A note on Kalman Filter

The Kalman Filter commonly employed by control engineers and other physical scientists has been successfully used in such diverse areas as the processing of signals in aerospace tracking and underwater sonar, and statistical quality control. More recently, it has been used in some nonengineering applications such as short-term forecasting, time series, survival analysis, and so on. In all of these situations, we have a set of equations governing the true state of a system and another set connecting the observations made at any given time on the system with its true state. The problem is that of predicting the true state of the system at any given time point based on available observations. The solution proposed in the vast literature of the subject depends on the assumptions made on the initial state of the system. In this paper, a method that is independent of the initial state is proposed. This is useful when the a priori information on the initial state is not available. The method is also applicable when some observations are missing.