Global Positioning System aka GPS is one of the most popular technologies we have in possession today. When it comes to how GPS works, the concern is also taken into account how the distances between the GPS receiver and the satellites are measured. It actually follows a mathematical method named ‘Trilateration’.
How Does a GPS Receiver Determine the Distance Between You and the Satellites?
GPS Works following simple fundamental physics. You just need to go through the sections to understand the simple logic and system behind it. It is amazing how a small addition to your device can track you in this huge world, isn’t it?
Time and Position of GPS Satellites
GPS systems usually have three basic parts that are the satellite, the ground station, and the receiver. Satellites emit radio signals and those signals detect our location. The ground station monitors the position of the satellites if they are in their accurate place or does it need any replacement.
32 active satellites are working for GPS technologies and 24 of them are core. The remaining 8 are referred to as emergency replacements. Each satellite has its own orbits. When one of the satellites is slightly out of its orbit, this replacement is undertaken immediately.
Atomic clocks are installed into the satellites so that they become free from time errors. Atomic clocks record an almost accurate time of emitting radio signals. Comparing this time with the related devices on the ground delivers information on time errors. The clocks can also be readjusted, but more generally facts on time errors are outfitted to GPS radio signals as correction factors.
Distance and Mismatches
To determine the positional accuracy at the centimeter level, the time difference has to be measured at the sub-nanosecond level. To achieve such accuracy, atomic clocks are needed in both satellites and receivers. But atomic clocks are way too big and expensive for our daily used devices.
The GPS receivers are equipped with comparatively cheap quartz clocks. These clocks are right up to 10 nanoseconds one day. This accuracy is regarded as enough to say that the time bias between the onboard satellites and the quartz clocks is the same for all of those satellites. Now this time bias can also be measured by determining the traveling time of the radio signals to four satellites.
Determining the Distance
Usually, it is said that we need three satellites to calculate the position. This triangulation method works for most cases but it leaves a big spot for errors. If one more satellite is added that means if four satellites work together, it can give us the perfect reading.
Imagine a spherical area around each satellite where the satellite is the center of that sphere. When two satellites work together, two circles overlap each other. That gives us a small range of our possible positions. Now if we take a third satellite, this third circle overlaps with the other two circles. It leaves us two possible spots.
In most cases, between these two spots, one spot is nearly impossible to be the right one. So it provides us an accurate position. But to measure the accurate distance between the GPS receiver and the satellites and to use the trilateration method, a fourth satellite is needed.
GPS radio signals include two parts that are a carrier phase mode and a pseudorandom code. This signal involves the information of the exact times and the satellites’ locations using atomic clocks. The receiver computes the relative positions between it and the satellites based on this information.
To calculate the distance between the receiver and the satellites we need a term called delta t. This delta t is the time difference between the time of the receiver’s clock and the time of the atomic clocks. So the distance is,
Distance(d)= Velocity(v) x Time difference (∆t)
Here velocity means the speed of light. If we multiply the time difference with the speed of light, we’ll be able to determine the accurate distance between the receiver and each of the satellites. So by modifying the equation we get,
Distance(d)= Speed of Light(c) x Time difference(∆t)
Q: What is the minimum certainty of GPS?
Ans: The United States government claims 4 meter RMS horizontal accuracy that is 7.8 meters 95% Confidence Interval for civilian (SPS) GPS. Vertical accuracy is not that good. Some devices/locations reliably can get 3-meter accuracy which is 95% of the time or better.
Q: What is the reason for GPS drift?
Ans: The GPS track departs from the road. The route usually follows the shape of the road but with lesser accuracy. It happens mainly because of reflections and shadows.
GPS can be a lifesaver. It boosts our confidence on the road. However, in rural areas sometimes they fail to provide the perfect location. Four satellites are right to determine the distance, but the more satellites are involved, the more chance of accuracy is there. Hopefully, this article has helped you to find the proper answer to the often asked question.