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Basics of Trilateration
Basically, when mapping the area of a landmark, it is assumed that no error will be associated with the process. Working as mobile beacons, the job can be completed with help of a number of robots for the precise determination of the position. But, in this procedure, some uncertainty may definitely arise. By the use of a multivariate Gaussian distribution, a person can measure the uncertainty in position of a particular landmark.
In the trilateration process, the angular measurements are taken by the process of triangulation, while the actual position of an object is measured by range measurements. Both these procedures have been used for a long period of time, mainly for maritime navigation and geodesy.
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Where is the principle of Geometric Trilateration Applied?
The basic principles used in the trilateration process are also used in modern navigation systems. Things can become clear by considering the example of aircraft and GPS receivers.
Radio beacons are used for applying triangulation on aircraft. In case of GPS receivers, the position of a particular object can be measured by applying the principle of geometric trilateration to satellites. To get the angles and ranges of a particular landmark, the mobile robots use a number of sensors.
After that, the principles of triangulation and trilateration are used in the estimation process. There are a number of instruments present where the use of sensor power varies. For example, the rate of angle measurement is very high in comparison to the other instruments such as sonar. But some of the measuring instruments today, such as stereo-cameras, are capable of finding angle as well as range simultaneously. A suitable environment is provided to a robot to perform its work, and the actual size of the robot often limits the number of sensors used.
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There are number of applications of geometric trilateration. Keeping the research for the robotic world aside, the research for geometric trilateration is one of the main subjects for current days. GDOP (or the Geometric Dilution of Precision) is a dimensionless number that is capable of capturing the errors, while performing estimation of the actual position of an object. Nowadays, dynamic scenarios are successfully created because of improvement over angle measurements as well as estimation of position.
GPS navigation is the biggest field that relies on trilateration to satellites at known positions. Chaffee and Abel and McKay and Pachter have been known to carry out certain experimental studies that have been material in investigating the error metrics for GPS trilateration, though the results are still elementary.
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Geometric Trilateration is one of the relatively unknown fields. Not too much of concrete info is available on the subject even online, and it is one of the hot topics for the researchers throughout the world. The analysis of trilateration discussed here, is expected to be used in development of an algorithm, which will be able to control the motion of the AUVs.
This will in turn help in optimizing the trilateration geometry in real-time applications, and it will definitely be a great boom in the GPS field.
Source: Paper on Minimizing Trilateration Errors in the Presence of Uncertain Landmark Positions, by Alexander Bahr John J. Leonard, Computer Science and Artificial Intelligence Lab, MIT, Cambridge, MA, USA