Take as a test signal a periodically modulated sinusoid with noise added, yn = sin[0.1tn + 4 sin(0.01tn)] + η ≡ sin(θn) + η , (19.69) where η is a Gaussian noise process with σ = 0.1. Design an extended Kalman filter to estimate the noise-free signal. Use a two-component state vector ~xn = (θn, θn−1), and assume for the internal model a linear extrapolation θn+1 = θn + (θn−θn−1). Take the system noise matrix Nx to be diagonal, and plot the predicted value of y versus the measured value of y if the standard deviation of the system noise is chosen to be 10−1 , 10−3 , and 10−5 . Use the identity matrix for the initial error estimate.