A survey of recursive algorithms for the solution of the discrete time Riccati Equation Original Research Article

The Riccati Equation plays a fundamental role in many fields of mathematics, science and engineering. Its solution constitutes an integral prerequisite to the solution of important problems in the above fields. Due to the importance of the Riccati Equation, there exists considerable literature on its algebraic as well as algorithmic solution. A very large number of those studies are devoted to the continuous time Riccati Equation. In this paper we present a survey of classical as well as more recent recursive algorithms that solve the discrete time Riccati Equatbn emanating from the Kaiman Filter as well as from the Lainiotis Filter equations either using per step calculations or the doubling principle. It is established that these algorithms converge fast and are numerically stable.