"raffaello" <rbrondi@n_o_s_p_a_m.gmail.com> schrieb im Newsbeitrag
news:xYidndsSFurZ0b7RnZ2dnUVZ_t6dnZ2d@giganews.com...
> Hi
>
> The problem i'm trying to face is to filter the accelerometer noise using
> a
> kalman filter without any other input. I'm new to kalman filter and i
> don't
> know exactly how to model and develop such a filter. As a first attempt i
> tried to describe the problem as follows:
>
> (p = position, v = velocity, a = acceleration, dt = time delta)
> |p|
> xhat_k = |v|
> |a|
>
> |1 dt dt^2/2|
> phy_k = |0 1 dt | \\updated with the time delta
> |0 0 1 | \\between two sensor readings
>
> H = |0 0 1|
>
> Q = process model covariance matrix
>
> R = measerement covariance matrix
>
> \\a priori estimate
> xhat_k^- = phy_k-1 * xhat_k-1 \\a priori state
> P_k^- = phy_k-1 * P_k-1 * phy_k-1^t + Q \\a priori covariance matrix
>
> \\measurement update
> z_k = measured acceleration
> K_k = P_k^- H^t (H P_k^- H^t + R)^-1
>
>
> \\a posteriori estimate
> xhat_k = xhat_k^- + K_k(z_k - Hxhat_k^-)
> P_k = (I – K_k H)P_k^-
>
>
> Using this model i got a result still affected by noise. Did i make some
> mistakes in the model?
>
> Tim Wescott<tim@seemywebsite.now> writes:
>
>> On 06/24/2010 11:32 AM, raffaello wrote:
>>> Hi,
>>>
>>> thanks for your reply. What i want to do is to track the position of a
>>> smartphone. I have a Motorola Milestone(this is the model
>>> http://developer.motorola.com/products/milestone/ ) which contains a
>>> LIS331DLH 3-axes accelerometer.
>>> I tried to use the pure accelerometers output to estimate the position of
>>> the device but there is to much noise and, if i leave my phone motionless
>>> on the table, the accelerometers give me a non zero value.
>>>
>>> How should i use the sensors of the smartphone to track its position?
>>> How should i correct my kalman filter to filter the accelerometers noise
>>> and to estimate the correct position of the phone?
>>
>> There was a long thread on this topic recently; just replace "iPhone"
>> with "Motorola Milestone" and you'll get the gist of it.
>>
>> http://www.dsprelated.com/showmessage/127160/1.php
>>
>> I don't think you can get there from here with the sensors you have
>> available -- but all the arguments have already been hashed out there.
>
> Right - you need rate sensors as well as linear.
And -- unless you're going to subject the thing to some pretty odd
gyrations -- much better rate sensors than you'll find in a cruddy old
phone.
--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
Reply by Randy Yates●June 24, 20102010-06-24
Tim Wescott <tim@seemywebsite.now> writes:
> On 06/24/2010 11:32 AM, raffaello wrote:
>> Hi,
>>
>> thanks for your reply. What i want to do is to track the position of a
>> smartphone. I have a Motorola Milestone(this is the model
>> http://developer.motorola.com/products/milestone/ ) which contains a
>> LIS331DLH 3-axes accelerometer.
>> I tried to use the pure accelerometers output to estimate the position of
>> the device but there is to much noise and, if i leave my phone motionless
>> on the table, the accelerometers give me a non zero value.
>>
>> How should i use the sensors of the smartphone to track its position?
>> How should i correct my kalman filter to filter the accelerometers noise
>> and to estimate the correct position of the phone?
>
> There was a long thread on this topic recently; just replace "iPhone"
> with "Motorola Milestone" and you'll get the gist of it.
>
> http://www.dsprelated.com/showmessage/127160/1.php
>
> I don't think you can get there from here with the sensors you have
> available -- but all the arguments have already been hashed out there.
Right - you need rate sensors as well as linear.
--
Randy Yates % "She has an IQ of 1001, she has a jumpsuit
Digital Signal Labs % on, and she's also a telephone."
mailto://yates@ieee.org %
http://www.digitalsignallabs.com % 'Yours Truly, 2095', *Time*, ELO
Reply by Tim Wescott●June 24, 20102010-06-24
On 06/24/2010 03:52 PM, pnachtwey wrote:
> On Jun 24, 10:04 am, Tim Wescott<t...@seemywebsite.now> wrote:
>> On 06/24/2010 05:15 AM, raffaello wrote:
>>
>>> Hi
>>
>>> The problem i'm trying to face is to filter the accelerometer noise using a
>>> kalman filter without any other input. I'm new to kalman filter and i don't
>>> know exactly how to model and develop such a filter. As a first attempt i
>>> tried to describe the problem as follows:
>>
>>> (p = position, v = velocity, a = acceleration, dt = time delta)
>>> |p|
>>> xhat_k = |v|
>>> |a|
>>
>>> |1 dt dt^2/2|
>>> phy_k = |0 1 dt | \\updated with the time delta
>>> |0 0 1 | \\between two sensor readings
>>
>> This is the model for a 3rd-order system, which presumably takes jerk as
>> an input.
> This looks like a second order model to me.
> Examples can be found in you Dan Simon book.
It has three states, arranged as a cascade of three integrators. If
you're modeling motion with an acceleration for an input then you
probably do want two states -- but that's not what this model has.
