From Wikipedia, the free encyclopedia

Position fixing is the branch of navigation concerned with the use of a variety of visual and electronic methods to determine the position of a ship, aircraft or person on the surface of the Earth.

These techniques include:

• Position lines and position circles
• Celestial navigation
• Radio navigation
• Satellite navigation system

Positions may be expressed as a bearing and range from a known landmark or as an angles of latitude and longitude relative to a map datum.

Generally speaking a position fix is calculated by taking into account measurements (referred to as observations) of distances or angles to reference points whose positions are known. In 2D surveys observations of three reference points are enough to compute a position in a two dimensional plane. In practice observations are subject to errors resulting from various physical and atmospheric factors which influence the measurement of distances and angles.

A practical example of obtaining a position fix would be for a ship to make distance measurements to three lighthouses positioned along the coast. These measurements could be made by using optical equipment or a timing signal transmitted by radio. Since all physical observations are subject to errors the resulting position fix is also subject to error. In fact the errors in the observations propagate and are 'magnified' when combined. The area of doubt surrounding a position fix is called an error ellipse.

In order to minimize this error, navigation systems generally use more than three reference points in order to compute a position fix. This approach is referred to as redundancy. As more redundant reference points are added the position fix becomes more accurate and the area of the resulting error ellipse decreases.

The process of combining multiple observations in this way in order to compute a position fix is equivalent to solving a system of linear equations. Navigation systems use regression algorithms such as Least squares in order to compute a position fix in 3D space. This is most commonly done by combining distance measurements to 4 or more GPS satellites which orbit the earth along paths of predetermined position.