Application of Kalman filtering to real-time preprocessing of geophysical data

An algorithm for automatic preprocessing of multiple data sequences in real-time is proposed. Based on a fixed-lag Kalman filter approach, it models the signal using a state vector that consists of the signal, its first three differences, and a special variable used to implement data editing functions. The smoothed output lessens some of the noise problems encountered in practice, and the method provides mechanisms for identification and removal of spikes, identification and measurement of steps, and filling of data gaps. Two versions of the algorithm are developed, one based on the conventional form of the Kalman filter, and one using a sequential processing technique. The computational requirements of each are analyzed and compared. An alternate approach for fixed-lag smoothing based on a one-step forward predictor and an L-step backward sweep, with L being the fixed lag, is also considered. It is shown that despite the greater complexity of the model used in the algorithms proposed, for L>30 the computational requirements are very similar to those of the alternate method