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The derivative of the solution of the Riccati matrix differential equation is described in this correspondence. Extensive use is made of the calculus of Vetter [8] and the formula for the derivative of the exponential matrix [5]. Additionally the differentiation of partitioned matrices and the differentiation with respect to a symmetric matrix are discussed. Application is made to the sensitivity analysis of optimal estimation systems.
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John Brewer (1977) studied this question.
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