on focusing matrices for wide band array processing a general class of transformation matrices for coherent signal subspace processing is presented these signal subspace transformation sst matrices are shown to generate a sufficient statistic for maximum likelihood bearing estimation two general forms for calculating sst matrices are presented and the rotational signal subspace rss focusing matrices proposed by h hung and m kaveh 1988 are shown to be a special case of the sst matrices an efficient procedure for computing a subset of the sst matrices utilizing householder transformations is presented the procedure reduces the computational load by a factor of 10 compared with that for the rss matrices the application of music to the coherently combined covariance matrix is also discussed and monte carlo simulations comparing the performance of householder sst matrices and rss matrices are performed

space time music consistent signal subspace estimation for wideband sensor arrays wideband direction of arrival doa estimation with sensor arrays is an essential task in sonar radar acoustics biomedical and multimedia applications many state of the art wideband doa estimators coherently process frequency binned array outputs by approximate maximum likelihood ml weighted subspace fitting or focusing techniques this paper shows that bin signals obtained by filter bank approaches do not obey the finite rank narrow band array model because spectral leakage and changes of the array response with frequency within the bin create ghost sources dependent on the particular realization of the source process therefore existing doa estimators based on binning are not consistent even when the array response is perfectly known in this paper under a more realistic array model which still has finite rank under a space time formulation signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying space time music type st music estimators to the dominant eigenvectors of the wideband space time sensor cross correlation matrix a novel consistent ml based st music subspace estimate is developed to estimate the number of sources active at each frequency by information theoretic criteria empirical st music subspaces are fed to any subspace fitting doa estimator at single or multiple frequencies simulations confirm that this approach allows better performance over binning approaches at sufficiently high signal to noise ratio when model mismatches exceed the noise floor

spatio temporal spectral analysis by eigenstructure methods this paper presents new algorithms for estimating the spatio temporal spectrum of the signals received by a passive array the algorithms are based on the eigenstructure of the covariance and spectral density matrices of the received signals they allow partial correlation between the sources and thus are applicable to certain kinds of multipath problems simulation results that illustrate the performance of the new algorithms are presented

solution and analysis of tdoa localization of a near or distant source in closed form point positioning and direction of arrival doa localization require separate estimators depending on whether the source is near or distant from the sensors the use of modified polar representation mpr for the source location enables the integration of the two estimators together and eliminates the knowledge needed if the source is in the near field or far field the previous work on mpr only provides an iterative implementation of the maximum likelihood estimator mle initialized by a coarse semidefinite relaxation sdr solution this paper proposes a formulation for time difference of arrival tdoa localization of a 2 d or 3 d source in mpr that would lead to a closed form solution through the minimization of a quadratic function with a quadratic constraint two techniques the successive unconstrained minimization sum and the generalized trust region subproblem gtrs are applied to solve the optimization detailed analysis in the first order for mean square and in the second order for estimation bias is performed for both methods the theoretical results illustrate that the closed form solution from each of the methods provides the cramer rao lower bound performance for gaussian noise the gtrs solution has better accuracy than the sum solution when the source signal is arriving at an azimuth or elevation angle close to zero 90 circ or 180 circ or when the measurement noise level is large they yield comparable performance with the mle albeit having less complexity and avoiding possible divergence behavior they outperform the closed form solutions from the literature in angle estimation and have smaller bias

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

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

efficient wideband source localization using beamforming invariance technique a novel scheme for wideband direction of arrival doa estimation is proposed the technique performs coherent signal subspace transformation by a set of judiciously constructed beamforming matrices the beamformers are chosen to transform each of the narrowband array manifold vectors into the one corresponding to the reference frequency regardless of the actual spatial distribution of the sources the focused data correlation matrix can thus be obtained without any preliminary doa estimation or iteration a simplified version of the beamspace root music algorithm is developed and used in conjunction with the proposed method to efficiently localize multiple wideband sources with a linear equally spaced array numerical simulations are conducted to demonstrate the efficacy of the new scheme

