Kalman Filtering: One Form Fits All - An Innovative, Pure Square Root Process

This paper addresses two problems associated with implementing Kalman Filters. The first problem concerns linear systems with colored/correlated plant and measurement noise processes. It is shown that by restructuring the system formulation, one convenient form of the Kalman Filter can be used to fit all colored/correlated noise cases. This formulation allows for direct measurement element processing even when its noise covariance matrix is non-diagonal. An extension of the restructuring process leads to an innovative, pure square root filtering process. The termn "pure" is used in the sense that both the time and measurement updating processes are elegant and simple without data compression which introduce round-off errors. The process formulates the square root using Set Matrices which contain the error covariance information.