I have accelerations measurement from an accelerometer and i want to use kalman filter to estimate and remove the bias so that when i find the position by integrating twice its not crap. How would i model the kalman filter especially A, B, Q, R, & H. Any help would be appreciated. thanks arvkr

# Accelerometer and Kalman Filter

On Wed, 18 Feb 2009 09:08:16 -0600, arvkr wrote:> I have accelerations measurement from an accelerometer and i want to use > kalman filter to estimate and remove the bias so that when i find the > position by integrating twice its not crap. How would i model the kalman > filter especially > A, B, Q, R, & H. > Any help would be appreciated. > thanks > arvkrYour question is tantamount to "How would I model my system". So, what's your system model? There's not going to be much meat in a Kalman filter that takes accelerometer input and coughs up position unless you have some other sensor that lets you know the position, at least once in a while or at low bandwidth or with lots of noise or _something_. _With_ such a sensor then the Kalman should 'cross-check' to get the best estimate. -- http://www.wescottdesign.com

>On Wed, 18 Feb 2009 09:08:16 -0600, arvkr wrote: > >> I have accelerations measurement from an accelerometer and i want touse>> kalman filter to estimate and remove the bias so that when i find the >> position by integrating twice its not crap. How would i model thekalman>> filter especially >> A, B, Q, R, & H. >> Any help would be appreciated. >> thanks >> arvkr > >Your question is tantamount to "How would I model my system". > >So, what's your system model? > >There's not going to be much meat in a Kalman filter that takes >accelerometer input and coughs up position unless you have some other >sensor that lets you know the position, at least once in a while or at >low bandwidth or with lots of noise or _something_. _With_ such a sensor>then the Kalman should 'cross-check' to get the best estimate. > >-- >http://www.wescottdesign.com >Yes i see your point, but my question is can a kalman filter remove the acceleration bias with just measurements of acceleration from the acceleromter and will this result in a better location of the position when integrated twice after bias removal?

On Feb 18, 12:00�pm, "arvkr" <krarv...@gmail.com> wrote:> >On Wed, 18 Feb 2009 09:08:16 -0600, arvkr wrote: > > >> I have accelerations measurement from an accelerometer and i want to > use > >> kalman filter to estimate and remove the bias so that when i find the > >> position by integrating twice its not crap. How would i model the > kalman > >> filter especially > >> A, B, Q, R, & H. > >> Any help would be appreciated. > >> thanks > >> arvkr > > >Your question is tantamount to "How would I model my system". > > >So, what's your system model? > > >There's not going to be much meat in a Kalman filter that takes > >accelerometer input and coughs up position unless you have some other > >sensor that lets you know the position, at least once in a while or at > >low bandwidth or with lots of noise or _something_. �_With_ such asensor> >then the Kalman should 'cross-check' to get the best estimate. > > >-- > >http://www.wescottdesign.com > > Yes i see your point, but my question is can a kalman filter remove the > acceleration bias with just measurements of acceleration from the > acceleromter and will this result in a better location of the position when > integrated twice after bias removal?- Hide quoted text - > > - Show quoted text -I think the answer is no, you need another independent source of information

On Wed, 18 Feb 2009 11:00:15 -0600, arvkr wrote:>>On Wed, 18 Feb 2009 09:08:16 -0600, arvkr wrote: >> >>> I have accelerations measurement from an accelerometer and i want to > use >>> kalman filter to estimate and remove the bias so that when i find the >>> position by integrating twice its not crap. How would i model the > kalman >>> filter especially >>> A, B, Q, R, & H. >>> Any help would be appreciated. >>> thanks >>> arvkr >> >>Your question is tantamount to "How would I model my system". >> >>So, what's your system model? >> >>There's not going to be much meat in a Kalman filter that takes >>accelerometer input and coughs up position unless you have some other >>sensor that lets you know the position, at least once in a while or at >>low bandwidth or with lots of noise or _something_. _With_ such a >>sensor > >>then the Kalman should 'cross-check' to get the best estimate. >> >>-- >>http://www.wescottdesign.com >> >> > > Yes i see your point, but my question is can a kalman filter remove the > acceleration bias with just measurements of acceleration from the > acceleromter and will this result in a better location of the position > when integrated twice after bias removal?Your question is equivalent to asking "can I build a car with just two wheels?". No, you cannot build a Kalman filter with just one input, any more than you can build a car with just two wheels. You need to do some more studying. You simply cannot implement a Kalman filter if you don't know how it works, and your question clearly indicates that you're missing the most basic underlayment of the foundation of Kalman filter theory. I suggest you get onto Wikipedia and read their excellent article on Kalman filtering. Pay close attention to the inputs to the "predict" and "correct" phases, and ponder how the "correct" phase could exist at all without a second input. Kalman filtering is not something that you can learn from web searches, although there is good information out there (I regularly use the Wikipedia article to remind me the exact order of operations). What you need is a book, and the book I recommend is Dan Simon's "Optimal State Estimation, Kalman, H-infinity, and Nonlinear Approaches", Wiley, 2006. It's a good book, and I love his approach (I even like his approach to theology, which you'll find in an appendix, even though I disagree with his conclusions). http://www.powells.com/partner/30696/biblio/0471708585. It costs a bundle, but it's worth it. -- http://www.wescottdesign.com