--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
Reply by pnachtwey●June 24, 20102010-06-24
On Jun 24, 10:04�am, Tim Wescott <t...@seemywebsite.now> wrote:
> On 06/24/2010 05:15 AM, raffaello wrote:
>
> > Hi
>
> > The problem i'm trying to face is to filter the accelerometer noise using a
> > kalman filter without any other input. I'm new to kalman filter and i don't
> > know exactly how to model and develop such a filter. As a first attempt i
> > tried to describe the problem as follows:
>
> > (p = position, v = velocity, a = acceleration, dt = time delta)
> > � � � � � |p|
> > xhat_k = |v|
> > � � � � � |a|
>
> > � � � � �|1 � dt �dt^2/2|
> > phy_k = |0 � 1 � � dt �| � \\updated with the time delta
> > � � � � �|0 � 0 � � 1 � | � \\between two sensor readings
>
> This is the model for a 3rd-order system, which presumably takes jerk as
> an input.
This looks like a second order model to me.
Examples can be found in you Dan Simon book.
Peter Nachtwey
Reply by Tim Wescott●June 24, 20102010-06-24
On 06/24/2010 11:32 AM, raffaello wrote:
> Hi,
>
> thanks for your reply. What i want to do is to track the position of a
> smartphone. I have a Motorola Milestone(this is the model
> http://developer.motorola.com/products/milestone/ ) which contains a
> LIS331DLH 3-axes accelerometer.
> I tried to use the pure accelerometers output to estimate the position of
> the device but there is to much noise and, if i leave my phone motionless
> on the table, the accelerometers give me a non zero value.
>
> How should i use the sensors of the smartphone to track its position?
> How should i correct my kalman filter to filter the accelerometers noise
> and to estimate the correct position of the phone?
There was a long thread on this topic recently; just replace "iPhone"
with "Motorola Milestone" and you'll get the gist of it.
http://www.dsprelated.com/showmessage/127160/1.php
I don't think you can get there from here with the sensors you have
available -- but all the arguments have already been hashed out there.
--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
Reply by raffaello●June 24, 20102010-06-24
Hi,
thanks for your reply. What i want to do is to track the position of a
smartphone. I have a Motorola Milestone(this is the model
http://developer.motorola.com/products/milestone/ ) which contains a
LIS331DLH 3-axes accelerometer.
I tried to use the pure accelerometers output to estimate the position of
the device but there is to much noise and, if i leave my phone motionless
on the table, the accelerometers give me a non zero value.
How should i use the sensors of the smartphone to track its position?
How should i correct my kalman filter to filter the accelerometers noise
and to estimate the correct position of the phone?
Thanks!
R. B.
Reply by Tim Wescott●June 24, 20102010-06-24
On 06/24/2010 05:15 AM, raffaello wrote:
> Hi
>
> The problem i'm trying to face is to filter the accelerometer noise using a
> kalman filter without any other input. I'm new to kalman filter and i don't
> know exactly how to model and develop such a filter. As a first attempt i
> tried to describe the problem as follows:
>
> (p = position, v = velocity, a = acceleration, dt = time delta)
> |p|
> xhat_k = |v|
> |a|
>
> |1 dt dt^2/2|
> phy_k = |0 1 dt | \\updated with the time delta
> |0 0 1 | \\between two sensor readings
This is the model for a 3rd-order system, which presumably takes jerk as
an input.
> H = |0 0 1|
And acceleration as an output, with velocity and position being clearly
unobservable.
> Q = process model covariance matrix
>
> R = measerement covariance matrix
>
> \\a priori estimate
> xhat_k^- = phy_k-1 * xhat_k-1 \\a priori state
> P_k^- = phy_k-1 * P_k-1 * phy_k-1^t + Q \\a priori covariance matrix
>
> \\measurement update
> z_k = measured acceleration
> K_k = P_k^- H^t (H P_k^- H^t + R)^-1
>
>
> \\a posteriori estimate
> xhat_k = xhat_k^- + K_k(z_k - Hxhat_k^-)
> P_k = (I – K_k H)P_k^-
>
>
> Using this model i got a result still affected by noise. Did i make some
> mistakes in the model?
At best what you are going to get with this construction is a 1st-order
lowpass filter of your accelerometer output, that wastes a bunch of
computation time on two states that it never uses.
So back off a bit, and tell us more: What are you _really_ doing? Why
do you want to filter your accelerometer output? What information do
you want to end up with?
--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
Reply by raffaello●June 24, 20102010-06-24
Hi
The problem i'm trying to face is to filter the accelerometer noise using a
kalman filter without any other input. I'm new to kalman filter and i don't
know exactly how to model and develop such a filter. As a first attempt i
tried to describe the problem as follows:
(p = position, v = velocity, a = acceleration, dt = time delta)
|p|
xhat_k = |v|
|a|
|1 dt dt^2/2|
phy_k = |0 1 dt | \\updated with the time delta
|0 0 1 | \\between two sensor readings
H = |0 0 1|
Q = process model covariance matrix
R = measerement covariance matrix
\\a priori estimate
xhat_k^- = phy_k-1 * xhat_k-1 \\a priori state
P_k^- = phy_k-1 * P_k-1 * phy_k-1^t + Q \\a priori covariance matrix
\\measurement update
z_k = measured acceleration
K_k = P_k^- H^t (H P_k^- H^t + R)^-1
\\a posteriori estimate
xhat_k = xhat_k^- + K_k(z_k - Hxhat_k^-)
P_k = (I – K_k H)P_k^-
Using this model i got a result still affected by noise. Did i make some
mistakes in the model?
Thanks for your help!