whole body inverse dynamics over a complete gait cycle based only on measured kinematics this paper presents a three dimensional 3d whole body multi segment model for inverse dynamics analysis over a complete gait cycle based only on measured kinematic data the sequence of inverse dynamics calculations differs significantly from the conventional application of inverse dynamics using force plate data a new validated smooth transition assumption was used to solve the indeterminacy problem in the double support phase kinematic data is required for all major body segments and hence a whole body gait measurement protocol is presented finally sensitivity analyses were conducted to evaluate the effects of digital filtering and body segment parameters on the accuracy of the prediction results the model gave reasonably good estimates of sagittal plane ground forces and moment however the estimates in the other planes were less good which we believe is largely due to their small magnitudes in comparison to the sagittal forces and moment the errors observed are most likely caused by errors in the kinematic data resulting from skin movement artefact and by errors in the estimated body segment parameters a digital filtering cut off frequency of 4 5 hz was found to produce the best results it was also shown that errors in the mass properties of body segments can play a crucial role with changes in properties sometimes having a disproportionate effect on the calculated ground reactions the implication of these results is that even when force plate data is available the estimated joint forces are likely to suffer from similar errors

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

estimation of the centre of rotation a methodological contribution the location of the centre of rotation of human joints that can be modelled as a spherical hinge can be estimated using kinematics information about the two adjacent bony segments involved recorded while the subject makes them move one relative to the other functional method in order to solve the relevant analytical problem several algorithms have been proposed most recently two methods one based on a spherical best fit approach and another based on the reuleaux construction have been presented as being different and submitted to comparative evaluation this paper modifies the second method taking all information in the data set into account and shows that having done this the two methods coincide analytically

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

direction of arrival estimation for wide band signals using the esprit algorithm a novel direction of arrival estimation algorithm is proposed that applies to wideband emitter signals a sensor array with a translation invariance structure is assumed and an extension of the esprit algorithm for narrowband emitter signals is obtained the emitter signals are modeled as the stationary output of a finite dimensional linear system driven by white noise the array response to a unit impulse from a given direction is represented as the impulse response of a linear system the measured data from the sensor array can then be seen as the output of a multidimensional linear system driven by white noise sources and corrupted by additive noise the emitter signals and the array output are characterized by the modes of the linear system the esprit algorithm is applied at the poles of the system the power of the signals sharing the pole is captured and the effect of noise is reduced the algorithm requires no knowledge storage or search of the array manifold as opposed to wideband extensions of the music algorithm this results in a computationally efficient algorithm that is insensitive to array perturbations simulations are presented comparing the wideband and esprit algorithm to the modal signal subspace method and the coherent signal subspace method

efficient mixed spectrum estimation with applications to target feature extraction we present a decoupled parameter estimation dpe algorithm for estimating sinusoidal parameters from both 1 d and 2 d data sequences corrupted by autoregressive ar noise in the first step of the dpe algorithm we use a relaxation relax algorithm that requires simple fast fourier transforms ffts to obtain the estimates of the sinusoidal parameters we describe how the relax algorithm may be used to extract radar target features from both 1 d and 2 d data sequences in the second step of the dpe algorithm a linear least squares approach is used to estimate the ar noise parameters the dpe algorithm is both conceptually and computationally simple the algorithm not only provides excellent estimation performance under the model assumptions in which case the estimates obtained with the dpe algorithm are asymptotically statistically efficient but is also robust to mismodeling errors

point of optimal kinematic error improvement of the instantaneous helical pivot method for locating centers of rotation this paper proposes a variation of the instantaneous helical pivot technique for locating centers of rotation the point of optimal kinematic error poke which minimizes the velocity at the center of rotation may be obtained by just adding a weighting factor equal to the square of angular velocity in woltring s equation of the pivot of instantaneous helical axes piha calculations are simplified with respect to the original method since it is not necessary to make explicit calculations of the helical axis and the effect of accidental errors is reduced the improved performance of this method was validated by simulations based on a functional calibration task for the gleno humeral joint center noisy data caused a systematic dislocation of the calculated center of rotation towards the center of the arm marker cluster this error in piha could even exceed the effect of soft tissue artifacts associated to small and medium deformations but it was successfully reduced by the poke estimation

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

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

combining image compression and classification using vector quantization we describe a method of combining classification and compression into a single vector quantizer by incorporating a bayes risk term into the distortion measure used in the quantizer design algorithm once trained the quantizer can operate to minimize the bayes risk weighted distortion measure if there is a model providing the required posterior probabilities or it can operate in a suboptimal fashion by minimizing the squared error only comparisons are made with other vector quantizer based classifiers including the independent design of quantization and minimum bayes risk classification and kohonen s lvq a variety of examples demonstrate that the proposed method can provide classification ability close to or superior to learning vq while simultaneously providing superior compression performance

