Reply by Vladimir Vassilevsky●April 16, 20092009-04-16
Tim Wescott wrote:
> If you have a 6-axis IMU, a distance measurement from a reference point,
> and a vehicle that's moving enough, you should be able to settle to an
> trajectory that is accurate but for a cylindrically symmetric uncertainty
> centered around the reference point (i.e., you'll have the right shape
> with respect to the reference point but you won't know which way north
> is).
>
> Add in a compass or distances to two references, and you should be there.
But would the INS be any useful if you have compass (or a steering wheel
position sensor) and odometer? The navigation by the trivial dead
reckoning is many orders more accurate then MEMS INS.
Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com
Reply by arvkr●April 16, 20092009-04-16
>If you have a 6-axis IMU, a distance measurement from a reference point,
>and a vehicle that's moving enough, you should be able to settle to an
>trajectory that is accurate but for a cylindrically symmetric uncertainty
>centered around the reference point (i.e., you'll have the right shape
>with respect to the reference point but you won't know which way north
>is).
>
>Add in a compass or distances to two references, and you should be
Thanks Tim. I have a slightly off topic question. Do you know of any good
doppler radar based speed sensor which consumes the lowest power and lowest
in size etc?
Reply by Tim Wescott●April 15, 20092009-04-15
On Wed, 15 Apr 2009 11:29:00 -0500, arvkr wrote:
>>As posed by the OP, frames of reference are not mentioned. In other
>>posts on similar topics this same OP has shown confusion about the need
>>for tracking heading along with position and velocity.
>>
>>
> Thanks for all the replies guys. As Tim has mentioned, i have had other
> posts in the forum talking about using just accelerometer ( 3 axis) to
> measure distance without any external sensor and that idea for valid
> reasons was quashed to death ( such as the bias grows at 1/2*t^2 when
> integrated etc). I am relatively new at the INS ( less than 6 weeks) and
> i am involved in a project of developing a low cost INS to measure the
> distance travelled, hence trying to get as much info as possible.
>
> IMU i am using spits out 3 axis acc, gyro readings. This coupled with
> another external sensor i have and 3d compass, i am trying to develop a
> low cost robust INS.
>
> Ideally i would have liked to just use the MEMS unit without any
> external sensors for ease of installation but as i mentioned Tim and
> others who have more experience than i do in this have strongly
> suggested thats not possible with low cost IMU.
>
> Can you guys think of any non-contact speed sensors which i might be
> able to replace my current speed sensor which has some tedious
> installation?
If you have a 6-axis IMU, a distance measurement from a reference point,
and a vehicle that's moving enough, you should be able to settle to an
trajectory that is accurate but for a cylindrically symmetric uncertainty
centered around the reference point (i.e., you'll have the right shape
with respect to the reference point but you won't know which way north
is).
Add in a compass or distances to two references, and you should be there.
--
http://www.wescottdesign.com
Reply by arvkr●April 15, 20092009-04-15
>As posed by the OP, frames of reference are not mentioned. In other
>posts on similar topics this same OP has shown confusion about the need
>for tracking heading along with position and velocity.
>
Thanks for all the replies guys. As Tim has mentioned, i have had other
posts in the forum talking about using just accelerometer ( 3 axis) to
measure distance without any external sensor and that idea for valid
reasons was quashed to death ( such as the bias grows at 1/2*t^2 when
integrated etc). I am relatively new at the INS ( less than 6 weeks) and i
am involved in a project of developing a low cost INS to measure the
distance travelled, hence trying to get as much info as possible.
IMU i am using spits out 3 axis acc, gyro readings. This coupled with
another external sensor i have and 3d compass, i am trying to develop a low
cost robust INS.
Ideally i would have liked to just use the MEMS unit without any external
sensors for ease of installation but as i mentioned Tim and others who have
more experience than i do in this have strongly suggested thats not
possible with low cost IMU.
Can you guys think of any non-contact speed sensors which i might be able
to replace my current speed sensor which has some tedious installation?
Reply by Tim Wescott●April 15, 20092009-04-15
Malachy Moses wrote:
>> Two questions:
>>
>> One: Why is acceleration a state? I thought you were measuring it.
