, Extract the inter-step segments (Leap Periods)

, Create a signal as the concatenation of the extracted inter-step segments

, Compute the Discrete Fourier Transform on VGRF followed by a magnitude operator

, Perform Low-pass filtering to reduce noise variance

, Perform post-processing to remove processing distortions

, Perform spectral subtraction PSD_Filtered_VGRF = PSD_VGRF-PSD_noise

, Compute the Inverse Discrete Fourier Transform to the processed signal

R. Katiyar, Clinical Gait Data Analysis based on Spacio-Temporal Features, International Journal of Computer Science and Information Security, vol.VII, issue.II, pp.174-183, 2010.

A. Kharb, V. Saini, Y. K. Jain, and S. Dhiman, A Review of Gait Cycle and Its Parameters, International Journal of Computational Engineering and Management, vol.13, pp.78-83, 2011.

J. Richards, The Comprehensive Textbook of Biomechanics, 2018.

T. Marasovic, M. Cecic, and V. Zanchi, Analysis and Interpretation of Ground Reaction Forces in Normal Gait, WSEAS Transactions on Systems, vol.8, issue.9, pp.1105-1115, 2009.

J. W. Kim, H. J. Jang, D. H. Hwang, and C. Park, A Step, Stride and Heading Determination for the Pedestrian Navigation System, Journal of Global Positioning Systems, vol.3, pp.273-279, 2004.

M. W. Whittle, Gait Analysis: An Introduction, 2006.

W. Weber and E. Weber, Mechanik der menschlichen Gehwerkzeuge: eine anatomischphysiologische Untersuchung, vol.1, p.1836

M. A. Cappozzo, Tosi V. Marey and Muybridge: How modern biolocomotion analysis started, 1992.

R. Bongaardt and O. G. Meijer, Bernstein's Theory of Movement Behavior: Historical Development and Contemporary Relevance, Journal of Motor Behavior, vol.32, issue.1, pp.57-71, 2000.

H. Elftman, The measurement of the external force in walking, Science, vol.88, issue.2276, pp.152-153, 1938.

D. A. Winter, Overall principle of lower limb support during stance phase of gait, Journal of Biomechanics, vol.13, issue.11, pp.923-927, 1980.

G. Bronwyn, The Biomechanics of Equine Locomotion, The Athletic Horse, pp.266-281, 2014.

A. Belli, P. Bui, A. Berger, A. Geyssant, and J. Lacour, A treadmill ergometer for threedimensional ground reaction forces measurement during walking, Journal of Biomechanics, vol.34, pp.105-112, 2001.

D. Sutherland, The Evolution of Clinical Gait Analysis Part I: Kinesiological EMG, Gait and Posture, vol.14, pp.61-70, 2001.

M. Zanfir, M. Leordeanu, and C. Sminchisescu, The Moving Pose: An Efficient 3D Kinematics Descriptor, ICCV, 2013.

B. Bilney, M. Morris, and K. Webster, Concurrent related validity of the GAITRite® walkway system for quantification of the spatial and temporal parameters of gait, Gait & posture, vol.17, issue.1, pp.68-74, 2003.

J. H. Viitasalo and P. V. Komi, Signal characteristics of EMG with special reference to reproducibility of measurements, Acta Physiol Scand, vol.93, issue.4, pp.531-540, 1975.

A. Stefano, J. H. Burridge, V. T. Yule, and R. Allen, Effect of gait cycle selection on EMG analysis during walking in adults and children with gait pathology, Gait Posture, vol.20, issue.1, pp.92-101, 2004.

S. Bronner and A. Noah, Comparative abilities of Microsoft Kinect and Vicon 3D motion capture for gait, Journal of Medical Engineering & Technology, pp.1-7, 2014.

T. Owings and M. Grabiner, Measuring step kinematic variability on an instrumented treadmill: how many steps are enough?, Journal of Biomechanics, vol.36, issue.8, pp.1215-1218, 2003.

W. Herzog, B. Nigg, L. Read, and E. Olsson, Asymmetries in Ground Reaction Force Patterns in Normal Human Gait, Medicine and Science in Sports and Exercise, vol.21, issue.1, pp.110-114, 1989.