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

rate distortion analysis of discrete hmm pose estimation via multiaspect scattering data we consider the problem of estimating the pose of a target based on a sequence of scattered waveforms measured at multiple target sensor orientations using a hidden markov model hmm representation of the scattered waveform sequence pose estimation reduces to estimating the underlying hmm states from a sequence of observations it is assumed that each scattered waveform must be quantized via an encoding procedure a distortion d is defined as the error in estimating the underlying hmm states and the rate r represents the size of the discrete hmm codebook rate distortion theory is applied to define the minimum rate required to achieve a desired distortion denoted as r d after deriving the rate distortion function r d we demonstrate that discrete hmm performance based on lloyd encoding is far from this bound performance is improved via block coding based on bayes vq results are presented for a canonical hmm problem and then for multiaspect acoustic scattering from underwater elastic targets although the examples presented here are for multiaspect scattering and pose estimation the results are of general applicability to discrete hmm state estimation

determining finger segmental centers of rotation in flexion extension based on surface marker measurement this paper describes the development of a novel algorithm for deriving finger segmental center of rotation cor locations during flexion extension from measured surface marker motions in vivo the algorithm employs an optimization routine minimizing the time variance of the internal link lengths and incorporates an empirically quantifiable relationship between the local movement of a surface marker around a joint termed surface marker excursion and the joint flexion extension the latter relationship constrains and simplifies the optimization routine to make it computationally tractable to empirically investigate this relationship and test the proposed algorithm an experiment was conducted in which hand cylinder grasping movements were performed by 24 subjects 12 males and 12 females spherical retro reflective markers were placed at various surface landmarks on the dorsal aspect of each subject s right grasping hand and were measured during the movements by an opto electronic system analysis of experimental data revealed a highly linear relationship between the surface marker excursion and the marker defined flexion extension angle the average r 2 in linear regression ranged from 0 89 to 0 97 the algorithm successfully determined the cors of the distal interphalangeal proximal interphalangeal and metacarpophalangeal joints of digits 2 5 during measured motions the derived cors appeared plausible as examined in terms of the physical locations relative to surface marker trajectories and the congruency across different joints and individuals

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

waves weighted average of signal subspaces for robust wideband direction finding existing algorithms for wideband direction finding are mainly based on local approximations of the gaussian log likelihood around the true directions of arrival doas assuming negligible array calibration errors suboptimal and costly algorithms such as classical or sequential beamforming are required to initialize a local search that eventually furnishes doa estimates this multistage process may be nonrobust in the presence of even small errors in prior guesses about angles and number of sources generated by inherent limitations of the preprocessing and may lead to catastrophic errors in practical applications a new approach to wideband direction finding is introduced and described the proposed strategy combines a robust near optimal data adaptive statistic called the weighted average of signal subspaces waves with an enhanced design of focusing matrices to ensure a statistically robust preprocessing of wideband data the overall sensitivity of waves to various error sources such as imperfect array focusing is also reduced with respect to traditional cssm algorithms as demonstrated by extensive monte carlo simulations

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

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

optimal average path of the instantaneous helical axis in planar motions with one functional degree of freedom this paper presents a model for determining the path of the instantaneous helical axis iha that optimally represents human planar motions with one functional degree of freedom fdof a human movement is said to have one fdof when all degrees of freedom dofs are coordinated such that all the kinematic variables can be expressed across movement repetitions as functions of only one independent dof except for a small natural intercycle variability quantified as lower than a prespecified value the concept of fdof allows taking into account that due to motor coordination human movements are executed in a repeatable manner our method uses the measurement of several repetitions of a given movement to obtain the optimal average iha path the starting point is a change of variables from time to a joint position magnitude generally an angle in this way instead of operating with the time dependent single valued trajectory of the successive cycles our model permits the representation of any motion variable e g positions and their time derivatives as a cloud of points dependent on the joint angle this allows the averaging to be performed over the displacements and their derivatives before determining the mean iha path we thus avoid the nonlinear magnification of errors and variability inherent in the iha computation moreover the iha path can be considered as a geometric attribute of the joint and the type of motion rather than of each single movement execution an experiment was performed that show the accuracy and usefulness of the method

