# A simple explanation of triangulation and trilateration

Triangulation and trilateration are both methods used in surveying, navigation, and geolocation to determine the position of a point by measuring angles or distances to it from known points. However, they differ in their approaches and applications.

## Triangulation:

**Principle**: Triangulation involves measuring the angles in a triangle formed by three known points. The position of an unknown point is determined by creating triangles and measuring the angles from these known points.**Usage**: It is commonly used in surveying and mapping, where the distance between two known points is measured, and the angles to the unknown point from these two points are used to determine its location.**Example**: A surveyor measuring angles from two known points to a distant tower to determine its location.

## Trilateration:

**Principle**: Trilateration is based on the measurement of distances. It involves determining the location of a point by measuring the distance from that point to three or more known points.**Usage**: Trilateration is widely used in GPS technology, where the distance from at least three GPS satellites is used to accurately determine the position of a GPS receiver on Earth.**Example**: A GPS receiver calculates its position by measuring its distance from multiple satellites and then using these distances to pinpoint its exact location.

This table outlines the key differences between triangulation and trilateration:

Aspect | Triangulation | Trilateration |
---|---|---|

Principle | Uses angles within triangles formed by three known points. | Uses distances from an unknown point to three or more known points. |

Measurement | Angles are measured. | Distances are measured. |

Application | Common in traditional surveying and mapping. | Basis for modern GPS technology. |

Calculation | Determines location by creating triangles and measuring the angles from known points to the unknown point. | Calculates location by measuring the distance from the unknown point to multiple known points. |

Equipment | Theodolites or similar instruments for angle measurement. | Distance measuring equipment, such as GPS receivers. |

Accuracy | Dependent on the precision of angle measurement. | Dependent on the precision of distance measurement. |

Example Usage | Surveying land, mapping, and architecture. | GPS navigation, mobile phone triangulation, and geolocation services. |

## Does GPS use trilateration or triangulation

GPS (Global Positioning System) primarily uses trilateration, not triangulation, to determine the location of a GPS receiver on the Earth’s surface. Here’s how it works:

### Trilateration in GPS:

**Distance Measurement**: GPS determines the distance from a GPS receiver to at least three satellites in orbit. These distances are calculated based on the time it takes for signals to travel from the satellites to the receiver.**Three-Dimensional Positioning**: By knowing the precise distance from multiple satellites, the GPS receiver can calculate its position in three dimensions: latitude, longitude, and altitude.**Four Satellites for Accuracy**: Although three satellites are theoretically sufficient for trilateration, in practice, a fourth satellite is used to correct for any timing inaccuracies in the GPS receiver’s clock.

### Not Triangulation:

**No Angle Measurement**: Unlike triangulation, GPS does not involve measuring angles from known points. Instead, it relies entirely on measuring distances.**Why Not Triangulation**: Triangulation is less feasible for a system like GPS because measuring angles to satellites from a moving point on the Earth’s surface would be less accurate and more complex than measuring distances.

**GPS uses trilateration by measuring distances from satellites to the GPS receiver to determine its precise location**, rather than measuring angles as in triangulation.

## What does the 4th satellite do in GPS?

**Basic Concept of Trilateration with Three Satellites**:

- In theory, a GPS receiver can determine its position in three-dimensional space—latitude, longitude, and altitude—using signals from three satellites. Each satellite signal helps to define a sphere on which the receiver must be located. The intersection of these three spheres narrows down the receiver’s location to two points, one of which is typically easily discarded (for example, if it’s located in space or deep underground).

**Need for a Fourth Satellite – Correcting Clock Errors**:

- The GPS receiver has its own internal clock, which is less accurate than the atomic clocks used by the satellites. This discrepancy can lead to timing errors in calculating the distances to the satellites.
- The signals from the satellites include timestamps based on their atomic clocks. The receiver calculates how long each signal took to arrive and, hence, the distance to each satellite. Any error in the receiver’s clock translates directly into an error in the calculated distance.
- By using a fourth satellite, the GPS system can solve for this timing error. Essentially, the receiver adjusts its own clock to match the precise timing of the satellite signals, improving the accuracy of the distance measurements.
- With four satellites, the system can determine an exact position in three-dimensional space and simultaneously correct the receiver’s clock error.

**Enhanced Precision and Reliability**:

- The inclusion of a fourth satellite not only corrects timing errors but also adds to the overall precision and reliability of the GPS system.
- In practice, GPS receivers often use signals from more than four satellites if available, further enhancing the accuracy of the location data.

While three satellites are sufficient for basic trilateration, a fourth satellite is crucial for correcting timing discrepancies between the GPS receiver’s clock and the highly accurate atomic clocks in the satellites, thereby ensuring the precision and reliability of the GPS positioning.