Time-varying analysis of heart rate variability signals with a Kalman smoother algorithm

A time-varying parametric spectrum estimation method for analysing non-stationary heart rate variability signals is presented. As a case study, the dynamics of heart rate variability during an orthostatic test is examined. In this method, the non-stationary signal is first modelled with a time-varying autoregressive model and the model parameters are estimated recursively with a Kalman smoother algorithm. The benefit of using the Kalman smoother is that the lag error present in a Kalman filter, as well as in all other adaptive filters, can be avoided. The spectrum estimates for each time instant are then obtained from the estimated model parameters. Statistics of the obtained spectrum estimates are derived using the error propagation principle. The obtained spectrum estimates can further be decomposed into separate components and, thus, the time variation of low- and high-frequency components of heart rate variability can be examined separately. By using the presented method, high resolution time-varying spectrum estimates with no lag error can be produced. Other benefits of the method are the straightforward procedure for evaluating the statistics of the spectrum estimates and the option of spectral decomposition.