the centre of rotation of the shoulder complex and the effect of normalisation shoulder motions consist of a composite movement of three joints and one pseudo joint which together dictate the humerothoracic motion the purpose of this work was to quantify the location of the centre of rotation cor of the shoulder complex as a whole dynamic motion of 12 participants was recorded using optical motion tracking during coronal scapular and sagittal plane elevation the instantaneous cor was found for each angle of elevation using helical axes projected onto the three planes of motion the location of an average cor for each plane was evaluated using digitised and anthropometric measures for normalisation when conducting motion in the coronal scapular and sagittal planes respectively the coefficients for locating the cors of the shoulder complex are 61 61 and 65 of the anterior posterior dimension the vector between the midpoint of the incisura jugularis and the xiphoid process and the midpoint of the seventh cervical vertebra and the eighth thoracic vertebra 0 1 and 2 of the superior inferior dimension the vector between the midpoint of the acromioclavicular joints and the midpoint of the anterior superior iliac spines and 57 57 and 78 of the medial lateral dimension 0 129 times the height of the participant knowing the location of the cor of the shoulder complex as a whole enables improved participant positioning for evaluation and rehabilitation activities that involve movement of the hand with a fixed radius such as those that employ isokinetic dynamometers

constrained least squares optimization for robust estimation of center of rotation this paper presents a new direct method for estimating the average center of rotation cor an existing least squares ls solution has been shown by previous works to have reduced accuracy for data with small range of motion rom alternative methods proposed to improve the cor estimation use iterative algorithms however in this paper we show that with a carefully chosen normalization scheme constrained least squares solutions can perform as well as iterative approaches even for challenging problems with significant noise and small rom in particular enforcing the normalization constraint avoids poor fits near plane singularities that can affect the existing ls method our formulation has an exact solution accounts for multiple markers simultaneously and does not depend on manually adjusted parameters simulation tests compare the method to four published cor estimation techniques the results show that the new approach has the accuracy of the iterative methods as well as the short computation time and repeatability of a least squares solution in addition application of the new method to experimental motion capture data of the thumb carpometacarpal cmc joint yielded a more plausible cor location compared to the previously reported ls solution and required less time than all four alternative techniques

focussing matrices for coherent signal subspace processing a class of focussing matrices is proposed for use in the coherent signal subspace method csm h wang and m kaveh ibid vol assp 33 aug 1985 when the directions of arrival of wideband sources fall into more than one group of one beamwidth each this class leads to performance substantially better than those suggested in previous studies on direction of arrival estimation new insight into the structures of various focussing matrices and their effect on the performance of csm is presented the performance of csm is compared for several classes of these matrices on the simulations as well as relative sufficiency analyses

the statistical performance of the music and the minimum norm algorithms in resolving plane waves in noise this paper presents an asymptotic statistical analysis of the null spectra of two eigen assisted methods music 1 and minimum norm 2 for resolving independent closely spaced plane waves in noise particular attention is paid to the average deviation of the null spectra from zero at the true angles of arrival for the plane waves these deviations are expressed as functions of signal to noise ratios number of array elements angular separation of emitters and the number of snapshots in the case of music an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise this result is validated by monte carlo simulations

the effect on conventional gait model kinematics and kinetics of hip joint centre equations in adult healthy gait abstract the conventional gait model cgm needs to benefit from large investigations on localization of the hip joint centre hjc incorrect positions from the native equations were demonstrated sangeux et al 2014 harrington et al 2007 more accurate equations were proposed but their impact on kinematics and kinetic cgm outputs was never evaluated this short communication aims at examining if adoption of new hjc equations would alter standard cgm outputs sixteen able bodied participants underwent a full 3 d optoelectronic gait analysis followed by a 3 d ultrasound localization of their hips data were processed through the open source python package pycgm2 replicating kinematic and kinetic processing of the native cgm compared with 3d ultrasound location hara equations improved the accuracy of sagittal plane kinematics 0 6 and kinetics 0 02 n m kg 1 for the hip the worst case participant exhibited harrington s equations reached a deviation of 3 for the sagittal kinematics in the coronal plane hara and harrington equations presented similar differences 1 for the hip whilst davis equations had the largest deviation for hip abduction 2 7 and hip abductor moment 0 10 n m kg 1 both harrington and hara equations improved the cgm location of the hjc hara equations improved results in the sagittal plane plus utilise a single anthropometrics measurement leg length that may be more robust however neither set of equations had significant effect on kinematics we reported some effects on kinetics particularly in the coronal plane which warrant caution in interpreting outputs using different sets of equations

