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Guest
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 Posted:
Tue Dec 20, 2005 9:16 am Post subject:
alpha ,beta ,gamma,upper diagonal filters |
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hi, i need technical help pertaining to these filters--
alpha,beta,gamma,upper diagonal |
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Stan Pawlukiewicz
Guest
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| Posted:
Tue Dec 20, 2005 5:16 pm Post subject:
Re: alpha ,beta ,gamma,upper diagonal filters |
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One Usenet Poster wrote:
| Quote: | Stan Pawlukiewicz wrote:
For a 3 state filter? Isn't that a bit of overkill for a fixed gain
filter where you don't need to calculate a state covariance?
An alpha-beta-gamma filter doesn't mandate 3 states. Typically these
track filters have 9 states: 3 position, 3 velocity, and 3 acceleration.
The same gain is applied to all 3 position states, for example.
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basicly three uncoupled filters.
| Quote: |
The U-D form is normally used with Kalman filters, although you should
be able to use this form with a fixed-gain filter.
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Again why? You can just write out the form of the filters.
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One Usenet Poster
Guest
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| Posted:
Tue Dec 20, 2005 5:16 pm Post subject:
Re: alpha ,beta ,gamma,upper diagonal filters |
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Stan Pawlukiewicz wrote:
| Quote: | For a 3 state filter? Isn't that a bit of overkill for a fixed gain
filter where you don't need to calculate a state covariance?
|
An alpha-beta-gamma filter doesn't mandate 3 states. Typically these
track filters have 9 states: 3 position, 3 velocity, and 3 acceleration.
The same gain is applied to all 3 position states, for example.
The U-D form is normally used with Kalman filters, although you should
be able to use this form with a fixed-gain filter.
Mike |
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Stan Pawlukiewicz
Guest
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| Posted:
Tue Dec 20, 2005 5:16 pm Post subject:
Re: alpha ,beta ,gamma,upper diagonal filters |
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hemanth261@gmail.com wrote:
| Quote: | hi, i need technical help pertaining to these filters--
alpha,beta,gamma,upper diagonal
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I've heard of alpha/beta filters and alpha/beta/gamma filters. These
are essentially really simple fixed gain tracking filters using two and
three states. Most introductory books on Kalman filtering will cover
them to some extent.
Can't say I've heard of upper diagonal filters in the same context as
those above. The ones above are often written in matrix form. |
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One Usenet Poster
Guest
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| Posted:
Tue Dec 20, 2005 5:16 pm Post subject:
Re: alpha ,beta ,gamma,upper diagonal filters |
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Stan Pawlukiewicz wrote:
| Quote: | Can't say I've heard of upper diagonal filters in the same context as
those above. The ones above are often written in matrix form.
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The U-D form writes the state covariance matrix as P = U D U', which
gives the filter good numerical stability.
Mike |
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Stan Pawlukiewicz
Guest
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| Posted:
Tue Dec 20, 2005 5:16 pm Post subject:
Re: alpha ,beta ,gamma,upper diagonal filters |
|
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One Usenet Poster wrote:
| Quote: | Stan Pawlukiewicz wrote:
Can't say I've heard of upper diagonal filters in the same context as
those above. The ones above are often written in matrix form.
The U-D form writes the state covariance matrix as P = U D U', which
gives the filter good numerical stability.
Mike
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For a 3 state filter? Isn't that a bit of overkill for a fixed gain
filter where you don't need to calculate a state covariance? |
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Dr Tam
Guest
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| Posted:
Wed Dec 21, 2005 12:46 am Post subject:
Re: alpha ,beta ,gamma,upper diagonal filters |
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"One Usenet Poster" <me@my.computer.org> wrote in message
news:11qg7d02bkn6h16@corp.supernews.com...
| Quote: | Stan Pawlukiewicz wrote:
For a 3 state filter? Isn't that a bit of overkill for a fixed gain
filter where you don't need to calculate a state covariance?
An alpha-beta-gamma filter doesn't mandate 3 states. Typically these
track filters have 9 states: 3 position, 3 velocity, and 3 acceleration.
The same gain is applied to all 3 position states, for example.
The U-D form is normally used with Kalman filters, although you should
be able to use this form with a fixed-gain filter.
Mike
Fixed - Gain - then it's a Wiener filter. |
Tam |
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Stan Pawlukiewicz
Guest
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| Posted:
Wed Dec 21, 2005 1:06 am Post subject:
Re: alpha ,beta ,gamma,upper diagonal filters |
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Dr Tam wrote:
| Quote: | "One Usenet Poster" <me@my.computer.org> wrote in message
news:11qg7d02bkn6h16@corp.supernews.com...
Stan Pawlukiewicz wrote:
For a 3 state filter? Isn't that a bit of overkill for a fixed gain
filter where you don't need to calculate a state covariance?
An alpha-beta-gamma filter doesn't mandate 3 states. Typically these
track filters have 9 states: 3 position, 3 velocity, and 3 acceleration.
The same gain is applied to all 3 position states, for example.
The U-D form is normally used with Kalman filters, although you should
be able to use this form with a fixed-gain filter.
Mike
Fixed - Gain - then it's a Wiener filter.
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But not necessarily the same fixed gain.
| Quote: |
Tam
IMHO, it's only a (optimal) Wiener filter if the process is stationary |
and the gain is the actual optimal gain. Kinematic processes, which is
what you typically use these things on are Wiener processes. They are
not stationary. |
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