square root householder subspace tracking a class of singular value decomposition svd type subspace trackers based on the overdetermined row householder principle is introduced these algorithms are maximally fast with a dominant operations count of 3nr multiplications per time update they can be regarded as square root forms of previously introduced conventional fast subspace trackers and offer interesting features such as perfectly orthonormal basis estimates lowest dynamic range requirements and highest numerical robustness and stability several variants of the method are proposed and studied experimentally

estimating the covariance matrix by signal subspace averaging an efficient algorithm is presented for estimating a covariance matrix consisting of a low rank signal term and a full rank noise term known apart from a scalar factor for each sample of the vector of sensor outputs the algorithm approximates in the least squares sense a rank one update of the covariance matrix under the side condition that the rank of the signal term remains bounded if the model noise is spatially colored the least squares approximation is preceded by spatial prewhitening it is shown that if the rank of the signal term is small compared to the number of sensors then the proposed algorithm requires substantially less computational work than conventional averaging some simulation results are included indicating that the proposed algorithm reduces the variance of some commonly used spectral estimators in off target directions without impairing their detection and resolution properties

adi scheme of a nonstandard fdtd method and its numerical properties an alternating direction implicit adi scheme for a nonstandard ns finite difference time domain fdtd method is proposed the ns fdtd method is derived by analyzing the dispersion relation two different groups of update coefficients are used to update the electric field and magnetic field respectively the dispersion property of the ns method is similar with that of the standard higher order method though it is only second order accurate in the space domain the total number of nonzero update coefficients for this method is fewer than that of the latter this small stencil property can be used to reduce computational burden in implicit formulation of this method the one step leapfrog adi scheme is adopted to examine this idea the detailed update equations of this adi scheme are derived the dispersion and stability properties are also analyzed and compared with the corresponding standard one the results show that the computational efficiency of the proposed method is higher than that of the standard one

on convergence of the nic algorithm for subspace computation the novel information criterion nic algorithm was developed by miao and hua in 1998 for fast adaptive computation of the principal subspace of a vector sequence the nic algorithm is as efficient computationally as the past method which was devised by yang in 1995 and also has an attractive orthonormal property although all available evidence suggests that the nic algorithm converges to the desired solution for any fixed leakage factor between zero and one a complete proof or disproof has not been found except for an arbitrarily small leakage factor this paper presents this long standing open problem with a discussion of what is known so far the results shown in this paper provide a new insight into the orthonormal property of the nic algorithm at convergence

validation of the greater trochanter method with radiographic measurements of frontal plane hip joint centers and knee mechanical axis angles and two other hip joint center methods several motion capture methods exist for predicting hip joint centers hjc these methods include regression models functional joints and projections from greater trochanters while regression and functional methods have been compared to imaging techniques the troch method has not been previously validated the purpose of this study was to compare frontal plane hjcs and knee mechanical axis angles estimated using the greater trochanter method with a regression bell and a functional method against those obtained using radiographs thirty five participants underwent a long standing anteroposterior radiograph and performed static and functional motion capture trials the bell functional and trochanter hjcs were constructed to predict mechanical axes and compare hjc locations one way repeated measures anovas were used to compare mechanical axes and hjc locations estimated by motion capture methods and measured using radiographs p 0 05 all methods overestimated mechanical axes compared to radiographs 2 but were not different mediolateral hjc locations and inter hjc widths were similar between methods however inter hjc widths were underestimated average 3 7 compared to radiographs the bell hjc was more superior and anterior to both functional and trochanter methods the trochanter hjc was more posterior to both methods the bell method outperformed the other methods in leg length predictions compared to radiographs although differences existed between methods all frontal plane hjc location differences were 1 7 cm this study validated the trochanter hjc prediction method mediolaterally and vertically with small respective correction factors therefore all hjc methods seem to be viable in predicting mechanical axes and frontal plane hjc locations compared with radiographs

fdtd local grid with material traverse often a finite difference time domain fdtd calculation requires a relatively higher mesh resolution in only small subvolumes of the total mesh space by locally applying finer grids local grids to these volumes the necessary resolution can be obtained computation time and memory requirements may be far less than for an fdtd space with the smaller mesh resolution throughout in many situations it is important that these local grids function when materials traverse the main grid local grid mg lg boundary surfaces since the volumes that require local grids may not be isolated in a homogeneous medium a local grid method which allows dielectric and or conducting materials to traverse the boundaries is developed three different fdtd problems that utilize the local grid method are used as validation tests results are compared with uniform mesh fdtd solutions

statistical shape modelling versus linear scaling effects on predictions of hip joint centre location and muscle moment arms in people with hip osteoarthritis abstract marker based dynamic functional or regression methods are used to compute joint centre locations that can be used to improve linear scaling of the pelvis in musculoskeletal models although large errors have been reported using these methods this study aimed to investigate if statistical shape models could improve prediction of the hip joint centre hjc location the inclusion of complete pelvis imaging data from computed tomography ct was also explored to determine if free form deformation techniques could further improve hjc estimates mean euclidean distance errors were calculated between hjc from ct and estimates from shape modelling methods and functional and regression based linear scaling approaches the hjc of a generic musculoskeletal model was also perturbed to compute the root mean squared error rmse of the hip muscle moment arms between the reference hjc obtained from ct and the different scaling methods shape modelling without medical imaging data significantly reduced hjc location error estimates 11 4 3 3 mm compared to functional 36 9 17 5 mm p

