>The kalman filter assumes unbiased measurements. So I would try to model 
>the bias explicitely. For example for the acceleration your 
>acceleromator gives you a sum of the correct acceleration and the 
>acceleration bias. Then your state vector needs to carry the real 
>acceleration and the bias and by making the assumption the bias is just 
>additive you can model the bias in your measurement function. Same goes 
>for the gyro. But I have not that much experience in navigation 
>measurements so I do not know what a gyro gives you and how you can 
>convert this data to a velocity with the help of a compass. But do not 
>forget that you need at least one unbiased measurement at the 
>intialization of the kalman filter (for example of the position) to have

>a chance to correctly estimate the bias.
>
Back at the kalman filter again. This is what i am trying to do. I have
accurate distance measurement and i differentiate it with respect to time
twice to get Acceleration. Now i add a scale factor and bias to this
acceleration. I am able to recover scale no problem using kalman filter
but
 bias of 0.09mg screws up the filter big time. Any idea what i am doing
wrong?
My State Variables are
x = [acc
     bias]
A = [1 0
     0 1]
H = [scaleFactor 1]

my measurement model i am assuming 
Measured Acc = True Acc * ScaleFactor + bias
u = 0
hence B doesn't matter

R = var(acc)
Q = lower than R

arvkr schrieb:
>>> North, east, and down are easy (for an arbitrary definition of
> "easy");
>>> so is latitude. Find the local compass declination and that should
>>> suggest a longitude. Only a few more measurements would be needed to
>>> resolve any remaining ambiguity. Making a real system that's capable
> of
>>> doing this would be ... challenging.
> 
> Yes its definitely challenging and it can be costly, i will worry about
> the cost later. Right now if i have 3d readings from gyro, compass and
> accelerometer how can i use a kalman filter to give me some version of
> corrected gyro and acceleration.
> http://www.ocf.berkeley.edu/~tmtong/kalman.php
> He is alluding to something similar. I am just trying to understand how to
> model kalman filter to correct gyro accelerometer readings both of which
> are affected by a scale, bias and random noise. I do understand this might
> still not be enough, but as long as the kalman filter doesn't diverge it
> should be better than the raw reading.


The kalman filter assumes unbiased measurements. So I would try to model 
the bias explicitely. For example for the acceleration your 
acceleromator gives you a sum of the correct acceleration and the 
acceleration bias. Then your state vector needs to carry the real 
acceleration and the bias and by making the assumption the bias is just 
additive you can model the bias in your measurement function. Same goes 
for the gyro. But I have not that much experience in navigation 
measurements so I do not know what a gyro gives you and how you can 
convert this data to a velocity with the help of a compass. But do not 
forget that you need at least one unbiased measurement at the 
intialization of the kalman filter (for example of the position) to have 
a chance to correctly estimate the bias.

>> 
>> North, east, and down are easy (for an arbitrary definition of
"easy");
>> so is latitude. Find the local compass declination and that should
>> suggest a longitude. Only a few more measurements would be needed to
>> resolve any remaining ambiguity. Making a real system that's capable
of
>> doing this would be ... challenging.

Yes its definitely challenging and it can be costly, i will worry about
the cost later. Right now if i have 3d readings from gyro, compass and
accelerometer how can i use a kalman filter to give me some version of
corrected gyro and acceleration.
http://www.ocf.berkeley.edu/~tmtong/kalman.php
He is alluding to something similar. I am just trying to understand how to
model kalman filter to correct gyro accelerometer readings both of which
are affected by a scale, bias and random noise. I do understand this might
still not be enough, but as long as the kalman filter doesn't diverge it
should be better than the raw reading.

On Tue, 03 Mar 2009 13:57:00 -0500, Rich Webb wrote:

> On Tue, 03 Mar 2009 12:00:13 -0600, "arvkr" <krarvind@gmail.com> wrote:
> 
> 
>>>Normally this is done by backing up the inertial measurements with GPS
>>>or
>>
>>>other radiolocation measurements -- what's holding you back from that?
>>>
>>>--
>>>http://www.wescottdesign.com
>>>
>>>
>>For the project i am working neither can i use GPS nor i have other
>>measurements, the challenge is to find out if a Dead Reckoning system
>>with accelerometer, compass and gyro will be good enough to estimate the
>>position somewhat accurately ( equal to GPS or slightly less accurate,
>>if its more accurate even better).
> 
> North, east, and down are easy (for an arbitrary definition of "easy");
> so is latitude. Find the local compass declination and that should
> suggest a longitude. Only a few more measurements would be needed to
> resolve any remaining ambiguity. Making a real system that's capable of
> doing this would be ... challenging.

This is exactly what I was referring to.  Yes, it can be done.  With 
really accurate gyros, really accurate accelerometers, really accurate 
compasses, and some really accurate maps of magnetic declination and 
variations in gravity, you can figure out your approximate longitude.

But it ain't easy, and it ain't cheap.

-- 
http://www.wescottdesign.com

On Tue, 03 Mar 2009 14:23:44 -0500, Jerry Avins wrote:

> Tim Wescott wrote:
> 
>    ...
> 
>> The task you're trying to perform is called "inertial navigation".
>>     ... it's still (or was until
>> quite recently) the way that they got airliners from point "A" to point
>> "B" over long expanses of water (there's legal reasons why they can't
>> use GPS).
> 
>    ...
> 
> Can you enlarge on that, please?
> 
> Jerry

What I'm about to say is very approximate -- I haven't kept up on this 
particular debate.  If you really want to know, go digging on the web and 
the FAA web site for the appropriate press releases.

