurate positioning information. Now, errors occurred in Satellite B because SA is activated or there is other interference. The receiver will consider that the position of Satellite B is at the position of Satellite B1. As a result, error measurement of the CD segment occurred. When the adjacent angle of 2 satellites is big, the CD segment will be small, and the positioning will be more accurate. If 4 satellites are located in different directions, the positioning accuracy will be enhanced because the chances of signal intersection of these satellites will be very small. Even if the SA is activated, the accuracy will be within 100m or better.

When installing a GPS receiver inside a car, satellite signals will be blocked when the car is approaching a tall building or high land; i.e. it will receive signals from fewer satellites. When the car is surrounded by tall buildings or towering barriers, it will be difficult to position its location. But it doesn't mean that the positioning will be accurate when the receiver receives signals from many satellites at the same time. The azimuth and elevation also affect the accuracy of positioning.

Multi-patch is another factor affecting positioning accuracy. Simply speaking, it refers to the reflection of signals in contact with barriers. The fringe/ghost (image)/echo signal as found in TV using traditional antenna is a typical example, though it is not seen on TV using cable. Signals will be reflected and delayed when they touch the barrier. In this case, the receiver will consider that the exact location of the source satellite is farther than it is. Yet, the error will not exceed 15ft.

Other factors affecting positioning accuracy include the ionosphere and troposphere in the atmosphere, internal clock error.

Many beginners ask how to choose a good GPS receiver? The answer is an open case. First, you should ask why you need a GPS before selecting a suitable one. If you want to use it in a car, a palm-sized GPS receiver will be sufficient. If you want to use it on a boat or in an airplane for navigation, you will need one with higher positioning accuracy or e-map function. If you want to use it on a boat, you will even need one with depth positioning.

After determining why you need a GPS, you can choose a suitable one for yourself. There are many options at different prices. The price and accessories all depend on your needs. If there are more than one options within your budget and needs, choose one that is easier to operate.