# Question on Kalman Filter

Started by 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

```