lower extremity control during turns initiated with and without hip external rotation the pirouette turn is often initiated in neutral and externally rotated hip positions by dancers this provides an opportunity to investigate how dancers satisfy the same mechanical objectives at the whole body level when using different leg kinematics the purpose of this study was to compare lower extremity control strategies during the turn initiation phase of pirouettes performed with and without hip external rotation skilled dancers n 5 performed pirouette turns with and without hip external rotation joint kinetics during turn initiation were determined for both legs using ground reaction forces grfs and segment kinematics hip muscle activations were monitored using electromyography using probability based statistical methods variables were compared across turn conditions as a group and within dancer despite differences in grfs and impulse generation between turn conditions at least 90 of each grf was aligned with the respective leg plane a majority of the net joint moments at the ankle knee and hip acted about an axis perpendicular to the leg plane however differences in shank alignment relative to the leg plane affected the distribution of the knee net joint moment when represented with respect to the shank versus the thigh during the initiation of both turns most participants used ankle plantar flexor moments knee extensor moments flexor and abductor moments at the push leg s hip and extensor and abductor moments at the turn leg s hip representation of joint kinetics using multiple reference systems assisted in understanding control priorities

fast rank adaptive subspace tracking and applications high computational complexity and inadequate parallelism have deterred the use of subspace based algorithms in real time systems we proposed a new class of fast subspace tracking fst algorithms that overcome these problems by exploiting the matrix structure inherent in multisensor processing these algorithms simultaneously track an orthonormal basis for the signal subspace and preserve signal eigenstructure information while requiring only o nr operations per update where n is the number of channels and r is the effective rank because of their low computational complexity these algorithms have applications in both recursive and block data processing because they preserve the signal eigenstructure as well as compute an orthonormal basis for the signal subspace these algorithms may be used in a wide range of sensor array applications including bearing estimation beamforming and recursive least squares we present a detailed description of the fst algorithm and its rank adaptive variation ra fst as well as a number of enhancements we also demonstrate the fst s rapid convergence properties in a number of application scenarios

bi iterative least square method for subspace tracking subspace tracking is an adaptive signal processing technique useful for a variety of applications in this paper we introduce a simple bi iterative least square bi ls method which is in contrast to the bi iterative singular value decomposition bi svd method we show that for subspace tracking the bi ls method is easier to simplify than the bi svd method the linear complexity algorithms based on bi ls are computationally more efficient than the existing linear complexity algorithms based on bi svd although both have the same performance for subspace tracking a number of other existing subspace tracking algorithms of similar complexity are also compared with the bi ls algorithms

analytical study of the effects of soft tissue artefacts on functional techniques to define axes of rotation abstract the accurate location of the main axes of rotation aor is a crucial step in many applications of human movement analysis there are different formal methods to determine the direction and position of the aor whose performance varies across studies depending on the pose and the source of errors most methods are based on minimizing squared differences between observed and modelled marker positions or rigid motion parameters implicitly assuming independent and uncorrelated errors but the largest error usually results from soft tissue artefacts sta which do not have such statistical properties and are not effectively cancelled out by such methods however with adequate methods it is possible to assume that sta only account for a small fraction of the observed motion and to obtain explicit formulas through differential analysis that relate sta components to the resulting errors in aor parameters in this paper such formulas are derived for three different functional calibration techniques geometric fitting mean finite helical axis and sara to explain why each technique behaves differently from the others and to propose strategies to compensate for those errors these techniques were tested with published data from a sit to stand activity where the true axis was defined using bi planar fluoroscopy all the methods were able to estimate the direction of the aor with an error of less than 5 whereas there were errors in the location of the axis of 30 40 mm such location errors could be reduced to less than 17 mm by the methods based on equations that use rigid motion parameters mean finite helical axis sara when the translation component was calculated using the three markers nearest to the axis

conjugate gradient eigenstructure tracking for adaptive spectral estimation a conjugate gradient iteration is derived that converges to the set of r dominant subdominant eigenpairs this iteration is used to construct two eigenstructure tracking algorithms that track the r dimensional dominant or subdominant subspaces of time varying data or data covariance matrices the two eigenstructure tracking algorithms have update complexities o m sup 2 r and the other o mr sup 2 where m is the data dimension the algorithms are customized to solve high resolution temporal and spatial frequency tracking problems they are compared with existing techniques by tying into published simulation based performance tests the algorithms demonstrate rapid convergence and tracking characteristics at a competitive cost

application of stable fem fdtd hybrid to scattering problems a recently developed stable finite element method fem finite difference time domain fdtd hybrid that eliminates the staircase approximation of complex geometries is tested by convergence studies for radar cross sections for a conducting sphere 1 db accuracy in all directions is obtained with nine cells per wavelength whereas the nasa almond requires a higher resolution of about 15 cells per wavelength for scatterers with a smooth boundary the results converge quadratically with the mesh size but for a horizontally polarized wave incident on the nasa almond the order of convergence is lower because of singular fields at the tip

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

estimation of the axis of a screw motion from noisy data a new method based on plucker lines the problems of estimating the motion and orientation parameters of a body segment from two n point set patterns are analyzed using the plucker coordinates of a line plucker lines the aim is to find algorithms less complex than those in conventional use and thus facilitating more accurate computation of the unknown parameters all conventional techniques use point transformation to calculate the screw axis in this paper we present a novel technique that directly estimates the axis of a screw motion as a plucker line the plucker line can be transformed via the dual number coordinate transformation matrix this method is compared with schwartz and rozumalski 2005 a new method for estimating joint parameters from motion data journal of biomechanics 38 107 116 in simulations of random measurement errors and systematic skin movements simulation results indicate that the methods based on plucker lines plucker line method are superior in terms of extremely good results in the determination of the screw axis direction and position as well as a concise derivation of mathematical statements this investigation yielded practical results which can be used to locate the axis of a screw motion in a noisy environment developing the dual transformation matrix dtm from noisy data and determining the screw axis from a given dtm is done in a manner analogous to that for handling simple rotations a more robust approach to solve for the dual vector associated with dtm is also addressed by using the eigenvector and the singular value decomposition

