What you have recommended will tend to stabilize the covariance matrix, but not for the reason you have given. If numerical stability is an issue you encounter

What you have recommended will tend to stabilize the covariance matrix, but not for the reason you have given. If numerical stability is an issue you encounter, I would caution against using it. Try [1] instead. You imply that any symmetric matrix is positive semi-definite. Take an orthogonal matrix U and a diagonal matrix D with one or more negative values. P = U * D * U.T is symmetric but not positive semi-definite. For example, if D[0,0] = -1 then U[:, 0].T * P * U[:,0] = -1. [1] https://en.wikipedia.org/wiki/Kalman_filter#Square_root_form https://en.wikipedia.org/wiki/Kalman_filter#Square_root_form