I'm implementing the an RTS Kalman smoother, with the backward pass (from Murphy's MLPP):

RTS Kalman smooth from Murphy MLPP

I'm having some issues with stability, and keep getting a non-positive definite smoothed covariance matrix $\Sigma_{t|T}$.

It seems that some way along the backward pass the eigenvalues for $\Sigma_{t+1|T}$ become very small.

Why might this be happening? And are there are any tricks to preventing it?

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