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  • $\begingroup$ And note that for a full Kalman filter, you skip a measurement by just doing the prediction step (update $\mathbf P$ and $\dot {\mathbf x}$ but don't apply correction). For your given lowpass filter you'd set $\alpha = 0$. $\endgroup$ Commented Feb 15, 2022 at 15:26
  • $\begingroup$ @Royi, could you please tell me where the 2/3 Sigma comes from? Is it the 50% probability? I am familiar with the 68–95–99.7 rule and this is the first time I hear about this 2/3 sigma. $\endgroup$ Commented Apr 5, 2023 at 22:02
  • $\begingroup$ @Rokai, I didn't mean 2/3 Sigma as $ \frac{2}{3} \sigma $ but as 2 or 3 Sigma. Anyhow, I made it clearer. $\endgroup$ Commented Apr 6, 2023 at 5:30
  • $\begingroup$ @Royi thanks. It seems that the OP understood $\frac{2}{3}$ too. $\endgroup$ Commented Apr 7, 2023 at 14:15