Hi, every body I am using Garmin handy GPS with low accuracy to establish BMs but there is needed high accuracy for this survey, but i am not able for now to have a high accuracy GPS due to time shortage, and there is plane to buy a high accuracy GPS after some days later (that time we will do some of our survey on the site), so is there a way to change my topographic surveyed coordinates with new measured coordinates?


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Just Z....or X and Y as well?
Yes … re-observe all your BMs with the high-accuracy gear. That’s the ONLY way.
Yes, it is possible, just not desirable. The more points you have the worse it gets. If you are planning to change the coordinates DO NOT send them to anyone. That is just asking for problems and possibly law suits. Consider renting a precision instrument to cover you until you can purchase. NEVER scrimp on control.
I mean coordinates as well as elevation(X,Y,Z)
If any one knows how to change it, it would be great if he/she fully describe the method(s), I know there is a way in liscad software but in closed triangulation and i am not sure for an open one.

Almost 5 meters in position and 10 meters in height. Not good for changes that you are asking. Rent a profesional equipment from the very beginning

Nav and Mapping grade GPS is out of the question. It’s an order of accuracy issue. You can’t maintain the required tolerance for the site with that equipment. Do what you may, but you’ll be doing the work over again with Survey grade equipment.

Like most replied here I wouldn't even attempt to collect any info with the low grade GPS. The issue being is your low accuracy device will not have relative info within itself. So the issue being is when you localize into your BM's with the survey grade GPS you will find that none of your BM's will check. 

you will have to redo the survey since if you use the ones you took with the garmins the coordinates will still be inaccurate as per the required 

If your question is about coordinate transformation between the Garmin-observed coordinate set and the survey-grade set by applying some sort of shift and/or rotation, the answer is not possible. The noise level (inaccuracy) of the Garmin-observed set will overshadow any possible correlation between the two coordinate sets. The low-accuracy set will help you plan for your BM establishing session.
If your question, on the other hand, is about exploring possible correlation of some sort between the two sets of coordinates, you might be able to do some stochastic modeling which is far beyond this discussion forum! This is similar to transforming between NAD27 and NAD83, where a simple shift and rotation is not possible because of the lack of accuracy with the NAD27 datum definition itself.
Hope this helps.
Thanks friends for your suggestions but...
my question is that is there a way if you survey a land site with incorrect (ex. x100,y200,z300) coordinates and then observe only BMs with high accuracy coordinate and change all surveyed data with new observed BMs coordinates?

of course, you can do it, but  for example if you use a Helmert transformation the residuals will be out away of scale 

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