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# singularity in normal equations

## singularity in normal equations

(OP)
As I am trying to create my own orbit determination program using the least squares differential correction method, I wanted to start with a simple model of a geo synchronous satellite orbiting spherical Earth. Everything went OK, at least as I think, but ended up with a problem that I couldn't solve. It is the singularity of the normal equations. I tried the method of singular value decomposition but that didn't help much. To solve the problem, I tried an initial state vector (nominal) that is almost the same as the vector I used to generate my observations: range, azimuth and elevation. But when I try an initial state vector that is somewhat different, the iterations diverge. Yes, it could be a problem of two faces: 1. the singularity of normal equations and 2. the divergence of iterations.
I am following the algorithm suggested by many including Vallado, Montenbruck and Tapley, and I am using Matlab on Windows XP.
My problem deepened by the fact that I am not modeling a complicated case, which, I assume, makes the model clear and simple. This lead me to think if it is a problem of algorithm; I mean, one needs to consider other  formulation or insert certain steps in the algorithm that is not found in books.
I have many details that I am not mentioning..
I appreciate much any comment or hint

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