3.4.7.1. Trilateration

The GNSS receivers use a technique called trilateration which involves computing the distance with the help of known distances (Garg, 2021). In trilateration, three satellites, each with a known position in space, are required.

Trilateration is a method used by GNSS receivers to determine their position using distances from satellites. To start, this technique needs signals from at least three satellites, which are positioned at known locations in space. Each satellite sends a signal to the receiver, and by calculating the distance to these satellites, the receiver can figure out its own position on the Earth.

Imagine you are trying to find your way to a hidden treasure in a park. You have three friends who are standing at different fixed points in the park, each yelling the distance you are from them. By knowing the distances to your friends (the satellites), you can pinpoint where you are on a map (the Earth) where their distances intersect.

For example, the first satellite broadcasts a signal to a GNSS receiver, and its angle is not known but the distance is known. In 2D space, this distance forms a circle, but in 3D space it forms a sphere (Figure 3.22).

When only one satellite's signal is received, the receiver can only determine that it is somewhere on the surface of an imaginary sphere, centered around the satellite. This is because the distance to the satellite can only tell the receiver how far it is from that point, but not where it is on the surface.

Think of standing at a point on the Earth and knowing you are 5 kilometers away from a lighthouse. You could be anywhere along the circumference of a circle with a 5-kilometer radius around the lighthouse. Thus, you cannot know your exact location; you could be in many different positions along that circle.

If two satellites are visible, the receiver location can be anywhere on a circle where the surfaces of the two spheres intercept. So, position location is still impossible as the GNSS position could be anywhere on that circle.

With signals from two satellites, the receiver can narrow down its location to the intersection of two spheres. These spheres represent the distance from each satellite. However, this still results in ambiguity, as the intersection can form a circle, where many possible locations exist.

Imagine now that you have two friends giving you directions again: one says you're 5 kilometers from their position and another says you’re 7 kilometers from theirs. Where they overlap creates a circular area. You could still be in multiple spots in that area, making it difficult to pinpoint your exact location.

But when a third satellite also becomes visible, the GNSS receiver can establish its position as being at one of two points on the previously derived circle where the third satellite sphere intercepts it.

Introducing a third satellite allows the receiver to further refine its position. The intersection of three spheres will typically lead to two potential locations. The receiver can then choose the location closest to the Earth's surface, thus resolving the ambiguity that was present with only two satellites.

Continue with your treasure hunt example. Now, a third friend joins in and shouts their distance. This extra piece of information helps you narrow down the possible locations much more, just like having three clues on a treasure map points you towards one specific landmark instead of two.

So fixing of location can be done, but only in two dimensions (latitude and longitude). With at least four satellites visible with their good geometry, four spheres will intersect at only one point in space, so receiver position can be accurately fixed in three dimensions (latitude, longitude and altitude).

With the signals from four satellites, the GNSS receiver can accurately determine its position in three-dimensional space, which includes latitude, longitude, and altitude. The intersection of four spheres allows for a single unique solution, thereby securing precise coordinates for the receiver’s location.

Visualize this as if you have four landmarks – two mountains, a river, and a big tree. Knowing how far you are from those specific points creates a unique intersection where you can stand, providing you with your exact coordinates. With enough landmarks and good spacing (geometry), finding your exact position becomes straightforward.

With five satellites visible, it is possible for the system to automatically detect an erroneous signal. With six satellites visible, it is possible for the system to automatically detect an erroneous signal, identify which satellite is responsible and exclude it from consideration.

Using additional satellites not only enhances the accuracy of the position but also allows the receiver to identify and disregard any faulty or inaccurate signals. This is particularly important in ensuring the reliability of the GNSS data being processed.

Think of a schoolyard where five teachers are giving you directions. If one teacher gives a wrong direction, having those extra teachers allows you to rely on the majority for the correct path. The more opinions you have, the less likely you are to get lost!

Altitudes derived from GNSS positions are known as geodetic altitudes, and were not initially used for aircraft navigation. Performance-based navigation requires that they, and the navigational information presented by the system, are based on the World Geodetic System (WGS-84) coordinate system, established in 1984.

The altitudes calculated by GNSS receivers are referred to as geodetic altitudes, which consider the Earth's shape and allow for precise elevation measurements. These measurements are standard in many navigation systems and are rooted in a comprehensive coordinate framework known as WGS-84, set in 1984.

Think of this like how your smartphone knows the height of a building by placing it on a standard measuring tape – just as all builders use the same reference for measurements, the GNSS system uses WGS-84 to ensure all users can reliably understand their location and altitude.

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