I am doing a comparison, of Kalman Extended Kalaan Unscented(sigma point) Kalman Filters and several varieties of Partile filters on a highly non-linear system, with both gaussian and non-gaussian noise. I know that Kalman Filters aren't going to work so well, but I am a little unclear how to properly set on the Kalman filter so that it gets to give it its best shot.
The first system is modeled like this % x(k+1) = 1 + sin(4e-2*pi*k) + beta*x(k) + v(k); % y(k) = (x(k).^(2))/5 + w(k);
where w(k) and v(k) are noise sources that are gaussian in the first comparison, and then uniform, gamma, TBD in the other cases.
My first thought was ignore the sin(*) term all together, and simulate an additional step input for the constant "1" term. As for the X^2 term in the measurement equation, I am cluless at the moment. What is the fair solution, using the simplest global linearization possible, or redoing the Kalman equations to use the non-linear terms? Any ideas?
Robert Posey