ECEn :777 Digital Signal Processing Questions & Answers

ECEn :777 Digital Signal Processing Questions & Answers 1st Equation - CORRECT ANSWER - Prediction of state estimate: x_hat(n|n-1) = A(n-1) * x_hat(n-1|n-1) = 2nd Equation - CORRECT ANSWER - Calculation of prediction error covariance, P(n|n-1) = A(n-1) * P(n-1|n-1) * A^H(n-1), 3rd Equation - CORRECT ANSWER - Calculate Kalman Gain, K(n) = P(n|n-1) * C^H(n) * [C(n) * P(n|n-1)*C^H(n) + Qv]^-1 4th Equation - CORRECT ANSWER - Calculate correction, x_hat(n|n) = x_hat(n|n-1) + K(n)*[y(n) - C(n)*x_hat(n|n-1)] 5th Equation - CORRECT ANSWER - Calculation of correction correlation matrix, P(n|n) = [I - K(n)*C(n)] * P(n|n-1) AR(1) difference equation - CORRECT ANSWER - x(n) =( sum from k = 1 to p of a(k)*x(n-k)) + w(n), where w(n) is 1-D noise and = [1,0,...,0]^T * w(n) correction error covariance matrix - CORRECT ANSWER - P(n|n) = E{e(n|n)e^H(n|n)} Correction Step, kalman filter - CORRECT ANSWER - x_hat(n|n) = K'(n) * x_hat(n|n-1) + K(n) * y(n) Covariance error matrix - CORRECT ANSWER - main diagonal, covariance: element x element error General Initial Values for Kalman Filter - CORRECT ANSWER - x_hat(0|0) = E{x(n)}, P(0|0) = E{x(n) * x_hat(n)}, or P(n|n) could be identity matrix, and x(n) can be unit vector Initial Conditions needed for Kalman Filter - CORRECT ANSWER - P(n|n), prediction correlation matrix, Qv, Qw, A, C(n), x