>
> Acceleration should definitely be one of the states. Simply because
> you are measuring acceleration does not somehow disqualify it from
> also being a state.
That would depend on how you're modeling the system, and how you're
measuring acceleration. If the higher-order inputs and dynamics are
unknown then you probably want to treat acceleration as a measurement,
not a state.
>> Two: If you _are_ measuring acceleration, how do you know what direction
>> it's coming from? IOW with an accelerometer you can measure
>> acceleration with respect to your vehicle frame of motion, but doesn't
>> that rotate with respect to the local inertial frame?
>>
>
> As posed by the OP, the problem is one of estimating distance
> travelled along the frame of reference defined by the heading of the
> vehicle/robot/whatever. Currently, the OP has not asked for an
> estimation of current position in some inertial frame.
As posed by the OP, frames of reference are not mentioned. In other
posts on similar topics this same OP has shown confusion about the need
for tracking heading along with position and velocity.
> If it were, then your point is completely valid, and changes the
> design of the state model etc., such that roll pitch and heading etc
> would probably form part of the state vector.
>
> In answer to the original question, which is:
>
> "Here is what i have, a measurement of a distance from an external
> sensor at
> a lower sampling rate and acceleration measurements from accelerometer
> (
> IMU at a higher rate). How can i use a kalman filter to fuse these to
> produce a good estimate of the position travelled."
>
> Ans: Change your H matrix each time interval so that it matches to the
> current measurement(s) being taken. For example, if your current
> measurement is a high-rate measurement of acceleration only, then your
> H matrix is [0 0 1]. If your current measurement is both position and
> acceleration, then your H matrix is [1 0 1] (correct dimensionality
> omitted for purposes of emphasis).
>
Or find a good treatment of a mixed continuous/discrete Kalman filter,
extend it to a multi-rate filter, and find how you can avoid a lot of
computations when you're not getting position fixes.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by Malachy Moses●April 15, 20092009-04-15
> Two questions:
>
> One: Why is acceleration a state? �I thought you were measuring it.
Acceleration should definitely be one of the states. Simply because
you are measuring acceleration does not somehow disqualify it from
also being a state.
>
> Two: If you _are_ measuring acceleration, how do you know what direction
> it's coming from? �IOW with an accelerometer you can measure
> acceleration with respect to your vehicle frame of motion, but doesn't
> that rotate with respect to the local inertial frame?
>
As posed by the OP, the problem is one of estimating distance
travelled along the frame of reference defined by the heading of the
vehicle/robot/whatever. Currently, the OP has not asked for an
estimation of current position in some inertial frame.
If it were, then your point is completely valid, and changes the
design of the state model etc., such that roll pitch and heading etc
would probably form part of the state vector.
In answer to the original question, which is:
"Here is what i have, a measurement of a distance from an external
sensor at
a lower sampling rate and acceleration measurements from accelerometer
(
IMU at a higher rate). How can i use a kalman filter to fuse these to
produce a good estimate of the position travelled."
Ans: Change your H matrix each time interval so that it matches to the
current measurement(s) being taken. For example, if your current
measurement is a high-rate measurement of acceleration only, then your
H matrix is [0 0 1]. If your current measurement is both position and
acceleration, then your H matrix is [1 0 1] (correct dimensionality
omitted for purposes of emphasis).
Reply by Randy Yates●April 14, 20092009-04-14
"arvkr" <krarvind@gmail.com> writes:
> [...]
Here's an old, but accessible text on the subject:
@book{brown,
title = "Introduction to Random Signal Analysis and Kalman Filtering",
author = "{Robert~Grover~Brown}",
publisher = "John Wiley and Sons",
year = "1983"}
--
% Randy Yates % "She's sweet on Wagner-I think she'd die for Beethoven.
%% Fuquay-Varina, NC % She love the way Puccini lays down a tune, and
%%% 919-577-9882 % Verdi's always creepin' from her room."
%%%% <yates@ieee.org> % "Rockaria", *A New World Record*, ELO
http://www.digitalsignallabs.com
Reply by Sebastian Doht●April 14, 20092009-04-14
Tim Wescott schrieb:
> arvkr wrote:
>>> arvkr wrote:
>>>>> Two questions:
>>>>>
>>>>> One: Why is acceleration a state? I thought you were measuring it.
