While evaluating a true position of a circle in any co-ordinate measuring machine ( CMM)
is there any standard to specify what kind of a calculation to be used to locate the position of a circle,
like LSQ method ( Gauss best fit), Outer tangential element, etc ?
Evaluation of True Position
There is a standard that explains the mathematical definitions of GD&T callouts. It is the ASME Y14.5.1M-1994 standard. However, this will not be much help in setting up the CMM. You need to select the correct methods for not only evaluating the feature but for establishing the datums you will use as references.
For example, if your primary datum is a plane, you should select an outer tangential element in order to simulate the datum in the same way it will see the mating part. You also need to insure that enough data points are used to get a true representation of the surface.
The secondary datum, if also a plane, needs to be constrained to be perpindicular to the primary datum. If this is not done, many CMM programs (for example Zeiss Calypso) will measure the second plane and establish the reference axis as the intersection point between the planes. This violates the intent of both the ISO 5459 and the ASME Y14.5M standards. In Calypso, there is a dialog box where you can select "ISO 5459" and the software will measure according to the standard.
Unfortunately, many drawings are poorly done and do not always have clear GD&T callouts. At the end of the day, all measurements are a compromise. It is typical to measure hole positions at a single level, even though the tolerance applies over the entire length. You will need to balance what you know about your manufacturing process, the risk of non-conformance, versus the cost of the measurement. If your process is prone to variation that you need to monitor, it may be necessary to measure position in 2 or more levels.
In many cases the least squares algorithm is useful, but be cautious. It can hide or filter out some form errors that might otherwise fall outside the tolerance. It is kind of like using average diameter. A severely oval shaped part may be out when using a 2-point instrument according to the standard, but the average could look great. In many cases GD&T determines the median line based on the midpoints between two point measurements. A best fit algorithm could be applied to a series of these points. The standards are not exactly clear on this point though.
I would also look at monitoring the process using the x and y coordinate measurements instead of position. These would be more relevant to controlling the process as long as the reference axes duplicated the machine tool axes.
Good luck!