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I am new to the robotics field and sensor fusion as well.

I am trying to localize my robot using the data from my camera and the odometery through extended Kalman filter.

I have the data offline, I synchronized them. However I have a trouble with constructing the $F, H$ matrices.

Any help?

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This is the advice I gave to BOB but will be useful for you as well.

I recommend you to run an ekf slam tutorial code and analyse it. There is a perfect one for you: robots.ox.ac.uk/~SSS06/Website/index.html It is the simplest EKF SLAM but quite well coded and easy to read if you know matlab. I am sure the most of your implementational questions will be easily answered by looking at this code.

Practical 1 & 2 in the above link contains 90% of the things you need for implementing mono ekf slam or 2d ekf slam.

Another material for theoretical aspect on slam is here

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