On Feb 19, 6:32�am, Tim Wescott <t...@seemywebsite.com> wrote:> On Wed, 18 Feb 2009 11:00:15 -0600, arvkr wrote: > >>On Wed, 18 Feb 2009 09:08:16 -0600, arvkr wrote: > > >>> I have accelerations measurement from an accelerometer and i want to > > use > >>> kalman filter to estimate and remove the bias so that when i find the > >>> position by integrating twice its not crap. How would i model the > > kalman > >>> filter especially > >>> A, B, Q, R, & H. > >>> Any help would be appreciated. > >>> thanks > >>> arvkr > > >>Your question is tantamount to "How would I model my system". > > >>So, what's your system model? > > >>There's not going to be much meat in a Kalman filter that takes > >>accelerometer input and coughs up position unless you have some other > >>sensor that lets you know the position, at least once in a while or at > >>low bandwidth or with lots of noise or _something_. �_With_ such a > >>sensor > > >>then the Kalman should 'cross-check' to get the best estimate. > > >>-- > >>http://www.wescottdesign.com > > > Yes i see your point, but my question is can a kalman filter remove the > > acceleration bias with just measurements of acceleration from the > > acceleromter and will this result in a better location of the position > > when integrated twice after bias removal? > > Your question is equivalent to asking "can I build a car with just two > wheels?". �No, you cannot build a Kalman filter with just one input,any> more than you can build a car with just two wheels. >You certainly can build a Kalman filter with one input or any number of inputs provided you have an accurate plant model. Is this one of those balancing problems? You probably need a rate gyro and an accelerometer together. H.

On Wed, 18 Feb 2009 09:43:05 -0800, HardySpicer wrote:> On Feb 19, 6:32 am, Tim Wescott <t...@seemywebsite.com> wrote: >> On Wed, 18 Feb 2009 11:00:15 -0600, arvkr wrote: >> >>On Wed, 18 Feb 2009 09:08:16 -0600, arvkr wrote: >> >> >>> I have accelerations measurement from an accelerometer and i want >> >>> to >> > use >> >>> kalman filter to estimate and remove the bias so that when i find >> >>> the position by integrating twice its not crap. How would i model >> >>> the >> > kalman >> >>> filter especially >> >>> A, B, Q, R, & H. >> >>> Any help would be appreciated. >> >>> thanks >> >>> arvkr >> >> >>Your question is tantamount to "How would I model my system". >> >> >>So, what's your system model? >> >> >>There's not going to be much meat in a Kalman filter that takes >> >>accelerometer input and coughs up position unless you have some other >> >>sensor that lets you know the position, at least once in a while or >> >>at low bandwidth or with lots of noise or _something_. _With_ such a >> >>sensor >> >> >>then the Kalman should 'cross-check' to get the best estimate. >> >> >>-- >> >>http://www.wescottdesign.com >> >> > Yes i see your point, but my question is can a kalman filter remove >> > the acceleration bias with just measurements of acceleration from the >> > acceleromter and will this result in a better location of the >> > position when integrated twice after bias removal? >> >> Your question is equivalent to asking "can I build a car with just two >> wheels?". No, you cannot build a Kalman filter with just one input, >> any more than you can build a car with just two wheels. >> > You certainly can build a Kalman filter with one input or any number of > inputs provided you have an accurate plant model. Is this one of those > balancing problems? You probably need a rate gyro and an accelerometer > together. > > > H.Example please? Note in advance that if you're using a Kalman filter as an observer in a control system (which is what you imply above), you'll be inputting a plant drive as well as a sensor reading -- and there's your two inputs. -- http://www.wescottdesign.com

On Wed, 18 Feb 2009 11:32:51 -0600, Tim Wescott <tim@seemywebsite.com> wrote:>Kalman filtering is not something that you can learn from web searches, >although there is good information out there (I regularly use the >Wikipedia article to remind me the exact order of operations). What you >need is a book, and the book I recommend is Dan Simon's "Optimal State >Estimation, Kalman, H-infinity, and Nonlinear Approaches", Wiley, 2006. >It's a good book, and I love his approach (I even like his approach to >theology, which you'll find in an appendix, even though I disagree with >his conclusions). > >http://www.powells.com/partner/30696/biblio/0471708585. It costs a >bundle, but it's worth it.How dependent is it on Matlab? That is, hard-wired to Matlab or reasonably useable with another procedural matrix toolset such as Scilab or Omatrix? -- Rich Webb Norfolk, VA

> >Example please? > >Note in advance that if you're using a Kalman filter as an observer in a>control system (which is what you imply above), you'll be inputting a >plant drive as well as a sensor reading -- and there's your two inputs. > >-- >http://www.wescottdesign.com >http://en.wikipedia.org/wiki/Kalman_filter#Examples Isn't similar to what i am trying to do? Can my acceleration measurements not be the noisy measurements in Z_k ( used to correct) and my model predictions with an initial estimate ( which i have to provide) be X_k. This was what i had in my mind when i asked the question of how will i derive my model. May be i have it all confused? arvkr

> >Example please? > >Note in advance that if you're using a Kalman filter as an observer in a>control system (which is what you imply above), you'll be inputting a >plant drive as well as a sensor reading -- and there's your two inputs. > >-- >http://www.wescottdesign.com >http://en.wikipedia.org/wiki/Kalman_filter#Examples Isn't similar to what i am trying to do? Can my acceleration measurements not be the noisy measurements in Z_k ( used to correct) and my model predictions with an initial estimate ( which i have to provide) be X_k. This was what i had in my mind when i asked the question of how will i derive my model. May be i have it all confused? arvkr