What is GNSS/GPS triangulation and how does it work?

Triangulation is a fundamental principle in satellite navigation, especially in systems such as GNSS (Global Navigation Satellite System) and GPS (Global Positioning System). This process allows the exact position of a receiver to be determined on the Earth's surface using signals from multiple satellites. In this article, we will explore how triangulation works in the context of GNSS/GPS, analyzing its theoretical and technical foundations.

What is triangulation?

Triangulation is a geometric method that uses the measurement of distances from two or more known points to calculate the position of an unknown point. In the context of GNSS, this technique is based on measuring the time it takes for a satellite signal to reach the receiver. By knowing the speed of light (approximately 299.792 km/s), the distance between the satellite and the receiver can be calculated.

How does GNSS/GPS triangulation work?

For a GNSS receiver to determine its exact position, it needs to receive signals from at least four satellites. The process is described in detail below:

1. Receiving signals: Each satellite sends radio signals that include the exact time the signal was sent and the position of the satellite at that time. The GNSS receiver captures these signals.

2. Distance calculation: By comparing the time it took for the signal to arrive from the satellite to the receiver, the distance to that satellite can be calculated. This calculation is done using the formula:

   Distance=Travel time×Speed ​​of light

   The distance is translated into a sphere in which the satellite is located. Therefore, if the receiver receives signals from three satellites, three spheres are generated in space.

3. Triangulation: With distances calculated from at least three satellites, the receiver can establish its position in three dimensions (latitude, longitude and altitude). If there are only three satellites, the position is determined on a 2D plane (latitude and longitude). However, with a fourth satellite, the receiver clock synchronization error can be corrected, allowing altitude to be calculated accurately.

The geometry of triangulation

The geometry of the triangulation is crucial for the accuracy of the GNSS system. Each satellite in the sky can be seen as a point in space that emits signals. The measured distance to each satellite can be represented as a sphere around each one. The intersection of these spheres is the receiver's position.

To understand better, let's visualize a scenario:

• Suppose there are three satellites: Satellite A, Satellite B and Satellite C. If the receiver measures distances to these three satellites, the three spheres will intersect at a single point in three-dimensional space, which represents the position of the receiver.

• When a fourth satellite is added, a new sphere is introduced. This allows not only to confirm the position of the receiver, but also to adjust any temporal errors that may be present in the receiver clock, which could become desynchronized with respect to the standard time of the GNSS system.

Errors in GNSS/GPS triangulation

Despite the precision offered by GNSS triangulation, several factors can affect the quality of the data obtained:

1. Clock errors: The satellite and receiver clocks may not be perfectly synchronized. Although satellites carry extremely precise atomic clocks, even a small discrepancy can lead to errors in distance calculations. This is one of the reasons why it is essential to have at least four satellites to make corrections.

2. Physical obstructions: Tall buildings, mountains and other structures can block satellite signals, causing what is known as the multipath effect, where the signal bounces off surfaces and arrives at the receiver with a delay. This can result in errors in triangulation.

3. Signal interference: Signals can be affected by atmospheric conditions such as the ionosphere and troposphere. These phenomena can alter the speed of signals as they pass through different layers of the atmosphere.

4. Number of satellites: System accuracy decreases if fewer than four satellites are available for triangulation. If there is less, the receiver cannot correct clock errors, resulting in lower accuracy of the calculated position.

The Importance of Position Geometry

Position geometry is critical to GNSS accuracy. Good satellite geometry refers to the arrangement of satellites in the sky. A sparse pattern of satellites provides better accuracy, while a closer configuration can result in larger errors.

To measure the quality of satellite geometry, DOP (Dilution of Precision) is used. A low DOP indicates good geometry, which translates into less error in the calculated position. On the contrary, a high DOP can lead to inaccurate results.

The different types of DOP include:

• PDOP (Position Dilution of Precision): Measures precision in three dimensions.

• HDOP (Horizontal Dilution of Precision): Measures the precision in the horizontal direction.

• VDOP (Vertical Dilution of Precision): Measures the precision in the vertical direction.

Synchronization in triangulation

Timing is crucial in GNSS triangulation. Since satellite signals travel at the speed of light, even a small temporal discrepancy can result in significant errors in the calculated location. Therefore, satellites must carry extremely precise clocks, which are continually compared to a master clock on Earth.

The receiver, by capturing signals from several satellites, can compare the time it took each signal to arrive and thus determine the distance to each satellite. This synchronization capability allows the GNSS system to calculate the exact position of the receiver in real time.