Bayesian phase tracking for multiple pulse signals

The problem of estimating the frequencies and phases of two superimposed pulse-like, repetitive signals is considered. A method of solving this problem based on Bayesian (i.e., sequential Monte-Carlo or particle) filtering is presented. The particular problem motivating the technique is estimation of the rate of maternal and foetal heartbeats, although the technique is applicable to other domains. Aspects of the problem leading to the solution are discussed, and the performance of the proposed technique is presented on both simulated signals and real heart signals. The resulting frequency estimator has very similar functionality to a phase-locked loop, and so the performance measure used is the time to lose phase lock. The estimator is also analysed in terms of the posterior Cramer-Rao bound on the phase estimation accuracy.

[1]  J. McNames,et al.  Tracking Tremor Frequency in Spike Trains Using the Extended Kalman Filter , 2005, 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference.

[2]  G. Kitagawa.  Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models , 1996 .

[3]  Ee-Chien Chang,et al.  Blind separation of fetal ECG from single mixture using SVD and ICA , 2003, Fourth International Conference on Information, Communications and Signal Processing, 2003 and the Fourth Pacific Rim Conference on Multimedia. Proceedings of the 2003 Joint.

[4]  Ercan E. Kuruoglu,et al.  Astrophysical Source Separation Using Particle Filters , 2004, ICA.

[5]  Pierre-Olivier Amblard,et al.  Phase tracking: what do we gain from optimality? Particle filtering versus phase-locked loops , 2003, Signal Process..

[6]  B. Anderson,et al.  Frequency tracking of nonsinusoidal periodic signals in noise , 1990 .

[7]  Mark McGuinness,et al.  Arnold tongues in human cardiorespiratory systems. , 2004, Chaos.

[8]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[9]  Patrick E. McSharry,et al.  A dynamical model for generating synthetic electrocardiogram signals , 2003, IEEE Transactions on Biomedical Engineering.

[10]  C. Andrieu,et al.  A Particle Filter for Model Based Audio Source Separation , 2000 .

[11]  John A. Crowe,et al.  Does fractality in heart rate variability indicate the development of fetal neural processes , 2004 .

[12]  M. Godinez,et al.  On-line fetal heart rate monitor by phonocardiography , 2003, Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE Cat. No.03CH37439).

[13]  Khaled Assaleh,et al.  Extraction of Fetal Electrocardiogram Using Adaptive Neuro-Fuzzy Inference Systems , 2007, IEEE Transactions on Biomedical Engineering.

[14]  Zoltán Benyó,et al.  An advanced method in fetal phonocardiography , 2003, Comput. Methods Programs Biomed..

[15]  Jeffrey M. Hausdorff,et al.  Physionet: Components of a New Research Resource for Complex Physiologic Signals". Circu-lation Vol , 2000 .

[16]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[17]  Thomas B. Schön,et al.  Marginalized particle filters for mixed linear/nonlinear state-space models , 2005, IEEE Transactions on Signal Processing.

[18]  Z. Schuss,et al.  A Singular Perturbation Method for the Computation of the Mean First Passage Time in a Nonlinear Filter , 1982 .

[19]  Dan Svenstrup,et al.  Monte Carlo methods for dynamical systems , 2009 .

[20]  J. S. Sahambi,et al.  Separation Performance of ICA Algorithms on FECG and MECG Signals Contaminated by Noise , 2004, AACC.

[21]  Ben-Zion Bobrovsky,et al.  Mean time to loose lock of phase tracking by particle filtering , 2006, Signal Process..

[22]  Jun S. Liu,et al.  Sequential Monte Carlo methods for dynamic systems , 1997 .

[23]  Dirk Callaerts,et al.  Comparison of SVD methods to extract the foetal electrocardiogram from cutaneous electrode signals , 1990, Medical and Biological Engineering and Computing.

[24]  A. K. Barros,et al.  FETAL HEART RATE VARIABILITY EXTRACTION BY FREQUENCY TRACKING , 2001 .

[25]  Carlos H. Muravchik,et al.  Posterior Cramer-Rao bounds for discrete-time nonlinear filtering , 1998, IEEE Trans. Signal Process..

[26]  S. Godsill,et al.  Multi-Object Tracking of Sinusoidal Components in Audio with the Gaussian Mixture Probability Hypothesis Density Filter , 2007, 2007 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics.

[27]  Nando de Freitas,et al.  Fast particle smoothing: if I had a million particles , 2006, ICML.

[28]  Nikos D. Sidiropoulos,et al.  Optimal Particle Filters for Tracking a Time-Varying Harmonic or Chirp Signal , 2008, IEEE Transactions on Signal Processing.

[29]  Neil J. Gordon,et al.  Editors: Sequential Monte Carlo Methods in Practice , 2001 .

[30]  Michael K. Pitt,et al.  Auxiliary Variable Based Particle Filters , 2001, Sequential Monte Carlo Methods in Practice.

[31]  D. T. Kaplan,et al.  Fetal ECG extraction with nonlinear state-space projections , 1998, IEEE Transactions on Biomedical Engineering.

[32]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[33]  Simon J. Godsill,et al.  On sequential simulation-based methods for Bayesian filtering , 1998 .

[34]  Hasan Al-Nashash,et al.  A novel technique for the extraction of fetal ECG using polynomial networks , 2005, IEEE Transactions on Biomedical Engineering.

[35]  William Fitzgerald,et al.  A Bayesian approach to tracking multiple targets using sensor arrays and particle filters , 2002, IEEE Trans. Signal Process..

[36]  Allan Kardec Barros,et al.  Heart instantaneous frequency (HIF): an alternative approach to extract heart rate variability , 2001, IEEE Transactions on Biomedical Engineering.

[37]  Michael Isard,et al.  Partitioned Sampling, Articulated Objects, and Interface-Quality Hand Tracking , 2000, ECCV.

[38]  J.H. Manton,et al.  A Bayesian approach to blind source recovery , 2004, Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004..

[39]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.

[40]  Olivier Sibony,et al.  Fetal electrocardiogram extraction based on non-stationary ICA and wavelet denoising , 2003, Seventh International Symposium on Signal Processing and Its Applications, 2003. Proceedings..

[41]  Shahriar Negahdaripour,et al.  A new method for the extraction of fetal ECG from the composite abdominal signal , 2000, IEEE Transactions on Biomedical Engineering.