>>>> You are right. I am measuring it and prob should have the state as acc
>>>> bias to estimate the bias. This is where i am struggling with since i
>> don't
>>>> seem to understand kalman filter fully and i have read several articles
>> on
>>>> the web, still haven't been able to fully get a grip on it.
>>> I have one book that talks about nothing but optimal state estimation
>>> (i.e. the Kalman filter and it's extended family), another that goes
>>> into detection, estimation and modulation theory (which has you
>>> derive Kalman filters as homework problems in at least two places), a
>>> couple of
>>
>>> adaptive control books (that treat the system identification phase of
>>> adaptive control as a Kalman filtering problem), a book on strapdown
>>> inertial navigation (which mostly talks about devices, but which has
>>> an excellent section on translating combined gyro and accelerometer
>>> data into just the sort of model you need), and access to the entire
>>> world wide web.
>>>
>>> This is backed up by a career doing various sorts of signal detection
>>> and estimation problems, building advanced control systems from scratch,
>>
>>> and other related activity.
>>>
>>> After all this, while I feel that I'm more than good enough to charge
>>> people money to design Kalman filtering algorithms I still don't feel
>>> I have wrapped my arms completely around the problem. I doubt that I
>>> would even if I won the lottery tomorrow, got my PhD in optimal
>>> estimation, and spent the rest of my life teaching and doing research.
>>>
>>> So I don't know if it's realistic for anyone to expect to figure this
>>> out by asking questions on USENET and reading web pages. I'm not
>>> even sure if I can recommend just one book -- I think to do what you
>>> want to do you need at least Dan Simon's book and a good book on
>>> strapdown inertial nav systems.
>>>
>>> Even then you'll find Simon's book to be an uphill battle unless you
>>> have a good grounding in stochastic process theory and state-space
>>> control -- so expect to do some supplementary reading. Further, I
>>> have yet to find a book on strapdown inertial navigation theory that
>>> gives a blow-by-blow analysis of an inertial navigation Kalman
>>> solution -- the one I have is the best of the lot, but it sure
>>> doesn't give an ABC description.
>>>
>>> Here's my bibliography -- the two end ones are currently on my
>>> 'essential reading' list for inertial nav stuff.
>>>
>>> Dan Simon, "Optimal State Estimation", Wiley 2006:
>>> http://www.powells.com/partner/30696/biblio/9780471708582
>>>
>>> Harry Van Trees, "Detection, Estimation, and Modulation Theory",
>>> Wiley, 1968: http://www.powells.com/partner/30696/biblio/9780471463825
>>>
>>> Karl Astrom & Bjorn Wittenmark, "Adaptive Control", Addison-Wesley,
>>> 1995: http://www.powells.com/partner/30696/biblio/9780486462783
>>>
>>> Bitmead, Gevers, Wertz, "Adaptive Optimal Control, The Thinking Man's
>>> GPC", Prentice-Hall, 1990:
>>> http://www.powells.com/partner/30696/biblio/0139468234
>>>
>>> Titterton, D. H. and Weston, J. L., "Strapdown Inertial Navigation
>>> Technology", AIAA, 2004:
>>> http://www.powells.com/partner/30696/biblio/9780863413582
>>>
>>> --
>>>
>>> Tim Wescott
>>> Wescott Design Services
>>> http://www.wescottdesign.com
>>>
>>> Do you need to implement control loops in software?
>>> "Applied Control Theory for Embedded Systems" was written for you.
>>> See details at http://www.wescottdesign.com/actfes/actfes.html
>>>
>>
>> Thanks a lot for the list of books, i will definitely take a look at
>> them.
>> As you said, web searches etc help only to a certain extent, i came
>> across
>> this book on the google books
>>
>> Estimation with applications to tracking and navigation
>> http://books.google.ca/books?id=xz9nQ4wdXG4C&pg=PA219&lpg=PA219&dq=kalman+filter+step+by+step&source=bl&ots=VnU1u3e6uZ&sig=WTZ3IS1DDcNIPAbvZBiBgnuU1is&hl=en&ei=FZDkScu3DZ_ulQf1koHgDg&sa=X&oi=book_result&ct=result&resnum=8#PPA253,M1
>>
>>
>> have you read this one before and if so how did u find it?
