# RTS Kalman smoother stability

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

• Welcome to Robotics tjp212. Adding a 'thanks' line to a question is not required, we all tend to be thankful for the people helping us, and expect other people to be thankful too, so saying it just adds noise to the question and distracts people from the problem posed. It may seem counter intuitive, but excessive politeness can itself be impolite, as giving people extra text to read, even if they ignore it, is disrespectful of their time. – Mark Booth Jul 26 '19 at 10:29