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The description is very hard to follow. It is incomplete, being based upon and making reference to a book that is not available online. The one-dimensional vectors are written wrongly in the matrix formulas (horizontal instead of vertical). IMO, this article needs a fundamental re-writing, it is extremely frustrating to read as it is.
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I am not comfortable making the edits, but I believe there are major errors here.
With respect to the backward messages b. It is stated:
Finally note that the description in Russel & Norvig 2003 pp. 550 excludes the point product, thought the procedure is required earlier.
I don't believe this is correct. It should be as in the book:
b_{k+1:t} = TO_{k+1}b_{k+2:t}
no point product with f, no normalization (this is a probability, NOT a distribution; it should certainly not sum to 1). This is only the backward message, implements the updates shown on pp. 545 eq (15.7).
You multiply the b with the corresponding f in each time slice to obtained the smoothed vectors sv. So as written, there are two multiplications by f taking place!
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--- <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Mihai preda|Mihai preda]] ([[User talk:Mihai preda|talk]] • [[Special:Contributions/Mihai preda|contribs]]) 16:22, 15 July 2008 (UTC)</small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->
The word 'umbrella' appears suddenly in the middle of the example.
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