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Cardiovascular signals such as arterial blood pressure (ABP), pulse oximetry (POX), and intracranial pressure (ICP) contain useful information such as heart rate, respiratory rate, and pulse pressure variation (PPV). We present a novel state-space model of cardiovascular signals and describe how it can be used with the extended Kalman filter (EKF) to simultaneously estimate and track many cardiovascular parameters of interest using a unified statistical approach. We analyze data from four databases containing cardiovascular signals and present representative examples intended to illustrate the versatility, accuracy, and robustness of the algorithm. Our results demonstrate the ability of the algorithm to estimate and track several clinically relevant features of cardiovascular signals. We illustrate how the algorithm can be used to elegantly solve several actively researched and clinically significant problems including heart and respiratory rate estimation, artifact removal, pulse morphology characterization, and PPV estimation.