kalman smoothing improves the estimation of joint kinematics and kinetics in marker based human gait analysis we developed a kalman smoothing algorithm to improve estimates of joint kinematics from measured marker trajectories during motion analysis kalman smoothing estimates are based on complete marker trajectories this is an improvement over other techniques such as the global optimisation method gom kalman filtering and local marker estimation lme where the estimate at each time instant is only based on part of the marker trajectories we applied gom kalman filtering lme and kalman smoothing to marker trajectories from both simulated and experimental gait motion to estimate the joint kinematics of a ten segment biomechanical model with 21 degrees of freedom three simulated marker trajectories were studied without errors with instrumental errors and with soft tissue artefacts sta two modelling errors were studied increased thigh length and hip centre dislocation we calculated estimation errors from the known joint kinematics in the simulation study compared with other techniques kalman smoothing reduced the estimation errors for the joint positions by more than 50 for the simulated marker trajectories without errors and with instrumental errors compared with gom kalman smoothing reduced the estimation errors for the joint moments by more than 35 compared with kalman filtering and lme kalman smoothing reduced the estimation errors for the joint accelerations by at least 50 our simulation results show that the use of kalman smoothing substantially improves the estimates of joint kinematics and kinetics compared with previously proposed techniques gom kalman filtering and lme for both simulated with and without modelling errors and experimentally measured gait motion

bayesian vs least squares inverse kinematics simulation experiments with models of 3d rigid body motion and 2d models including soft tissue artefacts abstract two simulation experiments are presented to gauge the accuracy of a new inverse kinematics method based on bayesian inference bik pataky et al 2019 j biomech in more realistic models than were considered previously the first application concerns planar kinematics in the presence of soft tissue artefacts and the second application concerns rigid body kinematics in 3d with finite helical axes fha the percentage of simulations in which bik was more accurate than least squares based methods was only high in cases of relatively large noise magnitudes noise sd 5 mm or when the rotation magnitude was very small 5 deg in the 3d fha model correlated parameters are the likely culprit of the low performance of bik also computation time is a major deficit of the bik approach 20 s for the movement between two time frames these results indicate that more research will be necessary to improve the accuracy of bik for complex biomechanical models at realistic noise levels and to reduce computation time

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

tops new doa estimator for wideband signals this paper introduces a new direction of arrival doa estimation algorithm for wideband sources called test of orthogonality of projected subspaces tops this new technique estimates doas by measuring the orthogonal relation between the signal and the noise subspaces of multiple frequency components of the sources tops can be used with arbitrary shaped one dimensional 1 d or two dimensional 2 d arrays unlike other coherent wideband methods such as the coherent signal subspace method cssm and waves the new method does not require any preprocessing for initial values the performance of those wideband techniques and incoherent music is compared with that of the new method through computer simulations the simulations show that this new technique performs better than others in mid signal to noise ratio snr ranges while coherent methods work best in low snr and incoherent methods work best in high snr thus tops fills a gap between coherent and incoherent methods

the finite helical axis of the knee joint a non invasive in vivo study using fast pc mri an understanding of the in vivo knee joint kinematics is critical for the further improvement and validation of knee joint models and for the development of better surgical and rehabilitative protocols unfortunately most studies exploring the finite helical axis fha tend to produce excellent qualitative results but quantitative results are often lacking thus the purpose of this study was to non invasively and in vivo quantify the tibiofemoral fha in a relatively large normal population during volitional knee extension using fast pc mri to report the data relative to consistent coordinate systems making it available for modeling input experimental comparison and for device design to determine the variability of the fha to investigate the screw home mechanism and to test the hypothesis that knee joint kinematics are independent of gender intra and inter subject repeatability was excellent the intra inter subject repeatability of the fha orientation in the frontal and axial planes was 1 8 3 3 and 3 7 6 0 of the average value respectively at the beginning of extension the fha was directed laterally and slightly superiorly and at the end of extension it was directed in the lateral inferior direction indicative of the screw home mechanism the fha location was not fixed during extension there was small but significant differences in all fha parameters between genders and normalizing positional data relative to epicondylar width helped to reduce this difference the data obtained in the current study forms an excellent base for future knee joint modeling and clinical studies

