# Kalman filter

Started by May 30, 2007
```The tranditional Kalman filter equation is as follows:
x(n)=F x(n-1)+w(n)
y(n)=H x(n)+v(n)
And x(n) is called "state".
If there are two states, x1(n) and x2(n),
x1(n)=F1 x1(n-1)+w1(n)
x2(n)=F2 x2(n-1)+w2(n)
y(n)=H1 x1(n)+H2 x2(n)+v(n)
Is it still the Kalman filter? How to make estimation? Or can you
refer me some papers?
Thanks.

```
```On May 30, 6:19 pm, heng <likemurs...@gmail.com> wrote:
> The tranditional Kalman filter equation is as follows:
> x(n)=F x(n-1)+w(n)
> y(n)=H x(n)+v(n)
> And x(n) is called "state".
> If there are two states, x1(n) and x2(n),
> x1(n)=F1 x1(n-1)+w1(n)
> x2(n)=F2 x2(n-1)+w2(n)
> y(n)=H1 x1(n)+H2 x2(n)+v(n)
> Is it still the Kalman filter? How to make estimation? Or can you
> refer me some papers?
> Thanks.

The Kalman filter equation applies to the multi-dimensional
case.  This is what you have:  x, y (using the traditional
form) are two-dimensional signals.

Let x_vec = [x1 x2]^T,  H_vec = [H1 H2], and so on and
so forth.

Hope that helps,
Julius

```
```>On May 30, 6:19 pm, heng <likemurs...@gmail.com> wrote:
>> The tranditional Kalman filter equation is as follows:
>> x(n)=F x(n-1)+w(n)
>> y(n)=H x(n)+v(n)
>> And x(n) is called "state".
>> If there are two states, x1(n) and x2(n),
>> x1(n)=F1 x1(n-1)+w1(n)
>> x2(n)=F2 x2(n-1)+w2(n)
>> y(n)=H1 x1(n)+H2 x2(n)+v(n)
>> Is it still the Kalman filter? How to make estimation? Or can you
>> refer me some papers?
>> Thanks.
>
>The Kalman filter equation applies to the multi-dimensional
>case.  This is what you have:  x, y (using the traditional
>form) are two-dimensional signals.
>
>Let x_vec = [x1 x2]^T,  H_vec = [H1 H2], and so on and
>so forth.
>
>Hope that helps,
>Julius
>
>your new system now would be of the form x(n+1)=Fx(n)+w(n) with
x(n)=[x1,x2]^T and F=diag[F1,F2] the same with H the covariance matrices
must have the appropriate dimensions so as the multiplications can be done.
```