a survey of formal methods for determining the centre of rotation of ball joints abstract the determination of an accurate centre of rotation cor from segment marker positions is of interest across a wide range of applications but particularly for clinical gait analysis and for estimating the hip joint centre during surgical intervention of the knee for limb alignment purposes for the first time in this survey of formal methods we classify analyse and compare different methods geometric algebraic bias compensated algebraic and pratt sphere fit methods as well as the centre transformation technique the holzreiter approach the helical pivot technique the schwartz transformation techniques the minimal amplitude point method and the stoddart approach for the determination of spherical joint centres from marker position data in addition we propose a new method the symmetrical cor estimation or score in which the coordinates of the joint centre must only remain constant relative to each segment thus not requiring the assumption that one segment should remain at rest for each method 1000 cor estimations were analysed with the application of isotropic independent and identically distributed gaussian noise standard deviation 0 1 cm to each of the marker positions to all markers on the segment simultaneously and the two in combination for the test conditions used here most techniques were capable of determining the cor to within 0 3 cm as long as the spherical range of motion rom of the joint was 45 or more under the most stringent conditions tested however the score was capable of best determining the cor to within approximately 1 2 mm with a rom of 20 the correct selection and application of these methodologies should help improve the accuracy of surgical navigation and clinical kinematic measurement

plane rotation based evd updating schemes for efficient subspace tracking we present new algorithms based on plane rotations for tracking the eigenvalue decomposition evd of a time varying data covariance matrix these algorithms directly produce eigenvectors in orthonormal form and are well suited for the application of subspace methods to nonstationary data after recasting evd tracking as a simplified rank one evd update problem computationally efficient solutions are obtained in two steps first a new kind of parametric perturbation approach is used to express the eigenvector update as an unimodular orthogonal transform which is represented in exponential matrix form in terms of a reduced set of small unconstrained parameters second two approximate decompositions of this exponential matrix into products of plane or givens rotations are derived one of which being previously unknown these decompositions lead to new plane rotation based evd updating schemes proteus whose main feature is the use of plane rotations for updating the eigenvectors thereby preserving orthonormality finally the proteus schemes are used to derive new evd trackers whose convergence and numerical stability are investigated via simulations one algorithm can track all the signal subspace evd components in only o lm operations where l and m respectively denote the data vector and signal subspace dimensions while achieving a performance comparable to an exact evd approach and maintaining perfect orthonormality of the eigenvectors the new algorithms show no signs of error buildup

an updating algorithm for subspace tracking in certain signal processing applications it is required to compute the null space of a matrix whose rows are samples of a signal with p components the usual tool for doing this is the singular value decomposition however the singular value decomposition has the drawback that it requires o p sup 3 operations to recompute when a new sample arrives it is shown that a different decomposition called the urv decomposition is equally effective in exhibiting the null space and can be updated in o p sup 2 time the updating technique can be run on a linear array of p processors in o p time

extension of the fdtd huygens subgridding algorithm to two dimensions this paper extends to two dimensions the finite difference time domain huygens subgridding algorithm previously published in the one dimensional case the algorithm is described in detail and several numerical experiments are provided to illustrate its possibilities and to demonstrate its effectiveness

new least squares solutions for estimating the average centre of rotation and the axis of rotation a new method is proposed for estimating the parameters of ball joints also known as spherical or revolute joints and hinge joints with a fixed axis of rotation the method does not require manual adjustment of any optimisation parameters and produces closed form solutions it is a least squares solution using the whole 3d motion data set we do not assume strict rigidity but only that the markers maintain a constant distance from the centre or axis of rotation this method is compared with other methods that use similar assumptions in the cases of random measurement errors systematic skin movements and skin movements with random measurement noise simulation results indicate that the new method is superior in terms of the algorithm used the closure of the solution consistency and minimal manual parameter adjustment the method can also be adapted to joints with translational movements

an evaluation of anatomical and functional knee axis definition in the context of side cutting abstract side cutting is commonly used to evaluate knee joint kinematics and kinetics in the context of anterior cruciate ligament injury risk many existing side cutting studies fail to clearly define the orientation of the femoral frame and the knee axis making comparisons between studies difficult a femoral frame constructed using the isb or existing functional methods does not necessarily have a medial lateral axis that is aligned with the axis of the knee a functional frame that directly aligns with the medial lateral knee axis was compared to the isb anatomical frame and the besier functional frame besier et al 2003 to determine whether the chosen frame would affect the interpretation of side cutting data kinematic and kinetic variables were calculated during three side cutting manoeuvres of 28 subjects differences in mean frame orientation were correlated with the differences in mean knee angle during side cutting the differences between the isb anatomical frame and the functional frames were significantly correlated with the differences in superior inferior and medial lateral axis orientations coefficients of multiple correlation showed a good to high cmcs 0 74 similarity between frames for knee angles and moments using a femoral anatomical frame rather than a functional frame most significantly affected offset rather than cross talk in knee angles and moments measured during side cutting there were no significant differences in offset or cross talk between the two functional methods maximum differences of

a hip joint kinematics driven model for the generation of realistic thigh soft tissue artefacts in human movement analysis accuracy and robustness of the algorithms used to determine the location of centres of rotation from stereophotogrametric data depend mainly on their capacity to deal with the artefacts due to soft tissue deformation sta while evaluating these algorithms using a mathematical simulation approach effectual realizations of stas are needed this study aimed at accomplishing this objective by modelling stas in twelve selected areas of the thigh as a linear function of the hip angles assuming no knee joint movement the proposed model was calibrated and assessed using ex vivo experiments this entailed that only the component of the sta due to skin stretching was accounted for photogrammetric data of markers placed on the skin and on hip bone and femur pins were recorded during passive flexion extension ab adduction rotation and circumduction of the hip joint artefact skin marker displacements were represented in a femur embedded anatomical frame model parameters were estimated by minimizing the least squares difference between measured and modelled stas the sta affecting a skin marker placed in a given thigh location of a given subject could be modelled with a high accuracy median root mean square difference over 4 subjects 3 trials 12 markers 3 coordinates 0 8 mm inter quartile range 1 0 mm this was also true for a hip joint movement different from the one used to calibrate the model high inter subject variability of the model parameters confirmed the subject dependency of the phenomenon

