The heart rate variability (HRV) signal represents one of the most promising markers of autonomic activity. However, the significance and meaning of the many different measures of the HRV are more complex than generally appreciated. The analysis of HRV shows that the structure generating the signal is not simply linear, but also involves nonlinear contributions. This article proposes an enhancement of these HRV components through the application of a noise-reduction method in state space. The method works directly in an embedding space and corrects noisy trajectories, projecting them onto local subspaces that are a good approximation of the original surface of the system attractor. At any iteration, the procedure returns a new time series with the relevant amount of subtracted noise. An empirical criterion, originally proposed, estimates the optimum iteration number to reach a good result in terms of signal-to-noise ratio. Ultimately, our goal is to verify a possible improvement of the diagnostic and prognostic power of HRV analysis through the use of new nonlinear approaches that appear as a promising tool in the early identification of dangerous cardiovascular events.