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Using their previous observation that Hoo filtering coincides with Kalman filtering in Krein space the authors develop square-root arrays and Chandrasekhar recursions for Hoo filtering problems. The H/sup /spl infin// square-root algorithms involve propagating the indefinite square-root of the quantities of interest and have the property that the appropriate inertia of these quantities is preserved. For systems that are constant, or whose time-variation is structured in a certain way, the Chandrasekhar recursions allow a reduction in the computational effort per iteration from O(n/sup 3/) to O(n/sup 2/), where n is the number of states. The Hoo square-root and Chandrasekhar recursions both have the interesting feature that one does not need to explicitly check for the positivity conditions required of the H/sup /spl infin// filters. These conditions are built into the algorithms themselves so that an Hoo estimator of the desired level exists if, and only if, the algorithms can be executed.
Daniel Kressner, Stefano Massei
Assyr Abdulle, Giacomo Garegnani, Andrea Zanoni