Thread Subject: Question on Iteration variables means?

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.

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.

--
  "The whole history of civilization is strewn with creeds and
  institutions which were invaluable at first, and deadly
  afterwards." -- Walter Bagehot

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

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.

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

John D'Errico wrote:
> 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
>
>
thanks John for explain this two term.
I think you give me the right answer, this will support me to understand
the whole detail in, Kalman filter from the
http://en.wikipedia.org/wiki/Kalman_filter