Optimal estimation of ship´s attitudes and attitude rates

Estimation of ship rotational motions induced by ocean waves plays a central role in many navigation and fire control applications. Inertial-type instruments are available which give good measurements of the attitude, but some form of signal processing is necessary to obtain angular rates or predict attitudes. Using optimal moving-average (or transversal) filters, we can obtain very good estimates of attitude rates as well as predictions of these values. Filter parameters can be changed adaptively to maintain good performance as the ship changes heading or velocity. The problem of designing these optimal filters is examined in detail and numerical results are given for a particular set of conditions. Two implementations of the adaptive filter are discussed. One is based on a recursive estimation of the process autocorrelations with the filter coefficients being recomputed at periodic intervals or whenever nonstationary conditions are detected. The second implementation is based on Widrow´s LMS algorithm. Both alternatives for the adaptive filter implementation are quite reasonable in terms of their computational requirements. The steady-state performance analysis can be considered to be a lower bound on the errors incurred by an adaptive filter.