Power Positioning System

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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 that influence the measurement of distances and angles.

A practical example of obtaining a position fix would be for a ship to take bearing measurements on three lighthouses positioned along the coast. These measurements could be made visually using a hand bearing compass, or in poor visibility electronically using radar or radio direction finding. Since all physical observations are subject to errors the resulting position fix is also subject to error. Although in theory two lines of position (LOP) are enough to define a point, in practice ‘crossing’ more LOPs provides greater accuracy and confidence, especially if the lines cross at a good angle to each other. Three LOPs are considered the minimum for a practical navigational fix. The three LOPs when drawn on the chart will in general form a triangle, known as a ‘cocked hat’. The navigator will have more confidence in a position fix that is formed by a small cocked hat with angles close to those of an equilateral triangle.

It is not true to say that the navigator’s true position is ‘definitely’ within the cocked hat on the chart. The area of doubt surrounding a position fix is called an error ellipse. To minimize the error, electronic navigation systems generally use more than three reference points to compute a position fix to increase the data 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 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 known paths.

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