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 pr eprocessing (or data ''editing'') is usually needed, In earlier work [ 5] the authors have developed an algorithm for multichannel data prepr ocessing, based on Kalman filtering and suitable for real-time geophys ical data collection applications, The present work presents results o f further investigations in the area of adaptive methods for estimatio n 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 e stimates are produced based on the correlation-innovations method intr oduced by Mehra (1970), This provides for direct estimation of R, and leads to a set of (n. m(2)) 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 measur ement vector dimensions respectively), an explicit algorithm has been developed for 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 mat rices, Since the time variant nature of the model prevents direct appl ication of the adaptive algorithm, a parallel implementation is propos ed, A first processor implements the time variant Kalman filter, using estimates of Q and R updated every N, samples, A second processor com putes these estimates, operating on the output of a steady state Kalma n 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 imp lemented by this second processor, Computational requirements are anal yzed and compared against those of other approaches, Simulations demon strate the performance of the method proposed, and show it to be super ior to other alternatives, An example showing application to real geop hysical data is also presented.