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I am trying to simulate the Kalman Filter. I have the covariance matrix P_{0|0}. Tell me please, how can I get the predicted (a priori) estimate covariance matrix on the (k-1) step? P_{k-1|k-1}?

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  • $\begingroup$ Can you please share a little bit more information about what you are trying to do and more importantly what have you done so far, possibly including some code (?). That should be k+1 by the way, that is, the prediction step (in the future). $\endgroup$
    – A_A
    Jun 8, 2016 at 9:10
  • $\begingroup$ if you wish, I can send the code of Kalman filter to your e-mail and will be glad if you look at that. However, I need to understand only what the P_{k-1|k-1} means in that equation. How can I get that from the task conditions? $\endgroup$
    – Timebird
    Jun 8, 2016 at 9:57

1 Answer 1

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Given the Covariance Matrix $ {P}_{k - 1 \mid k - 1} $ then:

$$ {P}_{k \mid k} = {F}_{k} {P}_{k - 1 \mid k - 1} {F}_{k}^{T} + {Q}_{k} $$

Where $ {F}_{k} $ is the Model Matrix at iteration $ k $ and $ {Q}_{k} $ is the Process Noise Covariance Matrix at iteration $ k $.

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  • $\begingroup$ Probably, I describe the question unclearly. What is P_{k-1|k-1} means in that equation? $\endgroup$
    – Timebird
    Jun 8, 2016 at 9:59
  • $\begingroup$ Are you after Smoothing using the Kalman Filter? $\endgroup$
    – Royi
    Jun 8, 2016 at 15:03

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