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Question on Kalman Filter

Started by Unknown November 18, 2003
In a dynamic model

x(k+1) = a*x(k) + w
z(k+1) = h*x(k+1) + v

In real application, how to get the noise variance matrix R of v? Generally
is it a time-variant value which should  be estimated from the random signal
z(k) itself? Or is it predetermined by the sensor property?

Thanks.




"tsj" <tsj3982@yahoo.com> writes:

> In a dynamic model > > x(k+1) = a*x(k) + w > z(k+1) = h*x(k+1) + v > > In real application, how to get the noise variance matrix R of v?
If everything is linear, you could just generate an estimate of it from the sensor or signal model properties.
> Generally is it a time-variant value which should be estimated from > the random signal z(k) itself?
It is usually time invariant (but it depends on your signal model).
> Or is it predetermined by the sensor property?
It's best taken from anything you might know about how the signal is measured. Ciao, Peter K. -- Peter J. Kootsookos "I will ignore all ideas for new works [..], the invention of which has reached its limits and for whose improvement I see no further hope." - Julius Frontinus, c. AD 84
So do we estimate R in real-time from the signal z(k+1) we get? Or is it a
pre-determined variable? What's the usual practice? Thanks.

Wei



"Peter J. Kootsookos" <p.kootsookos@remove.ieee.org> wrote in message
news:s68k75yxl0k.fsf@mango.itee.uq.edu.au...
> "tsj" <tsj3982@yahoo.com> writes: > > > In a dynamic model > > > > x(k+1) = a*x(k) + w > > z(k+1) = h*x(k+1) + v > > > > In real application, how to get the noise variance matrix R of v? > > If everything is linear, you could just generate an estimate of it > from the sensor or signal model properties. > > > Generally is it a time-variant value which should be estimated from > > the random signal z(k) itself? > > It is usually time invariant (but it depends on your signal model). > > > Or is it predetermined by the sensor property? > > It's best taken from anything you might know about how the signal is > measured. > > Ciao, > > Peter K. > > -- > Peter J. Kootsookos > > "I will ignore all ideas for new works [..], the invention of which > has reached its limits and for whose improvement I see no further > hope." > > - Julius Frontinus, c. AD 84

tsj wrote:

> So do we estimate R in real-time from the signal z(k+1) we get? Or is it a > pre-determined variable? What's the usual practice? Thanks. > > Wei > > "Peter J. Kootsookos" <p.kootsookos@remove.ieee.org> wrote in message > news:s68k75yxl0k.fsf@mango.itee.uq.edu.au... > > "tsj" <tsj3982@yahoo.com> writes: > > > > > In a dynamic model > > > > > > x(k+1) = a*x(k) + w > > > z(k+1) = h*x(k+1) + v > > > > > > In real application, how to get the noise variance matrix R of v? > > > > If everything is linear, you could just generate an estimate of it > > from the sensor or signal model properties. > > > > > Generally is it a time-variant value which should be estimated from > > > the random signal z(k) itself? > > > > It is usually time invariant (but it depends on your signal model). > > > > > Or is it predetermined by the sensor property? > > > > It's best taken from anything you might know about how the signal is > > measured. > > > > Ciao, > > > > Peter K. > > > > -- > > Peter J. Kootsookos > > > > "I will ignore all ideas for new works [..], the invention of which > > has reached its limits and for whose improvement I see no further > > hope." > > > > - Julius Frontinus, c. AD 84
Isn't this one of the problems withe Klman filters - we need an accurate model apriori. However, if you can switch off the signal you should me left with measurement noise - assuming this is possible. Tom