3.4.2. Basic principle of GPS

The GPS is based on very simple and quite ancient idea of determining the position, e.g., coordinates (x,y,z), given the distances and directions to other surrounding objects whose positions are known (Garg, 2021).

The basic principle of GPS relies on knowing both the location of certain reference points (like satellites) and the distances to those points from where you are. Imagine you are lost in a city and you know the locations of three landmarks. By measuring how far each landmark is from your position, you can calculate where you are in relation to them.

Think of it like a game of hide and seek where your friends (the reference objects) are hiding in fixed locations. By shouting out how far you are from each friend's location, you can figure out where you are standing in the park.

Let us consider three objects whose positions (i.e., their coordinates) as well as their distances from the unknown position of the observer are known. The observer's position can now be related to the known distances and positions of objects by using distance equation. Thus, from the known positions of the objects and their distances from observer's position, we get three distance equations involving three unknowns (x,y,z) corresponding to the position of the observer.

When using GPS, you determine your location by forming equations based on the distances to known reference points (satellites). If you know how far you are from three different points, you can create three equations that correspond to the three dimensions of space (x, y, z)—these are the coordinates you need to pinpoint your exact location.

Imagine you are trying to locate where your school is on a map. If you know the distance from your house to the grocery store, the library, and the park, you can figure out exactly where your school is in relation to those places by using those distances to form equations.

These three equations can be solved for the three unknowns i.e., x,y,z. The novelty of GNSS lies in the realization of above concept with the technology of late 20th century in a global navigation system.

Once you have your three distance equations, solving them will reveal your current coordinates. This mathematical solution is what GNSS (Global Navigation Satellite System) technology achieves today, utilizing advanced computation to provide instantaneous and accurate positioning.

It's similar to solving a mystery where you have clues (the distances to landmarks) but need to piece them together to figure out exactly where you are. Just like detectives use clues to uncover the truth, the GPS technology uses mathematical equations to determine your exact location.

It has the capability to provide estimates of position, velocity and time to an unlimited number of users instantaneously and continuously.

GPS technology allows users all over the world to receive their positioning data instantly and continuously. This means that whether you are a driver using GPS navigation, an aircraft in transit, or even a farmer optimizing fieldwork, you get accurate location information in real-time.

Think about how you use GPS in your car. As you drive, the GPS updates your position in real-time, showing you exactly where you are on the map, adjusting as you move for any turns or changes in direction. It's like having a friend in the passenger seat who can give you directions based on where you currently are.

The accuracy of GNSS height measurements depends on several factors but the most crucial one is the undulating shape of the Earth (Xu, 2010).

One major factor that influences how accurate your height measurements in GPS are is the shape of the Earth. The Earth isn't a perfect sphere but has an uneven surface due to mountains, valleys, and other geological features. These variations can affect how GPS calculates your altitude.

Picture trying to measure the height of a mountain with a tape measure while standing on an uneven, rocky surface. The bumps and dips of the ground can significantly change your reading, just like how the varied Earth surface can impact GPS height readings.

Height can be measured in two ways. The GNSS uses ellipsoidal height (h) above the reference ellipsoid that approximates the Earth's surface. The traditional, orthometric height (H) is the height above an imaginary surface called the geoid (Figure 3.15), which is determined by the Earth's gravity and approximated by MSL. The orthometric height is often referred as the MSL, and can be obtained by subtracting the geoid height (N) from the GNSS height (h) (i.e., H = h - N).

When GPS measures height, it primarily uses two methods: ellipsoidal height, which is based on a mathematical model of the Earth's shape, and orthometric height, which considers the gravitational field to provide a more precise finding. The difference between the two is commonly termed geoid height and has practical implications, especially in surveying and mapping.

Think of it like measuring the height of a cake. The ellipsoidal height tells you how tall the cake is from a standard surface (like a cutting board), while the orthometric height represents how high the cake stands on a countertop reflecting its gravity pull. The difference between the two tells us how much higher the cake's top is above the cutting board compared to the countertop.

In GNSS based determination of observer’s position, satellites act as reference points (i.e., known locations) from which receiver on the ground determines its position.

In GPS technology, satellites are crucial reference points used to determine where you are. Your GPS receiver picks up signals from these satellites and uses them to figure out its position on Earth by calculating how far it is from several satellites at once.

Imagine you're trying to find your way in a dark room. If you have a flashlight (the GPS receiver) that can point to several distant light sources (the satellites), you can determine your position by how far you are from those light sources. The closer you are to each one, the more accurate your ability to understand your location becomes.

By measuring the travel time of the signals transmitted from at least four satellites, the distances between the receiver and satellite will yield accurate position, velocity and time.

GPS receivers calculate position by measuring how long it takes for signals, sent from satellites, to reach them. Signals travel at the speed of light, so the time it takes to receive the signal allows the device to compute how far away each satellite is and, with that information, determine its precise location.

Think of it like a game of catch: if you throw a ball to a friend, you can tell how far away they are based on how long it takes for the ball to get to them. The GPS receiver uses a similar principle with satellite signals to measure distances quickly.

The GNSS receiver calculates the distance between each one of the satellite and receiver position, the GNSS receiver uses a method called trilateration to determine the GNSS receiver position (Figure 3.16).

Trilateration is the method that GPS uses to accurately determine the location of a receiver. By knowing the distances to at least three satellites, the receiver can pinpoint its location in three-dimensional space. The intersection points of the distances provide the exact coordinates.

Consider a game of 'hot and cold' where players determine their location based on clues from their friends. If each friend shouts 'hotter' or 'colder' based on your direction, you can zero in on the correct spot by finding the intersection of those clues. Similarly, trilateration helps in pinpointing the exact location by intersecting distances.

Though three-range measurements are sufficient but fourth observation is essential for solving the clock synchronization error between the receiver and satellite.

To accurately determine a GPS receiver's position, it typically relies on signals from at least four satellites. While three satellites provide enough information for a three-dimensional position, a fourth satellite is essential to correct the time discrepancy between the satellite's atomic clocks and the receiver's clock, which may not be as accurate.

It’s like needing a fourth friend in the 'hot and cold' game who can tell you exactly when you are standing still and when you should move. This friend corrects your uncertainties, just as the fourth satellite corrects timing errors in GPS calculations.

Even though GNSS technology provides us greater advantages, but it still has some limitations. Since GNSS satellite signals are too weak as compared to phone signals, they don’t work indoors, underwater, under trees, etc.

While GNSS technology has revolutionized navigation and positioning, it has limitations due to the weakness of the satellite signals. These signals can be obstructed by buildings, trees, or other structures, resulting in inaccurate or no positioning indoors or in other challenging environments.

Imagine trying to hear someone speaking on a phone while you are inside a crowded café. The noise and walls might make it difficult to hear the conversation clearly, just as buildings or trees block the GNSS signals, making it challenging to determine your location accurately.

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