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We present practical data assimilation algorithms based on the Kalman-Bucy filter (KBf) for combining satellite altimetry data with the nonlinear ocean circulation models. Data assimilation in such applications is computationally challenging because of the large dimensions of the state fields. Compared with the direct KBf, our KBf implementations provide computational savings of two orders of the magnitude of the linear dimension of the state field. We run twin experiments by interfacing our data assimilation algorithms with the NLOM, a nonlinear ocean circulation model developed at the Naval Research Laboratory.