I want to know if the correlated Noise covariance matrix is a positive definite or not?
and if not, is it possible to convert it to equivalent positive definite matrix?
Yes, covariance matrices are positive semi-definite, and in non-pathological cases positive definite.
Concerning your second questions (not that it matters, give they are pos.def.): What would you consider an "equivalent" matrix in this context?
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