J. Bigouette, J. Simon, K. Liu, and C. Docherty, Altered Vertical Ground Reaction Forces in Participants With Chronic Ankle Instability While Running, J Athl Train, vol.51, issue.9, pp.682-687, 2016.

D. Padua and L. Distefano, Sagittal Plane Knee Biomechanics and Vertical Ground Reaction Forces Are Modified Following ACL Injury Prevention Programs, Sports Health, vol.1, issue.2, pp.165-173, 2009.

A. Coetsee, ANALYSIS OF THE VERTICAL GROUND REACTION FORCES IN SPORTS PARTICIPANTS WITH ADDUCTOR-RELATED GROIN PAIN: A COMPARISON STUDY, 2016.

A. Abbasi, H. Sadeghi, and M. Khaleghi, GROUND REACTION FORCES ATTENUATION IN SUPINATED AND PRONATED FOOT, ISBS Conference, 2008.

A. Tonazzini, Blind Source Separation Techniques for Detecting Hidden Texts and Textures in Document Images, International Conference Image Analysis and Recognition, 2004.

K. Prakash, Blind Source Separation for Speech Music and Speech Speech Mixtures, International Journal of Computer Applications, vol.110, issue.12, pp.40-43, 2015.

E. Visser, Speech enhancement using blind source separation and two-channel energy based speaker detection, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2003.

T. Heittola, Musical Instrument Recognition in Polyphonic Audio Using Source-Filter Model for Sound Separation, 10th International Society for Music Information Retrieval Conference, 2009.

C. Yu, Blind source separation based x-ray image denoising from an image sequence, Review of Scientific Instruments, vol.86, 2015.

P. Duhamel, Blind multivariable equalization, Proc. DSP, pp.13-16, 1997.

J. R. Treichler, Practical blind demodulators for high-order QAM signals, Proc. IEEE, vol.86, pp.1907-1926, 1998.

U. Madhow, Blind adaptive interference suppression for Direct-Sequence CDMA, Proc. IEEE, vol.86, pp.2049-2069, 1998.

S. Haykin, Unsupervised Adaptive Filtering, pp.13-112, 2000.

T. Lee, Independent Component Analysis: Theory and Applications, 1998.

A. K. Barros, A. Mansour, and N. Ohnishi, Removing artifacts from electrocardiographic signals using independent components analysis, Neurocomputing, vol.22, issue.1-3, pp.173-186, 1998.

S. Dodel, J. M. Herrmann, and T. Geisel, Localization of brain activity -Blind separation of fMRI data, Neurocomputing, vol.32, pp.71-708, 2000.

D. Kundur and D. Hatzinakos, Blind image deconvolution, IEEE Signal Processing Magazine, 1996.

U. R. Abeyratne, A. P. Petropulu, and J. M. Reid, Higher-order spectra based deconvolution of ultrasound images, IEEE Trans. Ultrasonics, Ferroelectrics, and Frequency Control, vol.42, issue.6, pp.1064-1095, 1995.

R. H. Bates, Astronomical speckle imaging, Physics Reports, vol.90, issue.4, pp.203-297, 1982.

, Advances in Neural Information Processing Systems 9, vol.9, 1996.

A. Hyvarinen, E. Oja, P. Hoyer, and J. Hurri, Image feature extraction by sparse coding and independent component analysis, Proc. ICPR, pp.1268-1273, 1998.

, Localisation etidentificationparlaquadricovariance, Traitement du Signal, vol.7, issue.5, pp.397-406, 1990.

, Higher-order narrow-band array processing, Proc. Int'l Sig. Proc. Wkshp on HigherOrder Statistics, 1991.

J. L. Lacoume, P. O. Amblard, and . Comon, Statistiquesd'OrdreSuperieurPourle Traitement du Signal, 1997.

R. Huez, D. Nuzillard, and A. Billat, Denoising using blind source separation for pyroelectric sensors, EURASIP J. Appl. Signal Processing, vol.2001, issue.1, pp.53-65, 2001.

L. Tong, R. Liu, V. C. Soonandy, and . Huang, Indeterminacyandidentifiabilityofblind identification, IEEE Trans. Circuits and Systems, vol.38, issue.5, pp.499-509, 1991.

C. Jutten and J. Karhunen, Advances in Nonlinear Blind Source Separation, Proc. of the, p.4

, Int. Symp. on Independent Component Analysis and Blind Signal Separation, vol.41, issue.2, 2003.

