Final_1.pdf

APPENDIX

We describe the formulas for the Kalman filtering steps here. The notation
we use is the same as that discussed in the section on the Kalman filter.

1. Evaluate and using the state equation.


2. Find the observation YtandRby observing the system. Note that we
   have the matrix Hdefined as follows:

Yt=HXt+vt

3. Compute the Kalman gain Kt.


4. Evaluate given by.


5. Evaluate.

ˆˆ

Ptt||KH Ptt KH KRK

T T

=−() (^11) − 1 ()− +

ˆ

Ptt|

ˆˆ

XKYHXtt||−− 11 +−t( t tt )

ˆ

Xtt|

KPHHPH Rtt=+T()t T

−

ˆˆ

1

ˆˆ

ˆˆ

||

||

XAX

PAPA

tt t t

tt t t

T

−−−

−−−

=

=

111

111

ˆ

Ptt|− 1

ˆ

Xtt|− 1

Kalman Filtering 69