THE PHILOSOPHY, PRINCIPLES, AND PRACTICE OF KALMAN FILTER SINCE ANCIENT TIMES TO THE PRESENT IN ASTRONAUTICS

摘要

The conceptual basis for the ubiquitous Kalman filter in estimation theory (ET) can be traced since ancient times. Its progress is similar to any physical theory moving randomly across intuitive beginning, applications or experiments, and mathematical framework. The conceptual basis for the Kalman filter is the triplet of change, capture, and correct. Similar to many other discoveries its development has gone through controversies of priority as stated by Stigler, Arnold, Berry, or Whitehead laws. The reason being a large number of competent people are working around the same time and concepts float like gas molecules, condense, and finally crystallize. The connection of ET in mythological, medieval, or modern periods with celestial objects is quite interesting. The ancient Indian astronomers since 500 AD updated the parameters to predict the position of celestial objects for timing their Vedic rituals, the asteroid Ceres sighted by Piazzi on the first day of 1801 tracked for 41 days and subsequently lost was helped by Gauss to be sighted on the last day of that year, and during mid twentieth century the formulation by Kalman helped the Apollo project to the Moon. Presently the scale and magnitude of many difficult and interesting problems it has been able to handle could not have been contemplated by ancient Indian astronomers, Gauss or Kalman. There are many interesting perspectives in which the Kalman filter can be understood. One is as a sequential statistical analysis of a random process. Another is it is a recursive least squares together with evolving system dynamics between measurements. The unpretentious splitting of states and measurements, and switching between the dynamical evolution and update using the measurements leads to interesting possibilities like 'wholes are more than the sum of their parts' as stated by Minsky. Typical applications in astronautics include target tracking, evolution of the space debris scenario, fusion of GPS and INS data, study of the tectonic plate movements, and atmospheric data assimilation. However in spite of its attractive nature the design of a Kalman filter depends on the difficult tuning of the initial state, process, and measurement noise covariances. The paper briefly discusses some well known variants of the basic filter formulation. Finally an analogy of the filter with examples from science and society and the lessons they provide are also given.