The agenda: 1. The Kalman theory 2. Break for 20 minuts 3. More theory 4. Simulation of the filter. 5. Further discussion and exercises The Scalar Kalman.

Slides:

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Presentation transcript:

The agenda: 1. The Kalman theory 2. Break for 20 minuts 3. More theory 4. Simulation of the filter. 5. Further discussion and exercises The Scalar Kalman filter

Defenitions: S(n) = a(n)S(n-1) + W(n) a(n) is the projection of the last value of the sequence S to the next value of the sequence S. a(n) is not considered further, and is therefore equal one. X(n)=S(n) + V(n) W(n) and V(n) are both white gausian noise and they are orthorgonal.

The Scalar Kalman filter Since a(n) = 1 for all n

The Scalar Kalman filter Basic Algorithm:

The Scalar Kalman filter

The P(n) is defined: To obtain the optimal estimator, the P(n) must be minimized. The recursive estimation of P(n) can be found to be:

Solve following to obtain optimal estimator:

Break for 20 minutes

Solve following to obtain optimal estimator:

The Scalar Kalman filter Algorithm: Initialize n = 1 P(1) = some value (0) (1) = some value (0) 1.start loop Get n = n +1 go back to 1.

The Scalar Kalman filter Simulations - Normal (002)

The Scalar Kalman filter When to use a Kalman filter, compared to a LP filter? What can we do if the frequency that the kalman filter has to work with increses?