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From: Sara Silva <sara@de...>  20100531 11:01:33

Hi Brian, Yes, your problem seems to be very well constrained, so much that it got me immediately thinking that maybe it is not GP you need, but GAs. All you want to do is optimize parameters, so why not use a classic parameter optimization technique or, if you really want to use something more sophisticated, GAs? Really, removing so much from GPLAB to transform it into a simple GA does not make much sense. I think MATLAB has a GA toolbox. Cheers, Sara Brian Wylie wrote: > Hi there, > > I'm a little new to this interesting topic  but very interested in > investigating the usefulness of implementing GPLAB for calibration of > a magnetometer from measured XYZ samples. I'm struggling to get my > head around how to use GPLAB to do this however  although I'm sure it > must be possible because it is essentially a symbolic parameter > estimation problem. > > In essence, due to magnetic field disturbances and manufacturing > defects, a magnetometer which should measure a perfect sphere for all > aspect rotation instead measures an offset, rotated ellipsoid. This > ellipsoid can be represented by a function of parameters offsetX, > offsetY, offsetZ, scaleX, scaleY, scaleZ, and rotation angles phi, > theta, psi. > > I would love GPLAB to be able to estimate the above parameters > (essentially terminals in GPLAB) given orthogonal XYZ data. I have two > questions in line with this, however: > > 1) I'm not sure how to present the data to GPLAB. Clearly > testdatafilex should input the XYZ data, however I don't have any > "known output", such as the demo file which uses and x input and known > y output for that x input. > > However, what is known is what the expected magnitude of each XYZ > sample set should be. Because of the ellipsoid output, the magnitude > changes a lot depending on orientation, however a calibrated > magnetometer would output a perfect sphere, implying that the > magnitude would always be close to a known constant value for a > particular location on Earth. > > So I'd imagine that the fitness needs to be determined as calculating > the magnitude of all the datapoints once they have been calibrated, > comparing this to a known value, calculating error, and minimizing > error to find best fitness. > > The output would then be a function (GPLAB tree) which describes that > shifted, rotated ellipsoid. > > Any pointers on how to set this up would be really appreciated. > > 2) Ideally, GPLAB would find the best solution to be the correct form > of the ellipsoid, in which the above parameters are easily extracted. > Obviously I can't expect GPLAB to necessarily do this without some > "encouragement"  I'm guessing more likely that a different format > output is likely, which may be just as valid, just not what I am > looking for. > > Am I correct in saying the best would be to initialise GPLAB with a > tree with the correct format, and then allow GPLAB to only modify the > terminals (ie the parameters), ultimately finding the best fit only as > a parameter estimation exercise? (I know this limits the power of > genetic programming, but often a constrained form is desirable for > purposes of implementation.) > > I'd really appreciate any help in getting a start on this. > > Kind regards, > Brian > >  > > _______________________________________________ > gplabusers mailing list > gplabusers@... > https://lists.sourceforge.net/lists/listinfo/gplabusers > 
From: Brian Wylie <bswylie@gm...>  20100525 14:14:45

Hi there, I'm a little new to this interesting topic  but very interested in investigating the usefulness of implementing GPLAB for calibration of a magnetometer from measured XYZ samples. I'm struggling to get my head around how to use GPLAB to do this however  although I'm sure it must be possible because it is essentially a symbolic parameter estimation problem. In essence, due to magnetic field disturbances and manufacturing defects, a magnetometer which should measure a perfect sphere for all aspect rotation instead measures an offset, rotated ellipsoid. This ellipsoid can be represented by a function of parameters offsetX, offsetY, offsetZ, scaleX, scaleY, scaleZ, and rotation angles phi, theta, psi. I would love GPLAB to be able to estimate the above parameters (essentially terminals in GPLAB) given orthogonal XYZ data. I have two questions in line with this, however: 1) I'm not sure how to present the data to GPLAB. Clearly testdatafilex should input the XYZ data, however I don't have any "known output", such as the demo file which uses and x input and known y output for that x input. However, what is known is what the expected magnitude of each XYZ sample set should be. Because of the ellipsoid output, the magnitude changes a lot depending on orientation, however a calibrated magnetometer would output a perfect sphere, implying that the magnitude would always be close to a known constant value for a particular location on Earth. So I'd imagine that the fitness needs to be determined as calculating the magnitude of all the datapoints once they have been calibrated, comparing this to a known value, calculating error, and minimizing error to find best fitness. The output would then be a function (GPLAB tree) which describes that shifted, rotated ellipsoid. Any pointers on how to set this up would be really appreciated. 2) Ideally, GPLAB would find the best solution to be the correct form of the ellipsoid, in which the above parameters are easily extracted. Obviously I can't expect GPLAB to necessarily do this without some "encouragement"  I'm guessing more likely that a different format output is likely, which may be just as valid, just not what I am looking for. Am I correct in saying the best would be to initialise GPLAB with a tree with the correct format, and then allow GPLAB to only modify the terminals (ie the parameters), ultimately finding the best fit only as a parameter estimation exercise? (I know this limits the power of genetic programming, but often a constrained form is desirable for purposes of implementation.) I'd really appreciate any help in getting a start on this. Kind regards, Brian 