>
> I haven't seen it before. I like the table of contents, though. If the
> writing is clear it may be a good one to get in lieu of the Simon book
> (although I _really_ like Simon's clarity, and his attitude about how
> far so-called 'optimal' methods will take you).
>
> I didn't see anything in the table of contents that indicates that they
> directly address your problem, but it's extensive, and I only skimmed
> it. The "Application to Navigation" part should certainly be what
> you're looking for.
>
>> arvkr wrote:
>>>> Two questions:
>>>>
>>>> One: Why is acceleration a state? I thought you were measuring it.
>>> You are right. I am measuring it and prob should have the state as acc
>>> bias to estimate the bias. This is where i am struggling with since i
> don't
>>> seem to understand kalman filter fully and i have read several articles
> on
>>> the web, still haven't been able to fully get a grip on it.
>> I have one book that talks about nothing but optimal state estimation
>> (i.e. the Kalman filter and it's extended family), another that goes
>> into detection, estimation and modulation theory (which has you derive
>> Kalman filters as homework problems in at least two places), a couple of
>
>> adaptive control books (that treat the system identification phase of
>> adaptive control as a Kalman filtering problem), a book on strapdown
>> inertial navigation (which mostly talks about devices, but which has an
>> excellent section on translating combined gyro and accelerometer data
>> into just the sort of model you need), and access to the entire world
>> wide web.
>>
>> This is backed up by a career doing various sorts of signal detection
>> and estimation problems, building advanced control systems from scratch,
>
>> and other related activity.
>>
>> After all this, while I feel that I'm more than good enough to charge
>> people money to design Kalman filtering algorithms I still don't feel I
>> have wrapped my arms completely around the problem. I doubt that I
>> would even if I won the lottery tomorrow, got my PhD in optimal
>> estimation, and spent the rest of my life teaching and doing research.
>>
>> So I don't know if it's realistic for anyone to expect to figure this
>> out by asking questions on USENET and reading web pages. I'm not even
>> sure if I can recommend just one book -- I think to do what you want to
>> do you need at least Dan Simon's book and a good book on strapdown
>> inertial nav systems.
>>
>> Even then you'll find Simon's book to be an uphill battle unless you
>> have a good grounding in stochastic process theory and state-space
>> control -- so expect to do some supplementary reading. Further, I have
>> yet to find a book on strapdown inertial navigation theory that gives a
>> blow-by-blow analysis of an inertial navigation Kalman solution -- the
>> one I have is the best of the lot, but it sure doesn't give an ABC
>> description.
>>
>> Here's my bibliography -- the two end ones are currently on my
>> 'essential reading' list for inertial nav stuff.
>>
>> Dan Simon, "Optimal State Estimation", Wiley 2006:
>> http://www.powells.com/partner/30696/biblio/9780471708582
>>
>> Harry Van Trees, "Detection, Estimation, and Modulation Theory", Wiley,
>> 1968: http://www.powells.com/partner/30696/biblio/9780471463825
>>
>> Karl Astrom & Bjorn Wittenmark, "Adaptive Control", Addison-Wesley,
>> 1995: http://www.powells.com/partner/30696/biblio/9780486462783
>>
>> Bitmead, Gevers, Wertz, "Adaptive Optimal Control, The Thinking Man's
>> GPC", Prentice-Hall, 1990:
>> http://www.powells.com/partner/30696/biblio/0139468234
>>
>> Titterton, D. H. and Weston, J. L., "Strapdown Inertial Navigation
>> Technology", AIAA, 2004:
>> http://www.powells.com/partner/30696/biblio/9780863413582
>>
>> --
>>
>> Tim Wescott
>> Wescott Design Services
>> http://www.wescottdesign.com
>>
>> Do you need to implement control loops in software?
>> "Applied Control Theory for Embedded Systems" was written for you.
>> See details at http://www.wescottdesign.com/actfes/actfes.html
>>
>
> Thanks a lot for the list of books, i will definitely take a look at
> them.
