State filtering and parameter estimation for Hodgkin-Huxley model

This paper is concerned with state filtering and the parameter estimation problem of noisy Hodgkin-Huxley neuronal model. The Cubature Kalman filter is applied to solve the joint estimation problem as an effective means of dealing with system noise and observation noise. The proposed state filtering method is based on the only measurable variable - membrane potential. In addition, the method is applicable to the case when the parameters are unknown. In this case, the uncertain parameters are also estimated. Finally, simulation results are given to show the performance and advantages of the proposed scheme.

[1]  Donghai Li,et al.  Nonlinear-estimator-based robust synchronization of Hodgkin-Huxley neurons , 2008, Neurocomputing.

[2]  Richard J. Fitzgerald.  Phase Synchronization May Reveal Communication Pathways in Brain Activity , 1999 .

[3]  Eugene M. Izhikevich,et al.  Which model to use for cortical spiking neurons? , 2004, IEEE Transactions on Neural Networks.

[4]  J. Fell,et al.  The role of phase synchronization in memory processes , 2011, Nature Reviews Neuroscience.

[5]  Kaspar Anton Schindler,et al.  Synchronization and desynchronization in epilepsy: controversies and hypotheses , 2012, The Journal of physiology.

[6]  Leonid L Rubchinsky,et al.  Intermittent neural synchronization in Parkinson’s disease , 2011, Nonlinear Dynamics.

[7]  S. Feng,et al.  Estimation precision comparison of Cubature Kalman filter and Unscented Kalman filter , 2013 .

[8]  Bin Deng,et al.  Parameter estimation in Hodgkin-Huxley model with adaptive method , 2011, 2011 4th International Conference on Biomedical Engineering and Informatics (BMEI).

[9]  Ghanim Ullah,et al.  Tracking and control of neuronal Hodgkin-Huxley dynamics. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  S. Haykin.  Kalman Filtering and Neural Networks , 2001 .

[11]  S. Haykin,et al.  Cubature Kalman Filters , 2009, IEEE Transactions on Automatic Control.

[12]  Wei-Ping Zhu,et al.  Joint estimation of states and parameters of Hodgkin-Huxley neuronal model using Kalman filtering , 2014, Neurocomputing.

[13]  Marco Wiering,et al.  2011 INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS (IJCNN) , 2011, IJCNN 2011.

[14]  Michele Pace,et al.  Global parameter estimation of an Hodgkin-Huxley formalism using membrane voltage recordings: Application to neuro-mimetic analog integrated circuits , 2012, Neurocomputing.

[15]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[16]  Jianfeng Feng,et al.  A Self-Organizing State-Space-Model Approach for Parameter Estimation in Hodgkin-Huxley-Type Models of Single Neurons , 2011, PLoS Comput. Biol..