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From: Tim Wescott on 24 Jun 2010 18:59
On 06/24/2010 03:52 PM, pnachtwey wrote:
> On Jun 24, 10:04 am, Tim Wescott<t...(a)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
From: Randy Yates on 24 Jun 2010 22:09
Tim Wescott <tim(a)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(a)ieee.org %
http://www.digitalsignallabs.com % 'Yours Truly, 2095', *Time*, ELO
From: Tim Wescott on 24 Jun 2010 23:23
On 06/24/2010 07:09 PM, Randy Yates wrote:
> Tim Wescott<tim(a)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
From: JCH on 25 Jun 2010 02:44


"raffaello" <rbrondi(a)n_o_s_p_a_m.gmail.com> schrieb im Newsbeitrag
news:xYidndsSFurZ0b7RnZ2dnUVZ_t6dnZ2d(a)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?
>


Maybe this could solve your problem:

a = acceleration
v = velocity
p = position

a = dp^2/dt^2

Numerically change to difference equation

a_i = (p_i+1 - 2 * p_i + p_i-1) / h ^ 2
h = dt

EXAMPLE

<< Solved by Gaussian Method >>

8 Equations:

((p_2 - 2 * p_1 + p_0) / h ^ 2) - a_1 = 0
((p_3 - 2 * p_2 + p_1) / h ^ 2) - a_2 = 0
((p_4 - 2 * p_3 + p_2) / h ^ 2) - a_3 = 0
((p_5 - 2 * p_4 + p_3) / h ^ 2) - a_4 = 0
((p_6 - 2 * p_5 + p_4) / h ^ 2) - a_5 = 0
((p_7 - 2 * p_6 + p_5) / h ^ 2) - a_6 = 0
((p_8 - 2 * p_7 + p_6) / h ^ 2) - a_7 = 0
((p_1 - p_0) / h) - v_0 = 0

Known Values

a_1 = 10
a_2 = 50
a_3 = 70
a_4 = -90
a_5 = -45
a_6 = -30
a_7 = 80

h = 1

p_0 = 0 'Start Values
v_0 = 0

Solution

p_1 = 0
p_2 = 10
p_3 = 70
p_4 = 200
p_5 = 240
p_6 = 235
p_7 = 200
p_8 = 245



JCH



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