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Dan
Dan

Reputation: 1

Is it Kalman filter if the measurement model is dependent on the measurement?

I'm estimating parameters of a parabola y = ax^2 + bx + c, while measuring the x,y points. My states are s = [a,b,c] and my transition model is s(k+1) = Fs(k) + v(k), where F is just an identity matrix. My measurement model is z(k) = [x,y] = Hs(k) + w(k). Now it would seem that the measurement model would require EKF for the parabola, but the states a,b,c are not in nonlinear relation. The Jacobian H would look like H = [x^2 x 1], leaving out the rows of zeros for x term. Since the states are not present, I would be inclined to call this linear Kalman filter. But the inclusion of the measured x value seems to invoke Extended Kalman filter. How would you approach this?

There is even this paper, which suggest use of EKF. But it just seems like plain KF.

Upvotes: 0

Views: 166

Answers (1)

Dawson Beatty
Dawson Beatty

Reputation: 688

Your intuition is correct, just a linear Kalman Filter would be fine. The measurement model is linear in the states, so even though to determine the H matrix you square the x value, the measurement model is still linear.

I didn't read the paper that you linked to, but I can if you think that I am misunderstanding your question.

Upvotes: 0

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