|u(t) +w(t), y(t) = [1_0] x(t) +v(t), where the 0 disturbance w(t) and noise v(t) are...

Transcribed Image Text:

|u(t) +w(t), y(t) = [1_0] x(t) +v(t), where the 0 disturbance w(t) and noise v(t) are stationary, uncorrelated, zero-mean white Gaussian random processes 112(1) + [1] u(t) + w(t), y(t) = [1 with E{w(t)w¹ (7)} = o [11] (t−7) and E{v(t)v¹ (7)} = 8(t-7). Design a Kalman filter that optimally estimates r(t) given u(t) and y(t). Express both the solution S of the algebraic Riccati equation and the optimal state estimator gain H in terms of the intensity of the disturbance. Can a large o destabilize the estimation error dynamics? Consider a system described by i(t): = |u(t) +w(t), y(t) = [1_0] x(t) +v(t), where the 0 disturbance w(t) and noise v(t) are stationary, uncorrelated, zero-mean white Gaussian random processes 112(1) + [1] u(t) + w(t), y(t) = [1 with E{w(t)w¹ (7)} = o [11] (t−7) and E{v(t)v¹ (7)} = 8(t-7). Design a Kalman filter that optimally estimates r(t) given u(t) and y(t). Express both the solution S of the algebraic Riccati equation and the optimal state estimator gain H in terms of the intensity of the disturbance. Can a large o destabilize the estimation error dynamics? Consider a system described by i(t): =

Answer rating: 100% (QA)

Here are the steps to solve this problem 1 Define the system and measureme... View the full answer