H∞ fixed-lag smoothing filter for scalar systems

The solution of the H_∞ optimal linear fixed-lag smoothing problem is considered using a polynomial matrix description for the discrete system. The smoother is obtained from the solution of a linear equation and a spectral factorization calculation. The pole-zero properties of the optimal smoother are obvious in the polynomial representation, and insights into the measurement noise rejection properties of the smoother are obtained. Allowance is made for both dynamic cost weighting and colored measurement noise. The polynomial form of the smoothing filter may be incorporated into a self-tuning algorithm and a simple adaptive smoother is discussed