K. Zhang and A. Hyvarinen, On the Identifiability of the Post-Nonlinear Causal Model, pp.647-655, 2009.

Y. Deville, Matrix Factorization for Bilinear Blind Source Separation: Methods, Separability and Conditioning, 23rd European Signal Processing Conference (EUSIPCO), 2015.

A. Ziehe, M. Kawanabe, H. Stefan, and K. Muller, Blind Separation of Post-nonlinear Mixtures using Linearizing Transformations and Temporal Decorrelation, Journal of Machine Learning Research, vol.4, pp.1319-1338, 2003.

Y. Tan, Y. J. Wang, and J. M. Zurada, Nonlinear blind source separation using a radial basis function network, IEEE Transactions on Neural Networks, vol.12, issue.1, pp.124-134, 2001.

Z. Koldovsky, J. Malek, and P. Tichavski, Blind Speech Separation in Time-Domain Using BlockToeplitz Structure of Reconstructed Signal Matrices, INTERSPEECH, 2011.

V. Capdevielle, C. Servire, and J. L. Lacoume, Blind separation of wide-band sources in the frequency domain, vol.95, 1995.

C. Jutten and J. Herault, Blind separation of Sources, part I: An adaptive algorithm based on neuromimetic architecture, Signal Processing, vol.24, issue.1, pp.1-10, 1991.

J. Xi and J. P. Reilly, Blind separation and restoration of signals mixed in convolutive environment, ICASSP'97, 1997.

A. Belouchrani, K. Abed-meraim, J. F. Cardoso, and E. Moulines, A blind source separation technique using second-order statistics, IEEE Trans. Sig. Proc, vol.45, issue.2, pp.434-444, 1997.

E. Weinstein, M. Feder, and A. Oppenheim, Multichannel signal separation by decorrelation, IEEE Trans. Speech Audio Proc, vol.1, issue.4, pp.405-413, 1993.

S. Shamsunder and G. B. Giannakis, Multichannel blind signal separation and reconstruction, IEEE Trans. Speech, Audio Proc, vol.5, issue.6, pp.515-528, 1997.

A. Mansour, C. Jutten, and P. Loubaton, Subspace method for blind separation of sources and for a convolutive mixture model, Signal Processing VIII, Theories and Applications, pp.2081-2084, 1996.
URL : https://hal.archives-ouvertes.fr/hal-00802604

R. K. Prasad, H. Saruwatari, and K. Shikano, Problems in Blind Separation of Convolutive Speech Mixtures by Negentropy Maximization, IWAENC'03, 2003.

C. Jutten, L. Nguyen-thi, E. Dijkstra, E. Vittoz, and C. J. , Blind Separation of Sources: An Algorithm for Separation of Convolutive Mixtures, International Signal Processing Workshop, 1992.

C. Jutten and J. Herault, Blind Separation of Sources, part I: An adaptive Algorithm based on neuromimetic architecture, Signal Processing, vol.24, issue.1, pp.1-10, 1991.

A. J. Bell and T. J. Sejnowski, An information mzximization approach to blind separation and blind deconvolution, Neural Computation, vol.7, issue.6, pp.1129-1159, 1995.

L. Parra, C. Spence, and B. De-vries, Convolutive Source Separation with ML, ISIS'97, 1997.

J. F. Cardoso, Blind Signal Separation: Statistical Principles, Proc. IEEE, vol.9, pp.2009-2025, 1998.

L. Parra, C. Spence, and B. De-vries, Convolutive source separation and signal modeling with ML, ISIS'97, 1997.

R. H. Lambert and C. L. Nikias, Polynomial matrix whitening and application to the multichannel blind deconvolution problem, vol.3, pp.988-992, 1995.

K. Torkkola, Blind separation for audio signals -are we there yet?, ICA'99, 1999.

L. A. Lindgren and H. Broman, Source separation using a criterion based on second-order statistics, IEEE Trans. Sig. Proc, vol.46, issue.7, pp.1837-1850, 1998.

B. Yin and P. Sommen, Adaptive blind signal separation using a new simplified mixing model, ProRISC'99, 1999.

L. Parra and C. Spence, On-line convolutive source separation of non-stationary signals, IEEE J. VLSI Sig. Proc, vol.26, issue.1-2, pp.39-46, 2000.

