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state variables, Kalman filter
Hello,I have some question about using built-in Kalman filter function in some software..The transition equation is given by x_t = G * x_t-1 + e_t, where x_t is a vector n by 1, G matrix n by n and e_t is noiseBut my transition equation of interest has additional constant term c..x_t = c + G * x_t-1 + e_t ?How can I introduce the constant term c into the function?Thank you!
state variables, Kalman filter
that's right
Last edited by spinan on April 22nd, 2009, 10:00 pm, edited 1 time in total.
state variables, Kalman filter
..I think we also have to add it in the prediction equations..
state variables, Kalman filter
Treat the constant c as an extra state variable. The state variable now becomes [x c], and G becomes [G 0;0 1] and the corresponding error term is zero.
state variables, Kalman filter
Why can't we de-mean x_t, before feeding into the software, in which case c =0. Edit: But that would be true only if c is constant through out. If ct changes or assumed to change with "t", then as someone pointed out, it shall be another state variable.
Last edited by cryptic26 on April 22nd, 2009, 10:00 pm, edited 1 time in total.