How to model the event that the LM converges correctly?

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I'm utilizing the LM algorithm to solve a trakcing problem. I found that sometimes the LM algorithm will converge to the wrong position at the beginning, and then continue to converge to the wrong position. I would like to know, given the input data and initial parameters of LM, is it possible to model the event that the LM algorithm converges correctly? I want to infer the probability that the LM algorithm converges to the correct value.

Currently I can only adjust the initial parameters as close as possible to the initial position of the object I'm tracking to ensure initial convergence.

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