P. Sommen and B. Yin, A new convolutive blind signal separation algorithm based on second order statistics using a simplified mixing model, 2000.

S. Shamsunder and G. Giannakkis, Multichannel blind signal separation and reconstruction, IEEE Trans. Speech. Audio Proc, vol.5, issue.6, pp.515-528, 1997.

K. Sabri, M. E. Badaoui, F. Guillet, and J. Morin, Cyclostationary modeling of ground reaction force signals, Signal Processing, vol.90, issue.4, pp.1146-1152, 2010.

K. Sabri, Cyclosparsity: A New Concept for Sparse Deconvolution, Global Journal of Computer Science and Technology: F Graphics & Vision, vol.14, issue.4, 2014.

T. Mei and F. Yin, Blind separation of convolutive mixtures by decorrelation, Signal Processing, vol.84, issue.12, pp.2297-2213, 2004.

D. Burnett, N. H. Campbell-kyureghyan, P. Ceritto, and P. Quesada, Symmetry of ground reaction forces and muscle activity in asymptomatic subjects during walking, sit-to-stand, and stand-to-sit tasks, Journal of Electromyography and Kinesiology, vol.21, issue.4, pp.610-615, 2011.

A. Singh and A. Thakur, Human gait analysis using wavelet denoising and total variation filtering, 2015.

G. Jang and T. Lee, A probabilistic approach to single channel blind signal separation, Advances in neural information processing, 2003.

T. Hermle, C. Schwarz, and M. Bogdan, Employing ICA and SOM for spike sorting of multielectrode recordings from CNS, Journal of Physiology, 2004.

R. G. Baraniuk and D. L. Jones, A signal-dependent time-frequency representation: optimal kernel design, IEEE Transactions on Signal Processing, vol.41, issue.4, pp.1589-1602, 1993.

M. Emresoy and P. Loughlin, Weighted least squares implementation of Cohen-Posch timefrequency distributions, IEEE Transactions on Signal Processing, vol.46, issue.3, pp.753-757, 1998.

, SAS, 2013.

S. Krishnan, R. M. Rangayyan, B. G. , and F. C. , Adaptive time-frequency analysis of knee joint vibroarthrographic signals for noninvasive screening of articular cartilage pathology, IEEE Transactions on Biomedical Engineering, vol.47, issue.6, pp.773-783, 2000.

Z. M. Hussain and B. Boashash, Adaptive Instantaneous Frequency Estimation of Multicomponent FM Signals Using Quadratic Time-Frequency Distributions, IEEE Transactions on Signal Processing, vol.50, issue.8, pp.1866-1876, 2002.

F. Berthommier and S. Choi, Evaluation of CASA and BSS models for subband cocktail-party speech separation, Proc. ICA, 2011.

B. Gao, W. Woo, and S. Dlay, Single-channel source separation using EMD-subband variable regularized sparse features, IEEE Transactions on Audio, Speech and Language Processing, vol.19, issue.4, pp.961-976, 2011.

B. Gao, Single channel blind source separation, 2011.

L. Pang and X. Deng, A SCBSS methodology for time-frequency overlapped signals using nonnegative matrix factorisation, International Journal of Electronics, vol.104, issue.4, pp.624-634, 2016.

W. Xu, X. Liu, and Y. Gong, Document Clustering based on non-negative matrix factorization, SIGIR'03, 2003.

J. Sivic, B. C. Russell, A. A. Efros, Z. A. , and W. T. Freeman, Discovering objects and their location in images, ICCV'05, 2005.

D. Soukup and I. Bajla, Robust Object Recognition under Partial Occlusions Using NMF, Computational Intelligence and Neuroscience, p.14, 2008.

M. Kalayeh, H. Idrees, and M. Shah, NMF-KNN: Image Annotation using Weighted Multi-view Non-negative Matrix Factrorization, CVPR'14, 2014.

J. Marial, F. Bach, J. Ponce, and G. Sapiro, Online Learning for Matrix Factorization and Sparse Coding, JMLR, pp.19-60, 2010.

R. Sandler and M. Lindenbaum, Nonnegative Matrix Factorization with Earth Mover's Distance Metric for Image Analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.33, issue.8, pp.1590-1602, 2011.