Anyway:

There are a variety of concerns about the reliability of GPS.  The show-
stopper used to be that the DoD gave absolutely no guarantee that it 
wouldn't shut down the civilian-accessible channels any time it felt like 
denying would-be opponents the service.

That's never happened in practice -- the closest that they came was in 
Iraq I, but since they couldn't supply our own troops with mil-spec GPS 
units* they didn't want to cut it off from our guys (who were buying 
civilian units).

Since then the DoD has started fielding satellites that can shut it down 
on a region-by-region basis, so if it ever does get around to buying 
handheld mil-spec units it would, for example, be able let things go dark 
for Iraq III**.  So that's not as much of a concern -- but there is still 
some uneasiness about civilian flight safety depending on military whim.

The last time I looked the FAA was wavering, but I don't know if they've 
caved in and allowed combination GPS/INS solutions in lieu of the much 
more expensive pure-INS solution.

* Makes you wonder -- Rome ca. 300, US ca. 2000; the difference is???

** Just wait...

-- 
http://www.wescottdesign.com

Tim Wescott wrote:

   ...

> The task you're trying to perform is called "inertial navigation".  
>     ... it's still (or was until 
> quite recently) the way that they got airliners from point "A" to point 
> "B" over long expanses of water (there's legal reasons why they can't use 
> GPS).

   ...

Can you enlarge on that, please?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

On Tue, 03 Mar 2009 12:00:13 -0600, "arvkr" <krarvind@gmail.com> wrote:

>>
>>Normally this is done by backing up the inertial measurements with GPS or
>
>>other radiolocation measurements -- what's holding you back from that?
>>
>>-- 
>>http://www.wescottdesign.com
>>
>
>For the project i am working neither can i use GPS nor i have other
>measurements, the challenge is to find out if a Dead Reckoning system with
>accelerometer, compass and gyro will be good enough to estimate the
>position somewhat accurately ( equal to GPS or slightly less accurate, if
>its more accurate even better).

North, east, and down are easy (for an arbitrary definition of "easy");
so is latitude. Find the local compass declination and that should
suggest a longitude. Only a few more measurements would be needed to
resolve any remaining ambiguity. Making a real system that's capable of
doing this would be ... challenging.

-- 
Rich Webb     Norfolk, VA

>
>Normally this is done by backing up the inertial measurements with GPS or

>other radiolocation measurements -- what's holding you back from that?
>
>-- 
>http://www.wescottdesign.com
>

For the project i am working neither can i use GPS nor i have other
measurements, the challenge is to find out if a Dead Reckoning system with
accelerometer, compass and gyro will be good enough to estimate the
position somewhat accurately ( equal to GPS or slightly less accurate, if
its more accurate even better).

On Tue, 03 Mar 2009 09:56:40 -0600, arvkr wrote:


>>Case 1:
>>
>>Your vehicle is sitting perfectly still, and the accelerometer is biased
> 
>>by 1/2 m/s/s.
>>
>>Case 2:
>>
>>Your vehicle is accelerating at 1/2 m/s/s and your accelerometer bias is
> 
>>exactly zero.
>>
>>How do you tell the difference?
>>
>>
>>
>>--
>>http://www.wescottdesign.com
>>
>>
> 
> Yes, i give up on trying to use just accelerometer to estimate position
> accurately, kalman or any other filter will not produce the necessary
> results. Now say i have a 3d gyro data and 3d accelerometer data and 3d
> compass data, how would i go about designing a kalman filter to fuse
> information to remove the errors that exist in gyro and accelerometer to
> produce accurate estimation of position.?

With those inputs (or, for that matter, just the accelerometer and gyro 
inputs), you will find that while in theory you now have enough 
information to find your latitude, (a) you still don't know the longitude 
without more information, and (b) you need gyros with errors 
significantly smaller than the Earth's rotational rate to even determine 
latitude.

The task you're trying to perform is called "inertial navigation".  It 
_can_ be done just with gyros, accelerometers, and the occasional 
astronomical observation -- that's how they used to (and perhaps still 
do) maneuver long-range nuclear submarines, and it's still (or was until 
quite recently) the way that they got airliners from point "A" to point 
"B" over long expanses of water (there's legal reasons why they can't use 
GPS).

But it takes really good sensors.  They're expensive, and the fact that 
they're known as "strategic grade" in the biz might give you a clue of 
how thrilled the US State department would be if you were to export one 
out of the US.

Normally this is done by backing up the inertial measurements with GPS or 
other radiolocation measurements -- what's holding you back from that?

-- 
http://www.wescottdesign.com

>
>Case 1:
>
>Your vehicle is sitting perfectly still, and the accelerometer is biased

>by 1/2 m/s/s.
>
>Case 2:
>
>Your vehicle is accelerating at 1/2 m/s/s and your accelerometer bias is

>exactly zero.
>
>How do you tell the difference?
>
>
>
>-- 
>http://www.wescottdesign.com
>


Yes, i give up on trying to use just accelerometer to estimate position
accurately, kalman or any other filter will not produce the necessary
results. Now say i have a 3d gyro data and 3d accelerometer data and 3d
compass data, how would i go about designing a kalman filter to fuse
information to remove the errors that exist in gyro and accelerometer to
produce accurate estimation of position.?