They should reference the same article in the IEEE that MATLAB references for filtfilt:

Gustafsson, F., Determining the initial states in forward-backward filtering, IEEE Transactions on Signal Processing, April 1996, Volume 44, Issue 4, pp.988’€”992.

I only briefly skimmed this paper, though perhaps I should take a little deeper look.

Mark

]]>The caption doesn’t indicate how many adjacent values were used in calculating the mean used to pad the series. If the number of adjacent values used was one half filter width, then the boundary constraint is essentially identical to that achieved by reflecting the series about the terminal boundary, i.e. the ‘minimum slope’ constraint. Even if few adjacent values were used, the method still supresses any trend near the boundary

:) They don’t know how that figure was generated..

Mark T and others, it is non-causal filter with data extrapolation, see Mann’s paper

http://holocene.meteo.psu.edu/shared/articles/MannGRL04.pdf

It uses filtfilt. It is true that optimal smoothing should be applied for reconstructions, but remember that these people don’t talk to mainstream statisticians. Read mike’s paper and you’ll get the idea.

]]>As far as your radar problem, there are 100’s of papers in the IEEE and AIAA journals about this issue. All peer reviewed, some good, some bad, and some ugly. I have hard copies on 5-10 articles myself. Good luck

Fortunately, I’m clued in on this overall problem. I’ve been doing radar for 12 years now, just not to the level that this project requires. We (two on the signal processing) are designing from the ground up a type of system that’s never been done before. Oddly, the hardest part is the geometry involved with three bodies in motion (independently). I have to admit, however, I’ve read more books on radar in the last three months than I ever have in my life.

Re #69, Mark, did you get a chance to turn the crank on the error covariance term in Re #64?

Nope. Maybe later…

H is in the measurement model, not in the process model, and IMO scalar H wouldn’t be unrealistic.

Oops. I suppose it depends upon how you view the problem for H. I was seeing it more as H being what controlled actual temperatures to create tree-rings, i.e. tree-ring width is only a scalar multiplied by temp in this example, which is unrealistic I think. That would differ per tree, over time, etc., and then you’d have to add in the other forcers as well, yadda, yadda.

Mark

]]>I completely agree that generally H is not simply a scalar as in this simplified problem since that would be completely unrealistic in any process model.

H is in the measurement model, not in the process model, and IMO scalar H wouldn’t be unrealistic.

In the contrived example, H is never added, only multiplied, so there’s no issue.

That’s correct. In the derivation of optimal K you don’t need such operation.

]]>As far as your radar problem, there are 100’s of papers in the IEEE and AIAA journals about this issue. All peer reviewed, some good, some bad, and some ugly. I have hard copies on 5-10 articles myself. Good luck

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