Signal processing in movement analysis (a state-space approach)

Abstract Signal processing techniques in movement analysis (MA) are a pre-requisite for further processing of MA data and can heavily affect the reliability of these latter results. In this paper, a brief review of classical digital signal processing techniques used in MA will be outlined, but emphasis will be given to a particular class of methods based on the state-space approach and in particular on the application of Kalman filtering theory. It will be shown the use of these techniques for the solution of linear and non-linear filtering problems such as those, respectively, relative to the numerical smoothing/differentiation of noisy signals and relative to the filtering of multiple displacement data subject to kinematic constraints.

[1]  H R Busby,et al.  Smoothing noisy data using dynamic programming and generalized cross-validation. , 1988, Journal of biomechanical engineering.

[2]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[3]  W. Tsang,et al.  Identifiability of unknown noise covariance matrices for some special cases of a linear, time-invariant, discrete-time dynamic system , 1981 .

[4]  L. Jennings,et al.  On the use of spline functions for data smoothing. , 1979, Journal of biomechanics.

[5]  Peter Craven,et al.  Smoothing noisy data with spline functions , 1978 .

[6]  H. Woltring On optimal smoothing and derivative estimation from noisy displacement data in biomechanics , 1985 .

[7]  L. Jetto,et al.  Reliable in vivo estimation of the instantaneous helical axis in human segmental movements , 1990, IEEE Transactions on Biomedical Engineering.

[8]  Herman J. Woltring,et al.  A fortran package for generalized, cross-validatory spline smoothing and differentiation , 1986 .

[9]  Michael D. Lesh,et al.  A Gait Analysis Subsystem for Smoothing and Differentiation of Human Motion Data , 1979 .

[10]  L. Jetto,et al.  Low a priori statistical information model for optimal smoothing and differentiation of noisy signals , 1994 .

[11]  G. Wood Data smoothing and differentiation procedures in biomechanics. , 1982, Exercise and sport sciences reviews.

[12]  C L Vaughan,et al.  Smoothing and differentiation of displacement-time data: an application of splines and digital filtering. , 1982, International journal of bio-medical computing.

[13]  P. Bélanger Estimation of noise covariance matrices for a linear time-varying stochastic process , 1972, Autom..

[14]  P. Dierckx,et al.  Calculation of derivatives and Fouriercoefficients of human motion data, while using spline functions. , 1979, Journal of biomechanics.

[15]  A. Jazwinski Stochastic Processes and Filtering Theory , 1970 .

[16]  J. Cullum Numerical Differentiation and Regularization , 1971 .

[17]  G. Ferrigno,et al.  Comparison between the more recent techniques for smoothing and derivative assessment in biomechanics , 1992, Medical and Biological Engineering and Computing.

[18]  S. Iglehart,et al.  Estimation of a dispersion parameter in discrete Kalman filtering , 1974 .

[19]  V. A. Morozov,et al.  Methods for Solving Incorrectly Posed Problems , 1984 .

[20]  David A. Winter,et al.  Biomechanics and Motor Control of Human Movement , 1990 .

[21]  Tony T. Lee A direct approach to identify the noise covariances of Kalman filtering , 1980 .

[22]  D. Winter Biomechanics of Human Movement , 1980 .

[23]  H Hatze,et al.  The use of optimally regularized Fourier series for estimating higher-order derivatives of noisy biomechanical data. , 1981, Journal of biomechanics.

[24]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[25]  A Pedotti,et al.  A general computing method for the analysis of human locomotion. , 1975, Journal of biomechanics.

[26]  J C Pezzack,et al.  An assessment of derivative determining techniques used for motion analysis. , 1977, Journal of biomechanics.

[27]  D A Winter,et al.  Measurement and reduction of noise in kinematics of locomotion. , 1974, Journal of biomechanics.

[28]  H. Lanshammar On precision limits for derivatives numerically calculated from noisy data. , 1982, Journal of biomechanics.

[29]  B. Tapley,et al.  Adaptive sequential estimation with unknown noise statistics , 1976 .

[30]  L. Jetto,et al.  A new algorithm for the sequential estimation of the regularization parameter in the spline smoothing problem , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[31]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[32]  B. Fregly,et al.  A solidification procedure to facilitate kinematic analyses based on video system data. , 1995, Journal of biomechanics.

[33]  Bengt Carlsson,et al.  Optimal differentiation based on stochastic signal models , 1991, IEEE Trans. Signal Process..

[34]  Håkan Lanshammar,et al.  ENOCH - An Integrated system for measurement and analysis of human gait , 1977 .

[35]  Bengt Carlsson Digital differential filters and model based fault detection , 1990 .

[36]  G. Ferrigno,et al.  Technique for the evaluation of derivatives from noisy biomechanical displacement data using a model-based bandwidth-selection procedure , 1990, Medical and Biological Engineering and Computing.

[37]  E. M. Roberts,et al.  Fitting biomechanical data with cubic spline functions. , 1976, Research quarterly.

[38]  S. Fioretti,et al.  Numerical differentiation in movement analysis: how to standardise the evaluation of techniques , 1993, Medical and Biological Engineering and Computing.

[39]  P. Bloomfield,et al.  Numerical differentiation procedures for non-exact data , 1974 .

[40]  R. Mehra On the identification of variances and adaptive Kalman filtering , 1970 .

[41]  L. Jetto,et al.  Accurate derivative estimation from noisy data: a state-space approach , 1989 .