a principal component analysis approach to correcting the knee flexion axis during gait abstract accurate and precise knee flexion axis identification is critical for prescribing and assessing tibial and femoral derotation osteotomies but is highly prone to marker misplacement induced error the purpose of this study was to develop an efficient algorithm for post hoc correction of the knee flexion axis and test its efficacy relative to other established algorithms gait data were collected on twelve healthy subjects using standard marker placement as well as intentionally misplaced lateral knee markers the efficacy of the algorithm was assessed by quantifying the reduction in knee angle errors crosstalk error was quantified from the coefficient of determination r 2 between knee flexion and adduction angles mean rotation offset error o was quantified from the knee and hip rotation kinematics across the gait cycle the principal component analysis pca based algorithm significantly reduced r 2 p o knee to converge toward 11 9 8 0 of external rotation demonstrating improved certainty of the knee kinematics the within subject standard deviation of o hip between marker placements was reduced from 13 5 1 5 to 0 7 0 2 p baker et al 1999 and better than a null space algorithm schwartz and rozumalski 2005 for this healthy subject population

optimal reduced rank estimation and filtering this paper provides a unified view of and a further insight into a class of optimal reduced rank estimators and filters an alternating power ap method for computing the optimal reduced rank estimators and filters is derived and analyzed the ap method is a generalization of the conventional power method for subspace computation which is shown to be globally and exponentially convergent under weak conditions when the rank reduction is relatively large the ap method is computationally more efficient than the conventional methods the ap method is useful for adaptive computation of the canonical components of a desired reduced rank estimate which in turn facilitates the detection of a time varying rank the study shown in this paper is particularly useful for applications that involve a large number of sources and a large number of receivers where rank reduction is either inherent in the multivariate system or required to reduce the model complexity and or the computational load

robust estimation of dominant axis of rotation a simple method is developed for robustly estimating a fixed dominant axis of rotation aor of anatomical joints from surface marker data previous approaches which assume a model of circular marker trajectories use plane fitting to estimate the direction of the aor however when there is limited joint range of motion and rotation due to a second degree of freedom minimizing only the planar error can give poor estimates of the aor direction optimizing a cost function which includes the error component within a plane instead of only the component orthogonal to a plane leads to improved estimates of the aor direction for joints which exhibit additional rotational motion from a second degree of freedom results from synthetic data validation show the ranges of motion where the new method has lower estimation error compared to plane fitting techniques estimates of the flexion extension aor from empirical motion capture data of the knee and index finger joints were also more anatomically plausible

point estimation of the central orientation of random rotations data as three dimensional rotations have application in computer science kinematics and materials sciences among other areas estimating the central orientation from a sample of such data is an important problem which is complicated by the fact that several different approaches exist for this motivated by various geometrical and decision theoretical considerations however little is known about how such estimators compare especially on common distributions for location models with random rotations we examine four location estimators three of which are commonly found in different literatures and the fourth estimator a projected median is newly introduced our study unifies existing literature and provides a detailed numerical investigation of location estimators for three commonly used rotation distributions in statistics and materials science while the data generating model influences the best choice of an estimator the proposed projected median emerges as an overall good performer which can

on relative convergence properties of principal component analysis algorithms we investigate the convergence properties of two different stochastic approximation algorithms for principal component analysis and analytically explain some commonly observed experimental results in our analysis we use the theory of stochastic approximation and in particular the results of fabian 1968 to explore the asymptotic mean square errors amses of the algorithms this study reveals the conditions under which the algorithms produce smaller amses and also the conditions under which one algorithm has a smaller amse than the other experimental study with multidimensional gaussian data corroborate our analytical findings we next explore the convergence rates of the two algorithms our experiments and an analytical explanation reveals the conditions under which the algorithms converge faster to the solution and also the conditions under which one algorithm converges faster than the other

a theoretical study of the stability criteria for hybridized fdtd algorithms for multiscale analysis in this paper we propose two new hybrid two dimensional generalized finite difference time domain algorithms formulated by using the cell method and designed to analyze objects with fine details without using very small time steps dictated by the courant condition a detailed analysis of the stability of the proposed algorithms is presented with special attention devoted to the phenomenon of late time instabilities finally some rules are provided that would ensure the stability of the proposed algorithms

evaluation of knee functional calibration with and without the effect of soft tissue artefact functional calibration methods were devised to improve repeatability and accuracy of the knee flexion extension axis which is used to define the medio lateral axis of the femur coordinate system in gait analysis repeatability of functional calibration methods has been studied extensively in healthy individuals but not accuracy in the absence of a benchmark knee axis we captured bi plane fluoroscopy data of the knee joint in 17 subjects with unilateral total knee arthroplasty during treadmill walking the prosthesis provided a benchmark knee axis to evaluate the functional calibration methods stereo photogrammetry data of thigh and shank marker clusters were captured simultaneously to investigate the effect of soft tissue artefact sta three methods were tested the axis transformation technique att finds the best single fixed axis of rotation 2dofknee finds the axis that minimises knee varus valgus and trajajc finds the axis perpendicular to the trajectory in the transverse plane of the femur of a point located on the longitudinal axis of the tibia using fluoroscopy data functional axes formed an angle of less than 2 in the transverse plane with the benchmark axis true internal external range of movement was correlated with decreased accuracy for att while varus valgus range of movement was correlated with decreased accuracy for 2dofknee and trajajc sta had negative impact on accuracy and variability using stereo photogrammetry data the accuracy of 2dofknee was 1 7 sd 5 1 smaller than att 2 9 sd 5 1 but not to trajajc 1 7 sd 5 2 our results confirm that of previous studies which utilised the femur condylar axis as reference

a new method for estimating the axis of rotation and the center of rotation a new method is presented for estimating the parameters of two different models of a joint the two models are 1 a rotational joint with a fixed axis of rotation also referred to as a hinge joint and 2 a ball and socket model corresponding to a spherical joint given the motion of a set of markers it is shown how the parameters can be estimated utilizing the whole data set the parameters are estimated from motion data by minimizing two objective functions the method does not assume a rigid body motion but only that each marker rotates around the same fixed axis of rotation or center of rotation simulation results indicate that in situations where the rigid body assumption is valid and when measurement noise is present the proposed method is inferior to methods that utilize the rigid body assumption however when there are large skin movement artefacts simulation results show the proposed method to be more robust

