can anyone help design a state space model applying into Extended Kalman Filter

Terry <terryzz24@gmail.com> writes:

> the measurement equation is:
> y(t) = a1(t)+a2(t)*exp(-a3(t)*y(t-1)^2)*y(t-1)+a4(t)*exp(-
> a5(t)*y(t-1)^2)*y(t-2);
> 
> and the state equations are
> a1(t) = a1(t-1) + v1;
> a2(t) = a2(t-1) + v2;
> a3(t) = a3(t-1) + v3;
> a4(t) = a4(t-1) + v4;
> a5(t) = a5(t-1) + v5;
> 
> there is no measurement noise.

Then you still haven't read enough about Kalman filters.

Ciao,

Peter K.

-- 
"And he sees the vision splendid 
of the sunlit plains extended
And at night the wondrous glory of the everlasting stars."

 

sorry i may not clearly represent my question. In my point of view, KF
is a sort of estimator.

y(t) = a1(t)+a2(t)*exp(-a3(t)*y(t-1)^2)*y(t-1)+a4(t)*exp(-
a5(t)*y(t-1)^2)*y(t-2) + e(t);

during the estimation process

y_hat(t) = a1(t)+a2(t)*exp(-a3(t)*y(t-1)^2)*y(t-1)+a4(t)*exp(-
a5(t)*y(t-1)^2)*y(t-2);

the measurement error e(t) = y(t) - y_hat(t);

the measurement covariance Q(t) = cov(e(t));

then predicted covariance P(t|t-1) = F*P(t|t)*F+Q(t) where F is the
state process model.


If i want to apply EKF to y(t) = a1(t)+a2(t)*exp(-
a3(t)*y(t-1)^2)*y(t-1)+a4(t)*exp(-a5(t)*y(t-1)^2)*y(t-2) + e(t), how
can I the State-space mode?