A ballistocardiograph records the mechanical activity of the heart. We present a novel algorithm for the detection of individual heart beats and beat-to-beat interval lengths in ballistocardiograms (BCGs) from healthy subjects. An automatic training step based on unsupervised learning techniques is used to extract the shape of a single heart beat from the BCG. Using the learned parameters, the occurrence of individual heart beats in the signal is detected. A final refinement step improves the accuracy of the estimated beat-to-beat interval lengths. Compared to many existing algorithms, the new approach offers heart rate estimates on a beat-to-beat basis. The agreement of the proposed algorithm with an ECG reference has been evaluated. A relative beat-to-beat interval error of 1.79% with a coverage of 95.94% was achieved on recordings from 16 subjects.

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Abstract-Many methods have been developed for spectral analysis of irregularly sampled data. Currently, popular methods such as Lomb-Scargle and resampling tend to be biased at higher frequencies. Slotting methods fail to consistently produce a spectrum that is positive for all frequencies. In this paper, a new estimator is introduced that applies the Burg algorithm for autoregressive spectral estimation to unevenly spaced data. The new estimator can be perceived as searching for sequences of data that are almost equidistant, and then analyzing those sequences using the Burg algorithm for segments. The estimated spectrum is guaranteed to be positive. If a sufficiently large data set is available, results can be accurate up to relatively high frequencies.

Abstract-Order-selection criteria for vector autoregressive (AR) modeling are discussed. The performance of an order-selection criterion is optimal if the model of the selected order is the most accurate model in the considered set of estimated models: here vector AR models. Suboptimal performance can be a result of underfit or overfit. The Akaike information criterion (AIC) is an asymptotically unbiased estimator of the Kullback-Leibler discrepancy (KLD) that can be used as an order-selection criterion. AIC is known to suffer from overfit: The selected model order can be greater than the optimal model order. Two causes of overfit are finite sample effects and asymptotic effects. As a consequence of finite sample effects, AIC underestimates the KLD for higher model orders, leading to overfit. Asymptotically, overfit is the result of statistical variations in the order-selection criterion.To derive an accurate order-selection criterion, both causes of overfit have to be addressed. Moreover, the cost of underfit has to be taken into account. The combined information criterion (CIC) for vector signals is robust to finite-sample effects and has the optimal asymptotic penalty factor. This penalty factor is the result of a tradeoff of underfit and overfit. The optimal penalty factor depends on the number of estimated parameters per model order. The CIC is compared to other criteria such as the AIC, the corrected Akaike information criterion (AICc), and the consistent minimum description length (MDL).