POLYNOMIAL MATRIX SOLUTION TO THE DISCRETE FIXED-LAG SMOOTHING PROBLEM

The solution of the optimal linear fixed lag smoothing problem is considered using a polynomial matrix description for the discrete systems. The smoother is given by the solution of a diophantine equation and is equivalent to the transfer-function matrix form of the Wiener smoother. The pole-zero properties of the optimal smoother are more obvious in the polynomial representation and new insights into the measurement noise rejection properties of the smoother are obtained. The signal model is assumed to be stable and allowance is made for both dynamic cost weighting and coloured measurement noise. The model structure was determined by the needs of industrial smoothing problems. The polynomial form of filter may easily be included in a self-tuning algorithm and a simple adaptive smoother is described.