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Is Star*Net a Sequential Processing Machine?
Posted by amdomag on January 30, 2020 at 8:00 pmI tried going through the manual but I failed to find any information on how Star*Net builds up solution.
Any idea on how Star*Net operates. Is it a sequential processing machine? Is adjustment performed one loop at a time? Is output/result affected if command entry sequence is rearranged? TY.
bill-c replied 4 years, 3 months ago 3 Members · 2 Replies- 2 Replies
I have no inside information about that program, but having written my own pale imitation of it (2-D plane only), I have a pretty good idea what it must do for that situation.
There will be one or two preliminary passes through the inputs to check for legal input and make a rough estimate of all the coordinates. It will build the matrix and vectors that are needed for the least squares equations.
The equations are a linear approximation good for the region of each of the coordinates. It can’t solve the matrix with things like arctangents to compare angles to those specified and sqrt sum of squares for distance. So it uses approximations good only near the current coordinates.
Then it will solve the matrix/vector equation to find how much to move the coordinates (all at once) to improve the fit.
It then goes back to make new approximations based on the new coordinates, and re-solves the matrix/vector equation to tweak all the coords again.
It repeats until the fit is good enough or no longer improves.
Then it makes up the output report.
.I agree with @bill93 about how nonlinear least squares is implemented as an iterative procedure. But regarding the original questions from @amdomag, I assume that all modern least squares programs for surveyors and geodesists perform a simultaneous adjustment of the entire network. Yes, the procedure will be iterative, but the linearized matrix equation models the entire network at each iteration. Run-of-the-mill, consumer-grade computers have long had sufficient processing power to do that for land-surveyor-size networks. But yes, back in the 19th century and well into the 20th century, NGS’s predecessors had to break their large networks (i.e. having huge numbers of stations) down into manageable sections for separate least squares adjustments by manual / mechanical calculation, and even by the early electronic computers. If I recall correctly, one of the significant things about the original NAD83 was that it was the first time that the entire national geodetic network was adjusted in a single, simultaneous adjustment.
By the way, I think “sequential” in the context of least squares would refer to something rather different than what’s used in adjusting surveying networks. There are methods of recursive (sequential) least squares for the continuous estimation of the parameters of ongoing processes, such as the changing location of a space vehicle or the operating conditions in a chemical plant.
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