M. Berry, M. Browne, A. Langville, V. Pauca, and R. J. Plemmons, Algorithms and applications for approximate nonnegative matrix factorization, Computational Statistics and Data Analysis, vol.52, issue.1, pp.155-173, 2007.

V. Monga and M. Mihcak, Robust and Secure Image Hashing via Non-Negative Matrix Factorizations, IEEE Transactions on Information Forensics and Security, vol.2, issue.3, pp.376-390, 2007.

A. Cichocki, Noninvasive BCIs: Multiway Signal-Processing Array Decompositions, Computer, vol.41, issue.10, pp.34-42, 2008.

C. Damon, A. Liutkus, A. Gramfort, and S. Essid, Non-negative matrix factorization for singlechannel EEG artifact rejection, ICASSP'13, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00958775

N. Mohammadiha, P. Smaragdis, and A. Leijon, Supervised and Unsupervised Speech Enhancement Using Nonnegative Matrix Factorization, IEEE Transactions on Audio, Speech, and Language Processing, vol.21, issue.10, pp.2140-2151, 2013.

A. Ozerov and C. Fevotte, Multichannel Nonnegative Matrix Factorization in Convolutive Mixtures for Audio Source Separation, IEEE Transactions on Audio, Speech, and Language Processing, vol.18, issue.3, pp.550-563, 2010.

D. L. Sun and R. Mazumder, Non-negative matrix completion for bandwidth extension: A convex optimization approach, IEEE International Workshop on Machine Learning for Signal Processing, 2013.

A. Ozerov, C. Févotte, R. Blouet, and J. L. Durrieu, Multichannel nonnegative tensor factorization with structured constraints for user-guided audio source separation, ICASSP'11, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00564851

N. Bertin, R. Badeau, and E. Vincent, Enforcing Harmonicity and Smoothness in Bayesian NonNegative Matrix Factorization Applied to Polyphonic Music Transcription, IEEE Transactions on Audio, Speech, and Language Processing, vol.18, issue.3, pp.538-549, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00557088

C. Fevotte, N. Bertin, and J. Durrieu, Nonnegative Matrix Factorization with the ItakuraSaito Divergence: With Application to Music Analysis, Neural Computation, vol.21, issue.3, pp.793-830, 2009.

A. T. Cemgil, Bayesian Inference for Nonnegative Matrix Factorisation Models, Computational Intelligence and Neuroscience, p.17, 2009.

P. Hoyer, Non-negative Matrix Factorization with Sparseness Constraints, JMLR, pp.1457-1469, 2004.

D. E. Badawy, N. Q. Duong, and A. Ozerov, On-the-fly audio source separation, IEEE International Workshop on Machine Learning for Signal Processing, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01023221

N. Seichepine, S. Essid, C. Févotte, and O. Cappé, Soft Nonnegative Matrix Co-Factorization, IEEE Transactions on Signal Processing, vol.62, issue.22, pp.5940-5949, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01116863

D. Cai, X. He, J. Han, and T. S. Huang, Graph Regularized Nonnegative Matrix Factorization for Data Representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.33, issue.8, pp.1548-1560, 2011.

H. Lee and S. Choi, CUR+NMF for learning spectral features from large data matrix, IEEE International Joint Conference on Neural Networks, 2008.

C. Ding, T. Li, and W. Peng, Nonnegative Matrix Factorization and Probabilistic Latent Semantic Indexing: Equivalence, Chi-square Statistic, and a Hybrid Method, 21st National Conference on Artificial Intelligence and the 18th Innovative Applications of Artificial Intelligence Conference, 2006.

N. E. Huang, Hilbert-Huang transform and its applications, World Scientific, vol.16, 2014.

H. Pengju and C. Xiaomeng, A method for extracting fetal ECG based on EMD-NMF single channel blind source separation algorithm, Recent Innovations on Biomedical Engineering, vol.24, pp.17-26, 2016.

M. M. and K. Hirose, Single-Mixture Audio Source Separation by Subspace Decomposition of Hilbert Spectrum, IEEE Transactions on Audio, Speech, and Language Processing, vol.15, issue.3, pp.893-900, 2007.

A. Hayashi, H. Kameoka, T. Matsubayashi, and H. Sawada, Non-negative periodic component analysis for music source separation, 016 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA), 2016.