Kalman-Bucy Filter: Calculate Eqns

[dmorris619]

Homework Statement

Calculate the Kalman-Bucy Filter equations

Homework Equations

F=(0 1)'
K is unknown but y = X_1 + d/dt(v)
E=((Fw-Kv)(Fw-Kv)')=FQF' + KRK'
Q = E(ww') and R = E(vv')

The Attempt at a Solution

There is more to this question but I am just having trouble understanding where Q and R come from if w is q and v is 1.

 

[CEL]

Homework Statement

Calculate the Kalman-Bucy Filter equations

Homework Equations

F=(0 1)'
K is unknown but y = X_1 + d/dt(v)
E=((Fw-Kv)(Fw-Kv)')=FQF' + KRK'
Q = E(ww') and R = E(vv')

The Attempt at a Solution

There is more to this question but I am just having trouble understanding where Q and R come from if w is q and v is 1.

Q is the covariance of the process noise and R is the covariance of the measurement noise.

 

[dmorris619]

Right but where do they come from? Or how do i calculate it?

 

[CEL]

Right but where do they come from? Or how do i calculate it?

Q comes from the uncertainties in your processs model. R comes from the errors in your sensor.
They are specific to your particular problem.

 

[dmorris619]

Thats what I am unsure of. All I have is the F matrix and the output. So from this how do I get Q and R unless there is another way of getting the Kalman Equations without Q and R.

 

[CEL]

Thats what I am unsure of. All I have is the F matrix and the output. So from this how do I get Q and R unless there is another way of getting the Kalman Equations without Q and R.

You can use the Kalman filter without Q, but not without R. The values of Q and R should have been data of your problem.
By the way, I think the whole problem is ill-formulated. The state transition F should be square and not a vector.
Can you post the problem in its totality?