Least Squares from bird’s eye view
I am reading ‘Surveying and Geomatics Engineering’ book the was just put out by the ASCE. I’m trying to wrap my head around Least Squares Adjustment with GNSS data. I can follow a least squares adjustment with a traverse, but I want to see if I am following this text correctly for GNSS.
Chapter 5 page 141
There are two components for a least squares adjustment, functional model and stochastic model.
The functional model pretty much averages out the corrected observation generated from the RINEX file and the precise ephemeris. The software will use the data from the precise ephemeris files to improve the coordinates collected during the static observation. For this example I’ll use 4 hour static observation at 15 second intervals which will give me (4 hours * 60 minutes * 4-15 sec. interval = 960 observations)
The stochastic model takes the averaged coordinates for the 960 observations from the functional model and weights the positions according to the spread of the average or the standard deviation. The marks with the higher weights will hold their position more than the marks with the lower weight. The adjustment will process the best fit until the base line distance between each mark in the network is under a specified tolerance which could be 2 cm horizontally and 5 cm vertically. (Basically move the coordinates of the lower weighted marks more than the higher weighted marks would move until the vectors or baselines make sense to one another.)
This all happens on the reference ellipsoid (NAD83 2011) then is brought up to a map projection when the vectors are adjusted.
Let me know if I am understanding the basic concept. No need to get too detailed yet!
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