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

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

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

comparative evaluation of scapular and humeral coordinate systems based on biomedical images of the glenohumeral joint bio imaging techniques represent a powerful tool for shoulder joint biomechanical analysis however the restricted field of view may prevent the acquisition of complete scapula and humerus bone models and hence limiting the applicability of standardized anatomical coordinate system acs definitions the aim of this study was to propose acs definitions for both scapula and humerus which can be implemented when limited portions of the relevant bones are available magnetic resonance mr images of twenty right humeri and scapulae were acquired the proposed acss were assessed in terms of 1 sensitivity to bone morphological variation 2 intra and inter operator repeatability and 3 consistency with the anatomical cardinal directions a comparison with alternative acs definitions was also performed overall our acs scapular proposal and that presented in kedgley and dunning 2010 were found to be the least sensitive to the morphometric variability mean angular absolute deviation lower than 8 3 deg and they were characterized by a high intra and inter operator repeatability mean angular absolute deviation lower than 1 5 deg the humeral acs proposal showed a morphometric variability similar to amadi et al 2009b mean angular absolute deviation lower than 8 3 deg but a higher reproducibility the scapular and humeral acs mean angular deviation from the reference anatomical cardinal directions were smaller than 15 deg and 8 6 deg respectively the proposed scapular and humeral acs definitions are therefore suitable to be applied when a limited portion of the glenohumeral joint is available as it may occur in standard shoulder clinical exams

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

bayes risk weighted vector quantization with posterior estimation for image compression and classification classification and compression play important roles in communicating digital information their combination is useful in many applications including the detection of abnormalities in compressed medical images in view of the similarities of compression and low level classification it is not surprising that there are many similar methods for their design because some of these methods are useful for designing vector quantizers it seems natural that vector quantization vq is explored for the combined goal we investigate several vq based algorithms that seek to minimize both the distortion of compressed images and errors in classifying their pixel blocks these algorithms are investigated with both full search and tree structured codes we emphasize a nonparametric technique that minimizes both error measures simultaneously by incorporating a bayes risk component into the distortion measure used for the design and encoding we introduce a tree structured posterior estimator to produce the class posterior probabilities required for the bayes risk computation in this design for two different image sources we demonstrate that this system provides superior classification while maintaining compression close or superior to that of several other vq based designs including kohonen s 1992 learning vector quantizer and a sequential quantizer classifier design

spinal shape changes resulting from scoliotic spine surgical instrumentation expressed as intervertebral rotations and centers of rotation this paper reports the changes in spinal shape resulting from scoliotic spine surgical instrumentation expressed as intervertebral rotations and centers of rotation the objective is to test the hypothesis that the type of spinal instrumentation system cotrel dubousset versus colorado does not influence these motion parameters intervertebral rotations and centers of rotation of the scoliotic spines were computed from the pre and post operative radiographs of 82 patients undergoing spinal correction the three dimensional 3d reconstruction of six anatomical landmarks was achieved for each of the thoracic and lumbar vertebrae a least squares approach based on singular value decomposition was used to calculate the rigid body transformation parameters average centers of rotation for all intervertebral levels are located in the neural canal at the mid sagittal plane and approximately at the superior endplate level of the inferior vertebra intervertebral rotations have components in all planes 6 7 degrees frontal 5 5 degrees sagittal and 4 5 degrees transverse rms for all intervertebral levels nearly all intervertebral rotations and centers of rotation are not significantly different for the two instrumentation systems various intervertebral rotations and 3d reconstruction errors were simulated on a theoretical model of a lumbar functional unit to assess the proposed method intervertebral rotation errors were 1 7 degrees when simulating 3d errors of 3mm on the position of the landmarks maximum errors for the position of centers of rotation were below 1cm in the case of intervertebral rotations larger than 2 5 degrees most cases but were larger 38 mm for small intervertebral rotations 1 degrees the type of instrumentation system did not influence intervertebral rotations and centers of rotation these results provide valuable data for the development and validation of simulation models for surgical instrumentation of idiopathic scoliosis

direction finding for wide band signals using an interpolated array the authors derive a new direction finding algorithm for multiple wideband signals received by an arbitrary array and analyze its performance using an interpolation technique they generate a set of virtual arrays each for a different frequency band having the same array manifold the convergence matrices of these arrays are added to produce a composite covariance matrix direction of arrival doa estimates are obtained by eigendecomposition of this composite covariance matrix using the narrowband music algorithm or its variants closed form expressions for the asymptotic covariance matrix of the doa estimation errors are derived using a perturbation analysis evaluated for specific cases and compared with the cramer rao lower bound special attention is given to correlated and coherent signals the formulas for the error covariance are quite general and can be modified to provide results for other wideband doa estimation algorithms