on svd for estimating generalized eigenvalues of singular matrix pencil in noise several algorithms for estimating generalized eigenvalues ges of singular matrix pencils perturbed by noise are reviewed the singular value decomposition svd is explored as the common structure in the three basic algorithms direct matrix pencil algorithm pro esprit and tls esprit it is shown that several svd based steps inherent in the algorithms are equivalent to the first order approximation in particular the pro esprit and its variant tls pro esprit are shown to be equivalent and the tls esprit and its earlier version ls esprit are shown to be asymptotically equivalent to the first order approximation for the problem of estimating superimposed complex exponential signals the state space algorithm is shown to be also equivalent to the previous matrix pencil algorithms to the first order approximation the second order perturbation and the threshold phenomenon are illustrated by simulation results based on a damped sinusoidal signal an improved state space algorithm is found to be the most robust to noise

fast recursive subspace adaptive esprit algorithms a class of fast recursive esprit algorithms for adaptive on line source localization based on subspace tracking and adaptive rank reduction is introduced these adaptive esprit algorithms can be used for on line tracking of r maneuvering sources in space using the output of an n element sensor array where n 2r the fastest of our algorithms requires only o nr o r sup 3 complex arithmetic operations to update the estimated directions of arrival doas at each time instant these highly efficient algorithms are more than only a concatenation of a subspace tracker and a conventional batch esprit algorithm a special qr reduction to standard form is the key to the fast recursive algorithms detailed computer experiments substantiate the theoretical results

global convergence of oja s subspace algorithm for principal component extraction oja s principal subspace algorithm is a well known and powerful technique for learning and tracking principal information in time series a thorough investigation of the convergence property of oja s algorithm is undertaken in this paper the asymptotic convergence rates of the algorithm is discovered the dependence of the algorithm on its initial weight matrix and the singularity of the data covariance matrix is comprehensively addressed

a new method for estimating joint parameters from motion data joint centers and axes of rotation joint parameters are central to all branches of movement analysis in gait analysis the standard protocol used to determine hip and knee joint parameters is prone to errors arising from palpation anthropometric regression equations and misplaced alignment devices several alternative methods have been proposed but to date none have been shown to be accurate and reliable enough for use in the clinical setting this article describes a new method for joint parameter estimation the new method can be summarized as follows i the motions of two adjacent segments spanning a single joint are tracked ii the axis of rotation between every pair of observed segment configurations is computed iii the most likely intersection of all axes effective joint center and most likely orientation of the axes effective joint axis is found initial validation of the method was conducted on a hinged mechanical analog and a single healthy adult subject for the analog the center was found to be within 3 8 mm of the geometric center and 2 0 degrees of the geometric axis standard deviation for the adult subject hip centers varied on the order of 1 3 mm knee centers by 3 9 mm and knee axes by 2 0 degrees the results suggest that the new method is an objective precise and practical alternative to the standard clinical approach

bi iteration svd subspace tracking algorithms we present a class of fast subspace tracking algorithms that arise from a straightforward extension of bauer s 1957 classical bi iteration to the sequential processing case the bi iteration concept has an unexpected potential in subspace tracking our new bi svd subspace trackers are well structured and show excellent convergence properties they outperform the tqr svd subspace tracking algorithm detailed comparisons confirm our claims an application to rank and data adaptive signal reconstruction is also discussed

adaptive algorithms to track the parafac decomposition of a third order tensor the parafac decomposition of a higher order tensor is a powerful multilinear algebra tool that becomes more and more popular in a number of disciplines existing parafac algorithms are computationally demanding and operate in batch mode both serious drawbacks for on line applications when the data are serially acquired or the underlying model changes with time adaptive parafac algorithms that can track the sought decomposition at low complexity would be highly desirable this is a challenging task that has not been addressed in the literature and the topic of this paper given an estimate of the parafac decomposition of a tensor at instant t we propose two adaptive algorithms to update the decomposition at instant t 1 the new tensor being obtained from the old one after appending a new slice in the time dimension the proposed algorithms can yield estimation performance that is very close to that obtained via repeated application of state of art batch algorithms at orders of magnitude lower complexity the effectiveness of the proposed algorithms is illustrated using a mimo radar application tracking of directions of arrival and directions of departure as an example

bayesian inverse kinematics vs least squares inverse kinematics in estimates of planar postures and rotations in the absence of soft tissue artifact a variety of inverse kinematics ik algorithms exist for estimating postures and displacements from a set of noisy marker positions typically aiming to minimize ik errors by distributing errors amongst all markers in a least squares ls sense this paper describes how bayesian inference can contrastingly be used to maximize the probability that a given stochastic kinematic model would produce the observed marker positions we developed bayesian ik for two planar ik applications 1 kinematic chain posture estimates using an explicit forward kinematics model and 2 rigid body rotation estimates using implicit kinematic modeling through marker displacements we then tested and compared bayesian ik results to ls results in monte carlo simulations in which random marker error was introduced using gaussian noise amplitudes ranging uniformly between 0 2 mm and 2 0 mm results showed that bayesian ik was more accurate than ls ik in over 92 of simulations with the exception of one center of rotation coordinate planar rotation for which bayesian ik was more accurate in only 68 of simulations moreover while ls errors increased with marker noise bayesian errors were comparatively unaffected by noise amplitude nevertheless whereas the ls solutions required average computational durations of less than 0 5 s average bayesian ik durations ranged from 11 6 s for planar rotation to over 2000 s for kinematic chain postures these results suggest that bayesian ik can yield order of magnitude ik improvements for simple planar ik but also that its computational demands may make it impractical for some applications

