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.
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.