Question: A second-order discrete-time system can be described as follows:
The initial conditions are x1(0) = 1 and x2(0) = -1, and the disturbance is a zero-mean process with covariance matrix
The actual value of the state transition matrix's (2,1 ) element is unknown; however, it is thought to be a constants whose value 0.6 with a standard deviation of 0.2. Both state components are measured; the measurement error is a zero-mean process with covariance matrix
Simulate the actual system's response to a random disturbance input and the associated measurement. Design filters and document estimation performance for the following cases:
(a) Kalman filter with the actual system model.
(b) Kalman filter with the assumed system model.
(c) Parameter-adaptive filter with the assumed model.