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We introduce a patient- and time-specific technique to estimate the clinically more relevant aortic pressure (AP) waveform and beat-to-beat relative changes in cardiac output (CO) from multiple peripheral artery pressure (PAP) waveforms distorted by wave reflections. The basic idea of the technique is to first estimate the AP waveform by applying a new multichannel blind system identification method that we have developed (rather than the conventional generalized transfer function) to the PAP waveforms and then estimate the beat-to-beat proportional CO by fitting a Windkessel model to the estimated waveform in which wave distortion should be attenuated. We present an evaluation of the technique with respect to four swine datasets including simultaneous measurements of two peripheral AP waveforms, a reference AP waveform, and reference aortic flow probe CO during diverse hemodynamic interventions. Our results show an overall AP waveform error of 3.5 mmHg and an overall beat-to-beat CO error of 12.9% (after a single CO calibration in each animal). These estimation errors represent substantial improvements compared to those obtained with several alternative PAP waveform analysis techniques. With further successful testing, the new technique may ultimately be employed for automated and less invasive monitoring of central hemodynamics in various cardiovascular patients.