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We describe a novel model-based approach to estimate cardiac output (CO) and total peripheral resistance (TPR) continuously from peripheral arterial blood pressure (ABP) waveforms. Our method exploits the intra-beat and inter-beat variability in ABP to estimate the lumped time constant of a beat-to-beat averaged Windkessel model of the arterial tree, from which we obtain an uncalibrated estimate of CO. To estimate absolute CO, we determine the lumped arterial compliance using calibration data, and assuming either constant or state-dependent compliance. We applied our method to a porcine data set in which stroke volume was measured with an ultrasonic flowmeter. We obtain root-mean-square normalized errors of 11-13% across all pigs, lower than those obtained on the same data set using various other estimation methods. The CO estimates, and TPR estimates derived from them track intravenous drug infusions quite closely.