An Application of the Kalman Filter in Geoastronomy

This paper is presented as a contribution to the Symposium in honour of my distinguished colleague and long-time friend, S.K. Srinivasan. My intention in this paper is to provide a brief overview of an application of stochastic theory to geosastronomy, an area which Professor Srinivasan has not touched, but one in which there have been some remarkable advances in the past decade. Stochastic processes are inextricably mixed up in the recordings of signals from celestial bodies which constitute the basic raw material of geoastronomy. The Kalman filter (Kalman [1960], Kalman and Bucy [1960]), developed as an efficient method of including in an estimation process parameters whose values change during a period over which data are collected, uses stochastic-process models to predict their changes between epochs of observation. The use of the Kalman filter in extracting results of astonishingly high accuracy from the data contaminated by the stochastic “noise” is detailed in a recent paper by Herring et al. [1990], on which the present outline is largely based. The kinds of results that can be obtained relating to the surface and the interior of the Earth are illustrated herein by a few examples.