Kalman-Bucy Filter: Calculate Eqns

  • Thread starter Thread starter dmorris619
  • Start date Start date
  • Tags Tags
    Control Stochastic
Click For Summary

Discussion Overview

The discussion revolves around the calculation of the Kalman-Bucy Filter equations, focusing on the derivation and understanding of the covariance matrices Q and R, which represent process noise and measurement noise, respectively. Participants are exploring the theoretical aspects and practical implications of these matrices in the context of a homework problem.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the origins of the covariance matrices Q and R, given the provided F matrix and output.
  • Another participant states that Q is derived from uncertainties in the process model, while R comes from sensor errors, indicating these values are specific to the problem at hand.
  • A participant questions the necessity of Q and R for deriving the Kalman equations, suggesting that it may be possible to proceed without Q but not without R.
  • Concerns are raised about the formulation of the problem, with a suggestion that the state transition matrix F should be square rather than a vector.

Areas of Agreement / Disagreement

Participants do not reach a consensus on how to derive Q and R, with some asserting their necessity while others question the formulation of the problem itself. The discussion remains unresolved regarding the best approach to calculate these matrices.

Contextual Notes

Participants note that the values of Q and R should ideally be based on data specific to the problem, highlighting potential limitations in the provided information.

dmorris619
Messages
41
Reaction score
0

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.
 
Last edited:
Physics news on Phys.org
dmorris619 said:

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.
 
Right but where do they come from? Or how do i calculate it?
 
dmorris619 said:
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.
 
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.
 
dmorris619 said:
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?
 

Similar threads

Can the Kalman filter handle variations in sampling interval?
  • · Replies 2 ·
Replies
2
Views
2K
State prediction equation for Kalman filter
  • · Replies 4 ·
Replies
4
Views
2K
One-dimensional steady state conduction in Cylindrical coordinates
  • · Replies 3 ·
Replies
3
Views
2K
Light absorption by a three level atom
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How does the Kalman filter calculate derivatives?
  • · Replies 3 ·
Replies
3
Views
4K
Extended Kalman Filter: Helping hand to a newbie
  • · Replies 1 ·
Replies
1
Views
3K
Thermodynamics Power Cycle Energy Balance
  • · Replies 2 ·
Replies
2
Views
5K
Engineering How Do You Solve RCL Circuit Problems Using Kirchhoff's Loop Rule?
  • · Replies 13 ·
Replies
13
Views
3K
: Lyapunov Equation for backward continuous-time Kalman Filter
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Some notes on stochastic physics
  • · Replies 1 ·
Replies
1
Views
2K