We present a novel method for the blind reconstruction of the cardiac sympathetic nerve activity (CSNA) in the low-frequency (LF) band (0.04-0.15 Hz) using only heart rate and arterial blood pressure. The originality of the method consists in the application of blind source separation techniques to obtain an observer of CSNA. We show how this observer can be deduced from a linear model of the cardiovascular system by introduction of the fundamental assumptions about the independence of the cardiac sympathetic an parasympathetic outflow. In cardiovascular applications, the reliability of the observer has been assessed by verification of the fundamental assumption for the given data. A primer qualitative validation has been performed using the muscle sympathetic nerve activity as an indirect indicator of CSNA. Very satisfying and promising results have been obtained. Moreover, we have performed quantitative validations of the observer in various experimental conditions known to elicit selectively cardiac sympathetic or parasympathetic response. The experimental conditions include a supine-to-60 degrees tilt test, indirect sympathetic stimulation/inhibition by medication, and sympathetic stimulation by isometric handgrip. We show that the observer allows to highlight changing levels of the cardiac sympathetic activity in the LF band in all these experimental conditions.