Given the state equation XK+1 = A XK + NK
where the state matrix A is the “identity” matrix of dimension 2 and NK the system noise whose covariance matrix is written Q = σ2Id (Id : identity matrix).
The system is observed by the scalar equation:
where and are the components of the vector XK and where WK is the measurement noise of the variance .
and are the initial conditions.
1) Give the expression of the Kalman gain K(1) at instant “1” according to σ2 and .
2) Give the estimate of of X1 at instant “1” according to the first measurement of K(1) and the first measurement Y1.
We are considering the movement of a ...