Total least squares modelling of cardiovascular time series

Cardiovascular time series are often affected by noise and contain components generated by different physiological sources. Least squares (LS) modelling is a powerful tool to identify these components but it provides biased estimates when the input measurements are noisy. The total least squares (TLS) model is appropriate when noise is present in all the measures. If the noise is additive, zero-mean, independent and white, TLS method results in asymptotically unbiased, consistent estimates. The authors applied the TLS method to the following applications obtaining good results: impulsive response estimation of the transfer function which relates the respiratory sinus arrhythmia with the respiratory activity; estimation of oscillatory components in RR-interval time series, cancelling of the respiratory component in the RR-interval time series. A comparison with the LS method, performed on simulated signals, showed a better impulsive response estimation and a higher resolution frequency estimate also in a highly nonstationary environment.