Constrained Least Squares confusion - 2021

So I read what I could on those links and re-read some areas in PC DMIS core manual. I may have not been clear on my original post....

My problem with calling the new default ASME standard 'constrained least squares' is that someone without a proper understanding and is a little sick in the head, as we all may be, could mis-understand this as a least-squared fit...In essence, they could feel comfortable that a large external hit in the MMC direction may be averaged out and the plane or cylinder datum would be allowed to interfere with this surface hit point(datum feature). This is what I first thought when I read the term 'constrained least-squares'.

A while back when I read the manual on datums, I learned that the term 'constrained' is defined in the core manual as being 'external'. So why not just call the **** thing 'external'. 'External least-squares' seems much less ambiguous than 'constrained least-squares'

So maybe I misspoke when I said I didn't think this was least squares...I just wanted to see if you all felt some of my confusion in that the critical thing with this math type is that it is 'external' being a surface plate, pin gage, hard gage type measurement, when a simple 'least-squares' can have interference hit points with the datum. I associate least-squares with allowing for this interference. Knowing that 'constrained' means 'external' is not common knowledge in my opinion. Maybe, I just am not seasoned enough to realize everyone knows this, but this wasn't intuitive to me a year ago. I ran 2021 this week and it reminded me of this issue and wanted to post my confusion.

You all are an amazing group of people and have been an unbelievable resource to me, thanks.

So I read what I could on those links and re-read some areas in PC DMIS core manual. I may have not been clear on my original post....

My problem with calling the new default ASME standard 'constrained least squares' is that someone without a proper understanding and is a little sick in the head, as we all may be, could mis-understand this as a least-squared fit...In essence, they could feel comfortable that a large external hit in the MMC direction may be averaged out and the plane or cylinder datum would be allowed to interfere with this surface hit point(datum feature). This is what I first thought when I read the term 'constrained least-squares'.

A while back when I read the manual on datums, I learned that the term 'constrained' is defined in the core manual as being 'external'. So why not just call the **** thing 'external'. 'External least-squares' seems much less ambiguous than 'constrained least-squares'

So maybe I misspoke when I said I didn't think this was least squares...I just wanted to see if you all felt some of my confusion in that the critical thing with this math type is that it is 'external' being a surface plate, pin gage, hard gage type measurement, when a simple 'least-squares' can have interference hit points with the datum. I associate least-squares with allowing for this interference. Knowing that 'constrained' means 'external' is not common knowledge in my opinion. Maybe, I just am not seasoned enough to realize everyone knows this, but this wasn't intuitive to me a year ago. I ran 2021 this week and it reminded me of this issue and wanted to post my confusion.

You all are an amazing group of people and have been an unbelievable resource to me, thanks.