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### error ellipse in least square

Hello Mr Billy and my friends what is the basic idea of error ellipse in least square analysis .......what is the use of error ellipse...

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• Land Surveyor
Yes if the ellipse is small the error is small, & if the ellipse is large the error is large.
• Land Surveyor

Dear Mr. Kingsly,

When you have a overdetermined position, one calculated by more than the minimum number of required measurements (redundant data), the results of using the various data lead to different results. The error ellipse is an 2-D expression of confidence around the most probably correct position. The ellipse is oriented along the direction of the greatest variance and the major and minor axes are the variance along that direction and orthogonal to it.

The software can usually be directed to express the confidence as a percentage, roughly defined as the likelihood that the true position falls within the ellipse(95% would be larger than 90%, for example).

Generally speaking, observing the error ellipses will help you decide when further measurement would improve confidence or when a particular station or measurement may be erroneous. A rule of thumb is that smaller the ellipses the more precise the measurements or confidence of the results. Another general but definitely not rigid rule of thumb is the more circular the ellipses the more balanced the measurements.

JAC

• Land Surveyor
Thank you sir what is the semi major axis and semi minor axis represent s......
• Land Surveyor

A circle is a special ellipse. A circle has a radius.

If we draw a smooth closed curve, like a circle, but let the radii along one direction be long and the direction at right angles (orthogonal) be short, that closed curve is an ellipse. (Imagine the cross-section of a beach ball with someone sitting on it.) In an ellipse the long radius-like value is called the semi-major axis and the short radius-like value is called the semi-minor axis.

The circle is special in that the semi-major axis and the semi-minor axis would be equal - the radius is constant all around the circle - not so in a usual ellipse.

JAC

Land Surveyor

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