prediction of ground reaction forces and moments during various activities of daily living inverse dynamics based simulations on musculoskeletal models is a commonly used method for the analysis of human movement due to inaccuracies in the kinematic and force plate data and a mismatch between the model and the subject the equations of motion are violated when solving the inverse dynamics problem as a result dynamic inconsistency will exist and lead to residual forces and moments in this study we present and evaluate a computational method to perform inverse dynamics based simulations without force plates which both improves the dynamic consistency as well as removes the model s dependency on measured external forces using the equations of motion and a scaled musculoskeletal model the ground reaction forces and moments grf ms are derived from three dimensional full body motion the method entails a dynamic contact model and optimization techniques to solve the indeterminacy problem during a double contact phase and in contrast to previously proposed techniques does not require training or empirical data the method was applied to nine healthy subjects performing several activities of daily living adls and evaluated with simultaneously measured force plate data except for the transverse ground reaction moment no significant differences p 0 05 were found between the mean predicted and measured grf ms for almost all adls the mean residual forces and moments however were significantly reduced p 0 05 in almost all adls using our method compared to conventional inverse dynamic simulations hence the proposed method may be used instead of raw force plate data in human movement analysis using inverse dynamics

the qs householder sliding window bi svd subspace tracker a fast algorithm for computing the sliding window bi svd subspace tracker is introduced this algorithm produces in each time step a dominant rank r svd subspace approximant of an l timesn rectangular sliding window data matrix the method is based on the qs orthonormal square decomposition it uses two row householder transformations for updating and one nonorthogonal householder transformation for downdating in each time step the resulting algorithm is long term stable and shows excellent numerical and structural properties as known from pure householder type algorithms the dominant complexity is 4lr 3nr multiplications per time update which is also the lower bound in dominant complexity for an algorithm of this kind a completely self contained algorithm summary is provided and a fortran subroutine of the algorithm is available for download from http webuser hs furtwangen de strobach qsh bisvd for

validation of a functional method for the estimation of hip joint centre location the present study assesses the accuracy with which the subject specific coordinates of the hip joint centre hjc in a pelvic anatomical frame can be estimated using different methods the functional method was applied by calculating the centre of the best sphere described by the trajectory of markers placed on the thigh during several trials of hip rotations different prediction methods proposed in the literature and in the present investigation which estimate the hjc of adult subjects using regression equations and anthropometric measurements were also assessed the accuracy of each of the above mentioned methods was investigated by comparing their predictions with measurements obtained on a sample of 11 male adult able bodied volunteers using roentgen stereophotogrammetric analysis rsa assumed to provide the true hjc locations prediction methods estimated the hjc location at an average rms distance of 25 30 mm the functional method performed significantly better and estimated hjcs within a rms distance of 13 mm on average this result may be confidently generalised if the photogrammetric experiment is carefully conducted and an optimal analytical approach used the method is therefore suggested for use in motion analysis when the subject s hip range of motion is not limited in addition the facts that it is not an invasive technique and that it has relatively small and un biased errors make it suitable for regression equations identification with no limit to sample size and population typology

on intrinsic equivalences of the finite helical axis the instantaneous helical axis and the sara approach a mathematical perspective accurate determination of joint axes is essential for understanding musculoskeletal function whilst numerous algorithms to compute such axes exist the conditions under which each of the methods performs best remain largely unknown typically algorithms are evaluated for specific conditions only limiting the external validity of conclusions regarding their performance we derive exact mathematical relationships between three commonly used algorithms for computing joint axes from motion data finite helical axes fha instantaneous helical axes iha and sara symmetrical axis of rotation approach including relationships for an extension to the mean helical axes methods that facilitate determining joint centres and axes through the derivation of a sound mathematical framework to objectively compare the algorithms we demonstrate that the fha and sara approach are equivalent for the analysis of two time frames moreover we show that the position of a helical axis derived from the iha using positional data is affected by a systematic error perpendicular to the true axis direction whereas the axis direction is identical to those computed with either the fha or sara approach true direction finally with an appropriate choice of weighting factors the mean fha mfha method is equivalent to the symmetrical centre of rotation estimation score algorithm for determination of a centre of rotation cor and similarly equivalent to the sara algorithm for determination of an axis of rotation aor the deep understanding of the equivalences between methods presented here enables readers to choose numerically efficient robust methods for determining aors and cors with confidence

two algorithms for fast approximate subspace tracking new fast algorithms are presented for tracking singular values singular vectors and the dimension of a signal subspace through an overlapping sequence of data matrices the basic algorithm is called fast approximate subspace tracking fast the algorithm is derived for the special case in which the matrix is changed by deleting the oldest column shifting the remaining columns to the left and adding a new column on the right a second algorithm fast2 is specified by modifying fast to trade reduced accuracy for higher speed the speed and accuracy are compared with the pl algorithm the past and pastd algorithms and the fst algorithm an extension to multicolumn updates for the fast algorithm is also discussed

sliding window adaptive svd algorithms the singular value decomposition svd is an important tool for subspace estimation in adaptive signal processing we are especially interested in tracking the svd of a recursively updated data matrix this paper introduces a new tracking technique that is designed for rectangular sliding window data matrices this approach which is derived from the classical bi orthogonal iteration svd algorithm shows excellent performance in the context of frequency estimation it proves to be very robust to abrupt signal changes due to the use of a sliding window finally an ultra fast tracking algorithm with comparable performance is proposed

electric and magnetic losses modeled by a stable hybrid with explicit implicit time stepping for maxwell s equations a stable hybridization of the finite element method fem and the finite difference time domain fdtd scheme for maxwell s equations with electric and magnetic losses is presented for two dimensional problems the hybrid method combines the flexibility of the fem with the efficiency of the fdtd scheme and it is based directly on ampere s and faraday s law the electric and magnetic losses can be treated implicitly by the fem on an unstructured mesh which allows for local mesh refinement in order to resolve rapid variations in the material parameters and or the electromagnetic field it is also feasible to handle larger homogeneous regions with losses by the explicit fdtd scheme connected to an implicitly time stepped and lossy fem region the hybrid method shows second order convergence for smooth scatterers the bistatic radar cross section rcs for a circular metal cylinder with a lossy coating converges to the analytical solution and an accuracy of 2 is achieved for about 20 points per wavelength the monostatic rcs for an airfoil that features sharp corners yields a lower order of convergence and it is found to agree well with what can be expected for singular fields at the sharp corners a careful convergence study with resolutions from 20 to 140 points per wavelength provides accurate extrapolated results for this non trivial test case which makes it possible to use as a reference problem for scattering codes that model both electric and magnetic losses

