Adaptive estimation of noise covariance matrices in real-time preprocessing of geophysical data

Modern data acquisition systems record large volumes of data which are often not suitable for direct computer processing-a first stage of preprocessing (or data “editing”) is usually needed. In earlier work G. Noriega et al. (1992) the authors have developed an algorithm for multichannel data preprocessing, based on Kalman filtering and suitable for real-time geophysical data collection applications. The present work presents results of further investigations in the area of adaptive methods for estimation of noise covariance matrices Q and R, within the time-variant, fixed-lag Kalman filtering framework of the original problem. An algorithm is developed whereby asymptotically normal, unbiased, and consistent estimates are produced based on the correlation-innovations method introduced by Mehra (1970). This provides for direct estimation of R, and leads to a set of (n.m²) equations, not linearly independent, from which an appropriate subset must be selected to achieve estimation of up to (n.m) unknowns in Q. For the model considered (n=m.M, with M=4 the single-channel system order, and n and m the state and measurement vector dimensions respectively), an explicit algorithm has been developed far estimation of the (m.m) unknowns in Q, based on a least squares fit of a subset of the equations available. A new approach is also introduced to ensure positive-definiteness of the covariance matrices. Since the time variant nature of the model prevents direct application of the adaptive algorithm, a parallel implementation is proposed. A first processor implements the time variant Kalman filter, using estimates of Q and R updated every N_s samples. A second processor computes these estimates, operating on the output of a steady state Kalman filter based on a simplified model, in which data editing features, responsible for rendering the model time variant, have been removed. A spike/step removal filter, and a Riccati equation solver are also implemented by this second processor. Computational requirements are analyzed and compared against those of other approaches. Simulations demonstrate the performance of the method proposed, and show it to be superior to other alternatives. An example showing application to real geophysical data is also presented