>Using 'n' for time, to denote sampling:
>
>x(n+1) = A x(n) + B_i U(n) + B_n W(n)
>y(n) = C_m x(n) + D_i U(n) + D_n W(n)
>
>A = 1, B_i = 0, B_n = 0, C_m = 1, D_i = cos(theta(n)), D_n =
>cos(theta(n)), x(0) = C.
>
>This is saved from being a no-state model (A, B_i and B_n empty) by the
>constant error. Otherwise you don't have any states, so it's a little
>silly modeling it with state-space.
>
First of all, thanks for help! But I still have some questions:
1) To my knowledge, I think c_m = cos(theta(n)), so that it can go back
to the sensor relation function.
2) Why you say that A (=1) is empty?
3) y(n) is not in the form of measurement model: z(k)= H(k)x(k)+ v(k).
How to deal with U(n) when a kalman filter is used to estimate the state
of the sensor?
Thanks!
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Reply by Tim Wescott●February 7, 20052005-02-07
gorlic wrote:
> Tim Wescott wrote:
>
>> ...
>>
>>
>>>What are you really trying to do, and why do you want to model
>
> stateless
>
>>>systems with state-space representations?
>>
> I want to use the kalman filter to detect the sensor fault. Any better
> way?
>
> Thanks!
>
>
>
> This message was sent using the Comp.DSP web interface on DSPRelated.com
If you have a model of the expected sensor output in azimuth and you
expect the sensor to behave in a markedly different way when it is
broken then a kalman filter of some sort may be part of the solution --
your kalman filter structure would then have more to do with the vehicle
dynamics than the (nonexistent) sensor dynamics.
Have fun -- BIT has always struck me as a good way to generate false alarms.
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
Reply by gorlic●February 5, 20052005-02-05
Tim Wescott wrote:
>
> ...
>
>> What are you really trying to do, and why do you want to model
stateless
>> systems with state-space representations?
>
I want to use the kalman filter to detect the sensor fault. Any better
way?
Thanks!
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Reply by Jerry Avins●February 4, 20052005-02-04
Tim Wescott wrote:
...
> What are you really trying to do, and why do you want to model stateless
> systems with state-space representations?
Homework, probably.
Jerry
--
Engineering is the art of making what you want from things you can get.
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Reply by Tim Wescott●February 4, 20052005-02-04
gorlic wrote:
> In my sensor implementation, I got a function:
>
> Y(t)=cos(theta(t))*( U(t) + W(t)+ C )
>
> Where t denotes the sampling time, Y denotes the measured azimuth,
> 'theta' denotes the angle of the hilly road, U denotes the real
> azimuth(input), W denotes the zero mean Gaussian white noise, C denotes
> calibration error(constant).
>
> How to transfer this relation function to the state space model?
>
> Thanks!
>
>
> This message was sent using the Comp.DSP web interface on DSPRelated.com
Using 'n' for time, to denote sampling:
x(n+1) = A x(n) + B_i U(n) + B_n W(n)
y(n) = C_m x(n) + D_i U(n) + D_n W(n)
A = 1, B_i = 0, B_n = 0, C_m = 1, D_i = cos(theta(n)), D_n =
cos(theta(n)), x(0) = C.
This is saved from being a no-state model (A, B_i and B_n empty) by the
constant error. Otherwise you don't have any states, so it's a little
silly modeling it with state-space.
What are you really trying to do, and why do you want to model stateless
systems with state-space representations?
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
Reply by gorlic●February 4, 20052005-02-04
In my sensor implementation, I got a function:
Y(t)=cos(theta(t))*( U(t) + W(t)+ C )
Where t denotes the sampling time, Y denotes the measured azimuth,
'theta' denotes the angle of the hilly road, U denotes the real
azimuth(input), W denotes the zero mean Gaussian white noise, C denotes
calibration error(constant).
How to transfer this relation function to the state space model?
Thanks!
This message was sent using the Comp.DSP web interface on DSPRelated.com