A comparison of recursive weighted least squares estimation and Kalman filtering for source dynamic motion evaluation

The problem of compensating for underwater motion effects (heave component) arises in a number of areas of current interest, such as control and operation of autonomous, remotely operated vehicles; underwater seismic exploration; and float and buoy wave data analysis. Earlier treatments of the problem relied on frequency response methods to model the phenomenon, and subsequently applied Kalman filtering. Two models of the heave process are discussed in this paper. In the first, frequency-response-based higher-order models, including lead-lag factors, are obtained as a prelude to the application of the standard Kalman filter to estimate the heave component. The second model involves the discrete AutoRegressive Moving Average with external variables (ARMAX) form, which has proven useful in many application areas. The paper proposes the use of the recursive weighted least squares (RWLS) algorithm to solve the filtering problem on the basis of the ARMAX model. The algorithm is simpler than Kalman filtering in terms of the required knowledge of noise statistics, and thus provides an attractive alternative to Kalman filtering. The relation between the RWLS technique and Kalman filtering is explored. Computational results pertaining to the performance of the RWLS technique are given, and the effects of the method's weighting functions are discussed.