I am using BLS for orbit determination. As I have been doing a bunch of tests, I have come to wonder about the relationship between convergence threshold for the estimator and the maximum number of iterations. For example, when I get the error saying “maximal count (25) exceeded”, I could lower the convergence threshold. After lots of testing, I was able to figure out the pattern like this, but I am now curious about how this thing actually works. Is there a mathematical model that yields the ideal values for convergence threshold and max iterations? How does one decide what values to use for them?
There are no known ways to find proper settings. IT depends on the type of orbits, the number of measurements, their accuracy… I guess most of the time, orbit determination is a case were personal experience is the best guide. Trying new things as you did is surely the best way to learn, keeping in mind things may behave differently on different space missions (higher or lower orbits, more or less frequent measurements…)
I’d add that it’s part of the general trade off between accuracy (here of your parameter estimation) and computational load. If you want approximate yet fast results, set up a large threshold. If you have more time to spare or need a better fit, decrease it and allow for more iterations. The initial guess will also have a huge impact.