comparison of the score and ha methods for locating in vivo the glenohumeral joint centre a recent paper has described a new functional method the symmetrical centre of rotation score for locating joint centre position ehrig r m taylor w r duda g n heller m o 2006 a survey of formal methods for determining the centre of rotation of ball joints journal of biomechanics 39 15 2798 2809 for in vitro analyses the score method showed better precision than helical axis ha or sphere fitting methods despites ha determination is very sensitive to small angular velocity the international society of biomechanics has recommended to use ha for locating the glenohumeral joint centre this paper aims at comparing the score method with the ha method for locating in vivo the glenohumeral joint centre according to the movement characteristics nine subjects performed 10 cycles of three different movements at two different velocities for each test combination of movements the location of the centre of rotation was estimated with both methods score and ha analyses focused on the 3d location of the glenohumeral joint centre and on the repeatability of location standard deviation this study showed that score and ha methods yielded the same gh location nevertheless with score method the location of the glenohumeral joint centre was different according to the test this study evidenced that the score method was more precise than ha method error of 3 mm versus 4 6 mm and that the gh location with the score method was not affected by movements with slow velocities

the score residual a quality index to assess the accuracy of joint estimations abstract the determination of an accurate centre of rotation cor from skin markers is essential for the assessment of abnormal gait patterns in clinical gait analysis despite the many functional approaches to estimate cors no non invasive analytical determination of the error in the reconstructed joint location is currently available the purpose of this study was therefore to verify the residual of the symmetrical centre of rotation estimation score as a reliable indirect measure of the error of the computed joint centre to evaluate the score residual numerical simulations were performed to evaluate cor estimations at different ranges of joint motion a statistical model was developed and used to determine the theoretical relationships among the score residual the magnitude of the skin marker artefact the corrections to the marker positions and the error of the cor estimations to the known centre of rotation we found that the equation err 0 5rs provides a reliable relationship among the cor error err and the scaled score residual rs providing that any skin marker artefact is first minimised using the optimal common shape technique ocst measurements on six healthy volunteers showed a reduction of score residual from 11 to below 6 mm and therefore demonstrated consistency of the theoretical considerations and numerical simulations with the in vivo data this study also demonstrates the significant benefit of the ocst for reducing skin marker artefact and thus for predicting the accuracy of determining joint centre positions in functional gait analysis for the first time this understanding of the score residual allows a measure of error in the non invasive assessment of joint centres this measure now enables a rapid assessment of the accuracy of the cor as well as an estimation of the reproducibility and repeatability of skeletal motion patterns

functional knee axis based on isokinetic dynamometry data comparison of two methods mri validation and effect on knee joint kinematics this paper compares geometry based knee axes of rotation transepicondylar axis and geometric center axis and motion based functional knee axes of rotation faor two algorithms are evaluated to calculate faors gamage and lasenby s sphere fitting algorithm gl and ehrig et al s axis transformation algorithm sara calculations are based on 3d motion data acquired during isokinetic dynamometry aors are validated with the equivalent axis based on static mr images we quantified the difference in orientation between two knee axes of rotation as the angle between the projection of the axes in the transversal and frontal planes and the difference in location as the distance between the intersection points of the axes with the sagittal plane maximum differences between faors resulting from gl and sara were 5 7 and 15 4mm respectively maximum differences between faors resulting from gl or sara and the equivalent axis were 5 4 11 5mm and 8 6 12 8mm respectively differences between geometry based axes and ea are larger than differences between faor and ea both in orientation maximum 10 6 and location maximum 20 8mm knee joint angle trajectories and the corresponding accelerations for the different knee axes of rotation were estimated using kalman smoothing for the joint angles the maximum rms difference with the mri based equivalent axis which was used as a reference was 3 for the knee joint accelerations the maximum rms difference with the equivalent axis was 20 s 2 functional knee axes of rotation describe knee motion better than geometry based axes gl performs better than sara for calculations based on experimental dynamometry

in vivo estimation of the glenohumeral joint centre by functional methods accuracy and repeatability assessment abstract several algorithms have been proposed for determining the centre of rotation of ball joints these algorithms are used rather to locate the hip joint centre few studies have focused on the determination of the glenohumeral joint centre however no studies have assessed the accuracy and repeatability of functional methods for glenohumeral joint centre this paper aims at evaluating the accuracy and the repeatability with which the glenohumeral joint rotation centre ghrc can be estimated in vivo by functional methods the reference joint centre is the glenohumeral anatomical centre obtained by medical imaging five functional methods were tested the algorithm of gamage and lasenby 2002 bias compensated halvorsen 2003 symmetrical centre of rotation estimation ehrig et al 2006 normalization method chang and pollard 2007 helical axis woltring et al 1985 the glenohumeral anatomical centre ghac was deduced from the fitting of the humeral head four subjects performed three cycles of three different movements flexion extension abduction adduction and circumduction for each test the location of the glenohumeral joint centre was estimated by the five methods analyses focused on the 3d location on the repeatability of location and on the accuracy by computing the euclidian distance between the estimated ghrc and the ghac for all the methods the error repeatability was inferior to 8 25 mm this study showed that there are significant differences between the five functional methods the smallest distance between the estimated joint centre and the centre of the humeral head was obtained with the method of gamage and lasenby 2002