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

high resolution multiple wideband and nonstationary source localization with unknown number of sources in this paper a new algorithm for high resolution multiple wideband and nonstationary source localization using a sensor array is proposed the received signals of the sensor array are first converted into the time frequency domain via short time fourier transform stft and we find that a set of short time power spectrum matrices at different time instants have the joint diagonalization structure in each frequency bin based on such joint diagonalization structure a novel cost function is designed and a new spatial spectrum for direction of arrival doa estimation at hand is derived compared to the maximum likelihood ml method with high computational complexity the proposed algorithm obtains the doa estimates via one dimensional 1 d search instead of multidimensional search therefore its computational complexity is much lower than the ml method unlike the subspace based high resolution doa estimation techniques it is not necessary to determine the number of sources in advance for the proposed algorithm moreover the proposed method is robust to the effects of reverberation caused by multipath reflections hence it is suitable for multiple acoustic source localization in a reverberant room the results of numerical simulations and experiments in a real room with a moderate reverberation are provided to demonstrate the good performance of the proposed approach

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

underdetermined high resolution doa estimation a 2 rho th order source signal noise subspace constrained optimization for estimating the direction of arrival doa s of non stationary source signals such as speech and audio a constrained optimization problem cop that exploits the spatial diversity provided by an array of sensors is formulated in terms of a noise eliminated local 2 rho th order cumulant matrix the cop solution provides a weight vector to the look direction such that it is constrained to the 2 rho th order source signal subspace when the look direction is in alignment with the true doa otherwise it is constrained to the 2 rho th order noise subspace this weight vector is incorporated into the spatial spectrum to determine the degree of orthogonality between itself and either the 2 rho th order source signal subspace when the number of sources is unknown or the 2 rho th order noise subspace when the number of sources is known for a uniform linear array ula of m sensors the spatial spectrum for known number of sources can theoretically be shown to identify up to 2 rho m 1 sources realizing the difficulty in identifying stationarity in the received sensor signals the estimate of the noise eliminated local 2 rho th order cumulant matrix is marginalized over various possible stationary segmentations for a more robust doa estimation in this paper we focus on the use of local second and fourth order cumulants rho 1 2 and the proposed algorithms when rho 1 outperformed the kr subspace based algorithms and also the 4 music for globally non stationary non gaussian synthetic data and also for speech audio in various adverse environments we verified that the identifiability for rho 2 is improved by two folds compared to that for rho 1 with an ula

model guided derivation of lumbar vertebral kinematics in vivo reveals the difference between external marker defined and internal segmental rotations this study investigated whether the external marker defined spine inter segmental rotation is different from the internal vertebral rotation and explored how to estimate the latter from limited surface measurement a kinematic model was first created to elucidate analytically the relation between the external and internal rotations a novel approach guided by the model was proposed for deriving vertebral centers of rotation cors from measured planar trajectories of skin surface markers the approach involved a recursive procedure for establishing local anatomical coordinate systems and an optimization routine that identified the maximum likelihood circles best fitting the marker trajectories in local coordinate systems an experiment with 10 subjects 5 males and 5 females was conducted to test the approach along with the model skin surface markers were strategically placed over individual spinous processes and other body landmarks and recorded by an opto electronic system while sagittally symmetric load lifting movements were being performed for the majority 89 of measured motions the cor locations for lumbar vertebrae l2 l5 were derived successfully solutions resulting from the optimization routine met a convergence criterion governed by the model and were in agreement with existing data from radiographic or cadaveric studies empirical results confirmed the differences between the external marker defined inter segmental motions and corresponding internal vertebral rotations 1 1 5 8 degrees on average all statistically significant the study demonstrated the necessity and viability of quantifying internal vertebral kinematics when utilizing non invasive marker based measurement for spine related clinical diagnosis and biomechanical modeling

multi frequency co prime arrays for high resolution direction of arrival estimation this paper presents multi frequency operation for increasing the number of resolvable sources in high resolution direction of arrival doa estimation using co prime arrays a single frequency operation requires complicated and involved matrix completion to utilize the full extent of the degrees of freedom dofs offered by the co prime configuration this processing complexity is attributed to the missing elements in the corresponding difference coarray alternate single frequency schemes avoid such complexity by utilizing only the filled part of the coarray and thus cannot exploit all of the dofs for doa estimation we utilize multiple frequencies to fill the missing coarray elements thereby enabling the co prime array to effectively utilize all of the offered dofs the sources are assumed to have a sufficient bandwidth to cover all the required operational frequencies we consider both cases of sources with proportional and nonproportional power spectra at the employed frequencies the former permits the use of multi frequency measurements at the co prime array to construct a virtual covariance matrix corresponding to a filled uniformly spaced coarray at a single frequency this virtual covariance matrix can be employed for doa estimation the nonproportionality of the source spectra casts a more challenging situation as it is not amenable to producing the same effect as that of an equivalent single frequency filled coarray performance evaluation of the multi frequency approach based on computer simulations is provided under both cases of proportional and nonproportional source spectra

