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I am trying to learn about the inference and maximization basically EM of the linear dynamic systems(Kalman filters for example) from Bishop's book of Pattern Recognition and Machine Learning. However, I am not being able to follow the derivations given in there.

I have got the basic idea of what Kalman filters are and what they are used for. However, I am a bit confused with the learning steps(basically the derivation of the equations and all). They seem a bit complicated. I have spent lot of time trying to figure them out. But I still have some issues. Can anyone suggest me where I can get the idea. Because in the book, they haven't given the details of how it is derived(the equations.

My question is how this is derived. It is a piece from the 2nd last image. I might be asking too much but I am really finding it difficult to get how this is derived. I would really appreciate if someone could give me some pointers

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On the derivation of the kalman filter in general, many good references exist. Among them,

Simon, D. Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches

Durbin, J. and Koopman, S.J. Time Series Analysis by State Space Methods

Gibbs, B.P. Advanced Kalman Filtering, Least-Squares and Modeling: A Practical Handbook

For your precise question about the EM estimation with state-space models, perhaps you can turn to section 6.3 of

Shumway, R.H. and Stoffer, D.S. Time Series Analysis and Its Applications: With R Examples

where it is nicely explained.

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  • $\begingroup$ @Tusell. Thanks for the info. But I didn't understand the part related to the Bishop's book. I took a screenshot and added the part to this question. I could get a rough idea of the derivation of the kalman filter equations from this link google.com/…. But I didn't understand this part from the Bishop's book $\endgroup$ – user34790 Jan 3 '13 at 19:28
  • $\begingroup$ @F.Tussel stats.stackexchange.com/questions/46944/… $\endgroup$ – user34790 Jan 4 '13 at 14:47
  • $\begingroup$ I need to get to grips with Kalman filters too. Any recommendations for a concise overview of the concept? $\endgroup$ – conjectures May 4 '13 at 7:36
  • $\begingroup$ I think the first three references listed above are fine; the second will appeal to a wider audience, the first and third will probably be your choice if you have an engineering rather than an statistics background. $\endgroup$ – F. Tusell May 9 '13 at 13:58
  • $\begingroup$ A great reference for Kalman filter is the Harvey text (amazon.com/Forecasting-Structural-Models-Kalman-Filter/dp/…) $\endgroup$ – rbatt May 9 '13 at 14:27

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