soldier relevant body borne loads increase knee joint contact force during a run to stop maneuver the purpose of this study was to understand the effects of load carriage on human performance specifically during a run to stop rts task using opensim analysis tools knee joint contact force grounds reaction force leg stiffness and lower extremity joint angles and moments were determined for nine male military personnel performing a rts under three load configurations light 6kg medium 20kg and heavy 40kg subject based means for each biomechanical variable were submitted to repeated measures anova to test the effects of load during the rts body borne load significantly increased peak knee joint contact force by 1 2 bw p 0 001 and peak vertical p 0 001 and anterior posterior p 0 002 ground reaction forces by 0 6 bw and 0 3 bw respectively body borne load also had a significant effect on hip p 0 026 posture with the medium load and knee p 0 046 posture with the heavy load with the heavy load participants exhibited a substantial albeit non significant increase in leg stiffness p 0 073 and d 0 615 increases in joint contact force exhibited during the rts were primarily due to greater grfs that impact the soldier with each incremental addition of body borne load the stiff leg extended knee and large braking force the soldiers exhibited with the heavy load suggests their injury risk may be greatest with that specific load configuration further work is needed to determine if the biomechanical profile exhibited with the heavy load configuration translates to unsafe shear forces at the knee joint and consequently a higher likelihood of injury

a least squares algorithm for the equiform transformation from spatial marker co ordinates the present paper describes an algorithm for estimating the translation vector and the rotation matrix of a moving body from noisy measurements on the spatial co ordinates of at least three non collinear markers a sensitivity analysis of the estimated parameters and of the helical axis is presented in terms of characteristics of the marker distribution the implementation of the proposed algorithm in a fortran subroutine is appended

on updating signal subspaces the authors develop an algorithm for adaptively estimating the noise subspace of a data matrix as is required in signal processing applications employing the signal subspace approach the noise subspace is estimated using a rank revealing qr factorization instead of the more expensive singular value or eigenvalue decompositions using incremental condition estimation to monitor the smallest singular values of triangular matrices the authors can update the rank revealing triangular factorization inexpensively when new rows are added and old rows are deleted experiments demonstrate that the new approach usually requires o n sup 2 work to update an n n matrix and that it accurately tracks the noise subspace

adjustments to mcconville et al and young et al body segment inertial parameters body segment inertial parameters bsips are important data in biomechanics they are usually estimated from predictive equations reported in the literature however most of the predictive equations are ambiguously applicable in the conventional 3d segment coordinate systems scss also the predictive equations reported in the literature all include two assumptions the centre of mass and the proximal and distal endpoints are assumed to be aligned and the inertia tensor is assumed to be principal in the segment axes these predictive equations restraining both position of the centre of mass and orientation of the principal axes of inertia become restrictive when computing 3d inverse dynamics when analyzing the influence of bsip estimations on joint forces and moments and when evaluating personalized 3d bsips obtained from medical imaging in the current study the extensive data from mcconville et al 1980 anthropometric relationships of body and body segment moments of inertia afamrl tr 80 119 aerospace medical research laboratory wright patterson air force base dayton ohio and from young et al 1983 anthropometric and mass distribution characteristics of the adults female technical report afamrl tr 80 119 faa civil aeromedical institute oklaoma city oklaoma are adjusted in order to correspond to joint centres and to conventional segment axes in this way scaling equations are obtained for both males and females that provide bsips which are directly applicable in the conventional scss and do not restrain the position of the centre of mass and the orientation of the principal axes these adjusted scaling equations may be useful for researchers who wish to use appropriate 3d bsips for posture and movement analysis

bias compensated least squares estimate of the center of rotation abstract it is shown that a recently published least squares method for the estimation of the average center of rotation is biased consequently a correction term is proposed and an iterative algorithm is derived for finding a bias compensated solution to the least squares problem the accuracy of the proposed bias compensated least squares method is compared to the previously proposed least squares method by monte carlo simulations the tests show that the new method gives a substantial improvement in accuracy

comparison of anatomical functional and regression methods for estimating the rotation axes of the forearm numerous methods exist to estimate the pose of the axes of rotation of the forearm these include anatomical definitions such as the conventions proposed by the isb and functional methods based on instantaneous helical axes which are commonly accepted as the modelling gold standard for noninvasive in vivo studies we investigated the validity of a third method based on regression equations to estimate the rotation axes of the forearm we also assessed the accuracy of both isb methods axes obtained from a functional method were considered as the reference results indicate a large inter subject variability in the axes positions in accordance with previous studies both isb methods gave the same level of accuracy in axes position estimations regression equations seem to improve estimation of the flexion extension axis but not the pronation supination axis overall given the large inter subject variability the use of regression equations cannot be recommended

a new stable hybrid three dimensional generalized finite difference time domain algorithm for analyzing complex structures in this paper we propose a new stable hybrid three dimensional 3 d generalized finite difference time domain algorithm formulated by using of the cell method cm a finite volumes type method designed to analyze objects with fine details without using very small time steps dictated by the courant condition the new algorithm is an extension to the 3 d cases of an analogous hybrid two dimensional algorithm also formulated by the cm and presented earlier by the authors in a previous publication we carry out a detailed analysis of the stability of the proposed algorithm paying special attention to the phenomenon of late time instabilities finally the results of some numerical tests are provided to show the absence of instabilities and the efficiency of the hybrid algorithm

fast subspace tracking and neural network learning by a novel information criterion we introduce a novel information criterion nic for searching for the optimum weights of a two layer linear neural network nn the nic exhibits a single global maximum attained if and only if the weights span the desired principal subspace of a covariance matrix the other stationary points of the nic are unstable saddle points we develop an adaptive algorithm based on the nic for estimating and tracking the principal subspace of a vector sequence the nic algorithm provides a fast on line learning of the optimum weights for the two layer linear nn we establish the connections between the nic algorithm and the conventional mean square error mse based algorithms such as oja s algorithm oja 1989 lmser past apex and gha the nic algorithm has several key advantages such as faster convergence which is illustrated through analysis and simulation

projection approximation subspace tracking subspace estimation plays an important role in a variety of modern signal processing applications we present a new approach for tracking the signal subspace recursively it is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem we show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation the resulting algorithms have a computational complexity of o nr where n is the input vector dimension and r is the number of desired eigencomponents simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed