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.