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I'm reminded of the old joke. "How can you measure the height of a building with a barometer?" In your case the cheapest approach would be to go to Kmart and buy a roll of string. Climb to the top of the object you wish to measure, attach the GPS to the sring, lower the string to the bottom, tie a knot in the string to mark the top, pull the GPS back up and measure the string. But seriously... There are NO single unit GPS systems with a vertical accuracy of "a couple of inches". It turns out that the Z axis is the least accurate GPS position, and even high-end receivers with WAAS correction and time averaging can only get you within a couple of feet. To get down to a couple of inches vertically takes a survey grade unit with a base station and a radio link between them. You may additionally need 30+second acquisition times and/or post-processing of the data to find out where you were. If you are on top of a high mountain with excellent sattelite reception you can consider carrier phase processing instead of DGPS -- but you will need 45 minutes to get down to "a couple of inches". None of this is a cheap proposition -- figure $10000 or more. "A couple of inches" equates to 5 cm or .05 meter. There are vendors of survey grade equipment that will rent you gear with accuracy in that range for about $300 per day. Take a look at the attached URL to get an idea of what you are trying to get into.
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