> As you said, web searches etc help only to a certain extent, i came across
> this book on the google books
>
> Estimation with applications to tracking and navigation
> http://books.google.ca/books?id=xz9nQ4wdXG4C&pg=PA219&lpg=PA219&dq=kalman+filter+step+by+step&source=bl&ots=VnU1u3e6uZ&sig=WTZ3IS1DDcNIPAbvZBiBgnuU1is&hl=en&ei=FZDkScu3DZ_ulQf1koHgDg&sa=X&oi=book_result&ct=result&resnum=8#PPA253,M1
>
> have you read this one before and if so how did u find it?
I haven't seen it before. I like the table of contents, though. If the
writing is clear it may be a good one to get in lieu of the Simon book
(although I _really_ like Simon's clarity, and his attitude about how
far so-called 'optimal' methods will take you).
I didn't see anything in the table of contents that indicates that they
directly address your problem, but it's extensive, and I only skimmed
it. The "Application to Navigation" part should certainly be what
you're looking for.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by arvkr●April 14, 20092009-04-14
>arvkr wrote:
>>> Two questions:
>>>
>>> One: Why is acceleration a state? I thought you were measuring it.
>>
>> You are right. I am measuring it and prob should have the state as acc
>> bias to estimate the bias. This is where i am struggling with since i
don't
>> seem to understand kalman filter fully and i have read several articles
on
>> the web, still haven't been able to fully get a grip on it.
>
>I have one book that talks about nothing but optimal state estimation
>(i.e. the Kalman filter and it's extended family), another that goes
>into detection, estimation and modulation theory (which has you derive
>Kalman filters as homework problems in at least two places), a couple of
>adaptive control books (that treat the system identification phase of
>adaptive control as a Kalman filtering problem), a book on strapdown
>inertial navigation (which mostly talks about devices, but which has an
>excellent section on translating combined gyro and accelerometer data
>into just the sort of model you need), and access to the entire world
>wide web.
>
>This is backed up by a career doing various sorts of signal detection
>and estimation problems, building advanced control systems from scratch,
>and other related activity.
>
>After all this, while I feel that I'm more than good enough to charge
>people money to design Kalman filtering algorithms I still don't feel I
>have wrapped my arms completely around the problem. I doubt that I
>would even if I won the lottery tomorrow, got my PhD in optimal
>estimation, and spent the rest of my life teaching and doing research.
>
>So I don't know if it's realistic for anyone to expect to figure this
>out by asking questions on USENET and reading web pages. I'm not even
>sure if I can recommend just one book -- I think to do what you want to
>do you need at least Dan Simon's book and a good book on strapdown
>inertial nav systems.
>
>Even then you'll find Simon's book to be an uphill battle unless you
>have a good grounding in stochastic process theory and state-space
>control -- so expect to do some supplementary reading. Further, I have
>yet to find a book on strapdown inertial navigation theory that gives a
>blow-by-blow analysis of an inertial navigation Kalman solution -- the
>one I have is the best of the lot, but it sure doesn't give an ABC
>description.
>
>Here's my bibliography -- the two end ones are currently on my
>'essential reading' list for inertial nav stuff.
>
>Dan Simon, "Optimal State Estimation", Wiley 2006:
>http://www.powells.com/partner/30696/biblio/9780471708582
>
>Harry Van Trees, "Detection, Estimation, and Modulation Theory", Wiley,
>1968: http://www.powells.com/partner/30696/biblio/9780471463825
>
>Karl Astrom & Bjorn Wittenmark, "Adaptive Control", Addison-Wesley,
>1995: http://www.powells.com/partner/30696/biblio/9780486462783
>
>Bitmead, Gevers, Wertz, "Adaptive Optimal Control, The Thinking Man's
>GPC", Prentice-Hall, 1990:
>http://www.powells.com/partner/30696/biblio/0139468234
>
>Titterton, D. H. and Weston, J. L., "Strapdown Inertial Navigation
>Technology", AIAA, 2004:
>http://www.powells.com/partner/30696/biblio/9780863413582
>
>--
>
>Tim Wescott
>Wescott Design Services
>http://www.wescottdesign.com
>
>Do you need to implement control loops in software?
>"Applied Control Theory for Embedded Systems" was written for you.
>See details at http://www.wescottdesign.com/actfes/actfes.html
>