reading time 9 minutes, 1,800 words
photo from personal collection, inset pic from https://unsplash.com/photos/a-person-holding-a-cell-phone-while-driving-a-car-oKWHvYlKNKk
We don’t get lost, anymore:
I am a rare individual who has successfully managed to get lost on the way from home to the office, not once but twice. I am convinced that there is a missing 'GPS-gene' in me. Thanks to Google Maps and GPS, I can no longer get lost, no matter how much people around me may wish! GPS is an invaluable tool, for me, as I am, now, certain to reach my destination every time.
My first encounter with this technology was in 2004 during my involvement in an oil exploration project. This venture led me on a field trip to the intriguing landscape of southern Yemen, specifically the Hadramout region near Sayun. Aerial views of this terrain resembled cracks on mud, as the aircraft descended, these cracks unfolded into a maze of table-like plateaus interspersed by deep valleys, which accentuated the steep precipice of the plateaus. Each of these plateaus presented vast stretches of arid land with no discernible features, creating a landscape that appeared identical in every direction.
Three exploratory wells were drilled in this region, and our task was to visit and inspect them. Given that the landscape exhibited uniformity in all directions, locating a specific site felt akin to a ship navigating through open waters. Our contractors used GPS devices to take us to the three wells. This introduction to the GPS technology left a lasting impression upon me.
Let us now understand how the GPS system works. If any reader is curious to know how navigation systems worked before all these electronics came in, this is explained in and earlier post “The Pre-GPS Navigation Method”
How GPS Works:
In the 1960’s, Department of Defence (DoD) of USA conceived a plan to have a global navigation system. The details of the evolution of this idea into the present day GPS need not concern us. In the early 2000’s, this Global Positioning System (GPS) was made available to everyone on earth. The primary system of GPS is a constellation of 24 satellites orbiting the earth in six equidistant orbital planes at about 20,000 Km above earth. Accordingly, an orbital plane will have four satellites each. At that orbital height, each satellites circles the earth once every 12 hours. The arrangement is such that, at least four satellites will be visible from any point on the surface of earth always. The figure below schematically shows the arrangement of this constellation of 24 satellites.
Trilateration Process:
Trilateration process is the core mechanism of the GPS system. This explains how a GPS device locates itself on the surface of the earth. Imagine we don't know where we are. All we have is a radio receiver. Now, think of a radio transmitter (let's call it point 'A') sending a message with the time and its location. By comparing the radio time with our watch, we can calculate how long the signal travelled to reach us. From this, using the known speed of radio signal i.e. 300,000 km/s we can calculate how far we are from the point ‘A’, say this distance is ‘x’. Therefore, from ‘A’ if we draw a circle of the radius ‘x’, our location will be on the circumference of this circle as shown in figure 4.
Points on the circle means too many places where we can be located. Let us have one more radio transmitter doing the same thing. Let the second transmitter be located at point ‘B’ and at a distance of ‘y’ from our location. Then according to the second radio, our possible location will be at the circumference of the circle of radius ‘y’ drawn from the point ‘B’. Since our location has to be on both the circles, there are only two points that will be common to both the circles. These are the points of intersection of the two circles, shown as red dots in figure 5.
Now let us introduce a third radio transmitter in the vicinity. Say we receive a signal from the third transmitter located at point ‘C’ and this is at a distance ‘z’ from our location. Our likely location must be where all three circles intersect, i.e. point common to all three circles. As shown in figure 6, this results in just one point, which could be either of the two points where the circles from figure 5 intersect.
To avoid confusions we need to take note of the following:
Our receiver knows the location of the transmitter and the distance, using this information, our receiver calculates the circle from the location of the transmitter. The transmitter is at the center of the circle.
Our location lies on the circle not inside the area of the circle
Stepping up to 3-Dimension:
So far, we have discussed in 2-dimension using circles. Signals transmitted from a radio transmitter or a GPS satellite will not be going as a circle. These signals will be like an expanding bubble, i.e. spherically shaped. Which means the signal will be in 3-dimension, so the circles are replaced with spheres. Our likely location will be on the surface of the sphere. When two spheres intersect, instead of the two points that we got in 2-dimension, in 3-dimension, we get an entire circle as our likely locations. This is shown in the figure 7 below:
When there are three spheres, then there will be two points that are common to the three spherical surfaces as shown in the figure 8 below:
When there are four transmitters then the possible location reduces to a single point as shown in the figure 9 below:
Understanding that one common point exists for all three spheres is tricky, even with the aid of figure 9 above. Let us breakdown the reasoning for this.
Our location has to be on the surface of each sphere.
Hence, our location has to be at points that are common to all the spheres.
When there are two spheres the common points are many along the circle of intersection of the two spheres.
When there are three spheres, we can only be at any of the points on the circle formed by intersection of the first two spheres. There will only be two such points common to all the three spheres.
With the fourth sphere, our location has to be one of the two points, discovered in point ‘d’ above, that lies on the surface of the fourth sphere.
Yes, there is a possibility that the fourth sphere may go through both the points ‘p’ & ‘q’, however such chances will be rare. With additional transmitters, i.e. more than four, such possibilities can be entirely eliminated.
It may also be noted, that with this 3-dimensional configuration such systems can not only locate us on ground but can also compute our height above the ground. Any ‘Mission Impossible’ fans may remember how Benji, looking at his GPS tracker, does not realise that he is following Ethan on a 2-dimensional view, when actually Ethan was running over rooftops not on the streets.
Coming to GPS:
The process described above is at the heart of the GPS navigation. The radio transmitters explained above will be the GPS satellites hovering over earth. As discussed earlier at any point in time from each point on surface of earth at least four of the GPS satellites will be visible. It may be noted that four is the minimum number of satellites visible. Practically, this number will be higher, giving better accuracy of location. The satellites will constantly be in motion. At every instant that it sends out a beep it informs its location and the time. Using these two pieces of information our GPS device, say our smart phone for instance, computes it’s location.
Google Maps provide an underlying terrestrial map of the region where we are, our device superimposes the GPS location on the layer of Google Maps. That is how we know our location graphically. Google Maps is just one of the service providers, there are other companies providing such maps. Similarly, GPS is just one of the service providers. There are other companies with such a constellation of satellites as well.
The smart devices using GPS location, Google Maps and real-time traffic data can compute the optimum path to our destination and estimate the expected time of arrival. With the infusion of AI into this, the results get more exciting, as computation gets faster and less cumbersome.
One peeve I have with Google Maps is that it does not consider quality of roads while suggesting shortest travel distance. Often, I see Google showing routes that have poor quality roads or narrow roads. With AI technology, it will not be very difficult for Google Maps to estimate such factors too. Google Maps should improve in this aspect.
This post will be incomplete unless we speak of a less desired outcome of this. Since we are constantly moving with our GPS devices, in our smart phones, we are always being tracked. It is very convenient that we get a Google alert when it is time to leave, depending on the traffic situation, for the movie for which we have booked tickets. At the same time, it is a little annoying that by our own volition we become subject to surveillance. It feels like, straight out of the movie the ‘Truman Show’, or rather better described as an amalgamation of two of dystopias authored in the last century George Orwell’s ‘1984’ and Aldous Huxley’s ‘Brave New world’. How will humanity handle this? Let us see.
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