A Comparison Between Wiener Filtering, Kalman Filtering, and Deterministic Least Squares Estimation*

A bstract The least squares estimation procedures used in different disciplines can be classified in four categories: Wiener filtering, b. Autoregressive estimation, c. Kalman filtering, d. Recursive least squares estimation. The recursive least squares estimator is the time average form of the Kalman filter. Likewise, the autoregressive estimator is the time average form of the Wiener filter. Both the Kalman and the Wiener filters use ensemble averages and can basically be constructed without having a particular measurement realisation available. It follows that seismic deconvolution should be based either on autoregression theory or on recursive least squares estimation theory rather than on the normally used Wiener or Kalman theory. A consequence of this change is the need to apply significance tests on the filter coefficients. The recursive least squares estimation theory is particularly suitable for solving the time variant deconvolution problem.