Path: news.mathworks.com!not-for-mail
From: "John D'Errico" <woodchips@rochester.rr.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Question on Iteration variables means?
Date: Sat, 17 May 2008 08:25:03 +0000 (UTC)
Organization: John D'Errico (1-3LEW5R)
Lines: 66
Message-ID: <g0m4ov$3k4$1@fred.mathworks.com>
References: <g0gl13$v4i$1@news.cn99.com> <g0hqgu$qp0$1@canopus.cc.umanitoba.ca> <g0hr38$pki$1@fred.mathworks.com> <g0m2b9$8ej$1@news.cn99.com>
Reply-To: "John D'Errico" <woodchips@rochester.rr.com>
NNTP-Posting-Host: webapp-03-blr.mathworks.com
Content-Type: text/plain; charset="ISO-8859-1"
Content-Transfer-Encoding: 8bit
X-Trace: fred.mathworks.com 1211012703 3716 172.30.248.38 (17 May 2008 08:25:03 GMT)
X-Complaints-To: news@mathworks.com
NNTP-Posting-Date: Sat, 17 May 2008 08:25:03 +0000 (UTC)
X-Newsreader: MATLAB Central Newsreader 869215
Xref: news.mathworks.com comp.soft-sys.matlab:468980


asm23 <asmwarrior@gmail.com> wrote in message 
<g0m2b9$8ej$1@news.cn99.com>...
> John D'Errico wrote:
> > roberson@ibd.nrc-cnrc.gc.ca (Walter Roberson) wrote in message 
> > <g0hqgu$qp0$1@canopus.cc.umanitoba.ca>...
> >> In article <g0gl13$v4i$1@news.cn99.com>, asm23  
> > <asmwarrior@gmail.com> wrote:
> >>> hi, I'm new to this forum, I want to know the meaning of these 
variables 
> >>> for iteration.
> >>> such as:
> >>> X(k|k-1)
> >>> X(k|k)
> >>> X(k-1|k-1)
> >>> ....
> >>> What's the difference between them? Can someone explain it? thank 
you 
> >>> very much.
> >> I think you must have miscopied or mistyped, as those are quite
> >> unlikely to come up in real code in the form written.
> >>
> >> '|' is bitwise 'or'. Any value bitwise or'd with itself is going to
> >> be the same value. Thus, X(k|k) would be the same X(k), and
> >> X(k-1|k-1) would be the same as X(k-1).
> >>
> >> k|k-1 has some interesting mathematical properties in binary, but 
> >> it is fairly unlikely that you have described the question correctly
> >> so I will not describe the mathematical properties. k&k-1 has more
> >> interesting properties and sometimes occurs in code, but k|k-1 seldom
> >> does.
> > 
> > I would not assume its a typo, merely not
> > useful as Matlab syntax.
> > 
> > These may be notations that are valid in
> > some other context, but the context is all
> > important. We cannot know what is meant
> > out of context.
> > 
> > John
> Thanks for your two reply, I notices that I have made a mistake, the 
> X(k|k-1) is not the matlab code, they have exist in Kalman filter 
> Algorithms, recursion formula often use this as some estimated value or 
> expected value. But I don't know what's their meanings.

I was wondering if this was your question.

X(k | k-1)

refers to your estimate of the system state (X)
at time k, given the information up to time k-1.
Thus it is a prediction to a future time from the
past data.

The term

X(k | k)

is similar, but now it is your updated estimate
of the system state at time k, having seen the
current measurement of the process.

HTH,
John