Nice thought. Here's some geeky stuff to ponder upon.......
Your cheapie handheld receivers use what we call Coarse Acquisition Code on the L1 frequency. The problem with this is that the signals get delayed by the ionosphere and the delay will depend upon where the satellite is with respect to you and where you are in the world. Low elevation satellite ranges tend to be noisier as they have more stuff to filter through, additional troposphere to deal with. The ionosphere noise varies with latitude, what time of day, what azimuth is has to you and also where we are in the 11 year solar cycle. What I am saying is that your simple handheld receiver has a lot to try and compensate for and it does this with an ionospheric model and a tropospheric model. Not to mention that the signal correlators on your typical handheld are good enough for a handheld - that is the ranges behind the position calculation do not have to be that good because most users are only expecting a few metres of accuracy - why increase the price of the product needlessly ? The WAAS and EGNOS augmentation satellite signals help improve upon these models but they are still models which have been forecast from prior data so your position is probably biased and may be biased for some time so averaging may look good but your average is probably biased. Comparing position fixes between two receivers is very dodgy because the sky view at both receivers is rarely the same so you can not guarantee that both receivers were using exactly the same satellites at the same time. Also you may have different receiver hardware, different firmware and my earlier comment about the fundamental accuracy of these handhelds. When your WAAS and EGNOS position indicates 3m acccuracy, that is based on the least squares fix of all the satellite ranges used with the augmentation signals. If you only have four satellite ranges but they all agree well with one another then the position statistic could be very good, however all four satellite ranges could be biased ! The 3m indication is a statistical amount - it does not mean that all your positions are within 3m - it suggests that a percentage of your position fixes are within 3m. Whats happening with the other percentage of positions ?......................could be anywhere. How big the percentage is depends upon the statistic being used, you often see 1,2...x sigma or CEP Circular Error Probability but here we are perhaps delving too deep.
The only way to get a really good improvement on your fix is to access the individual satellite ranges and preferably the carrier phase(s) too, some of the cheapies will provide low quality L1 phase. Get your data in a RINEX file and see the post processing online links that I posted earlier. These can process your raw data with respect to multiple ground stations equipped with very high quality geodetic receivers. If you wait a little while, you can also use very accurate post processed orbits, ionospheric and tropospheric data all of which can improve your handheld positions. However one last point, a cheapie can only get you so far because you run into the underlying limitations of the silicon and firmware inside. Do not forget you also have the issue of height - GPS gives you a spheroidal height - getting a mean sea level elevation requires the use of a model - typically this is okay over short distances for relative height differences but there can be some dramatic differences between spheroid height and mean sea level. The UK has an east-west tip of a few metres - India has a 180m difference from south to north.
I am thinking that perhaps a presentation at HE 2011 could be useful. If there is enough interest, I could put one together and do a preliminary run through at the next Cave Electronics and Surveying Group meeting early 2011 with some example data from Mulu 2011 as I will be taking a professional GPS out there and should have the post processed results by then, subject to canopy coverage. GPS signals do not like wet foliage !