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

doa estimation of quasi stationary signals with less sensors than sources and unknown spatial noise covariance a khatri rao subspace approach in real world applications such as those for speech and audio there are signals that are nonstationary but can be modeled as being stationary within local time frames such signals are generally called quasi stationary or locally stationary signals this paper considers the problem of direction of arrival doa estimation of quasi stationary signals specifically in our problem formulation we assume i sensor array of uniform linear structure ii mutually uncorrelated wide sense quasi stationary source signals and iii wide sense stationary noise process with unknown possibly nonwhite spatial covariance under the assumptions above and by judiciously examining the structures of local second order statistics soss we develop a khatri rao kr subspace approach that has two notable advantages first through an identifiability analysis it is proven that this kr subspace approach can operate even when the number of sensors is about half of the number of sources the idea behind is to make use of a virtual array structure provided inherently in the local sos model of which the degree of freedom is about twice of that of the physical array second the kr formulation naturally provides a simple yet effective way of eliminating the unknown spatial noise covariance from the signal soss extensive simulation results are provided to demonstrate the effectiveness of the kr subspace approach under various situations

a correction for axis misalignment in the joint angle curves representing knee movement in gait analysis this paper derives a simple mathematical model relating changes in the orientations of the two cartesian coordinate systems involved in recording knee movement and the varus valgus and the internal external rotation angles for describing the knee s motion rotation matrices are given for changing the orientations of the two cartesian coordinate systems in such a way that the quadratic variations in the varus valgus and in the external internal angles are minimal these estimated rotation matrices are used to correct for axis misalignment the correction is calibrated by considering the impact of the new orientation of the thigh cartesian coordinate system on the hip joint angles the procedure is applied to kinematic data collected on normal subjects the uncertainty about the specification of the thigh cartesian coordinate system is shown to explain some of the between subject variability in the varus valgus and in the internal external rotation angles curves

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

quantization of multiaspect scattering data target classification and pose estimation in many sensing scenarios the observed scattered waveforms must be quantized for subsequent transmission over a communication channel rate distortion theory plays an important role in defining the bit rate required to achieve a desired distortion the distortion is typically defined in the context of signal reconstruction with the goal of achieving high fidelity synthesis of the compressed data for sensing applications however the objective is often not simply signal reconstruction but classification performance as well other related metrics include target pose estimation we consider multiaspect wave scattering in which classification and pose estimation are performed based on the quantized scattering data moreover rate distortion theory is employed to place bounds on pose estimation performance when both the target identity and pose are unknown a priori it is demonstrated that block coding with bayes vq may yield performance approaching the bound example results are presented for measured acoustic waveforms scattered from underwater elastic targets

detection and estimation in sensor arrays using weighted subspace fitting the problem of signal parameter estimation of narrowband emitter signals impinging on an array of sensors is addressed a multidimensional estimation procedure that applies to arbitrary array structures and signal correlation is proposed the method is based on the recently introduced weighted subspace fitting wsf criterion and includes schemes for both detecting the number of sources and estimating the signal parameters a gauss newton type method is presented for solving the multidimensional wsf and maximum likelihood optimization problems the global and local properties of the search procedure are investigated through computer simulations most methods require knowledge of the number of coherent noncoherent signals present a scheme for consistently estimating this is proposed based on an asymptotic analysis of the wsf cost function the performance of the detection scheme is also investigated through simulations

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

the cramer rao bound on frequency estimates of signals closely spaced in frequency unconditional case the paper analyzes the cramer rao cr bound on frequency estimation covariance for the unconditional or stochastic signal model it addresses the problem of n signals closely spaced in temporal or spatial frequency the main result is that for this regime the cr bound decomposes into a product of simple scalar factors that individually reflect frequency separation signal powers and covariances data sampling grid and sample size the factored expression provides useful insight into the behavior of the bound for closely spaced frequencies the result also leads to a new formula for the signal to noise snr threshold at which an unbiased frequency estimator can resolve signals closely spaced in frequency interestingly with a simple modification the formulae are identical to those recently obtained for the conditional or deterministic signal model

wideband array processing using a two sided correlation transformation a new method for broadband array processing is proposed the method is based on unitary transformation of the signal subspaces we apply a two sided transformation on the correlation matrices of the array it is shown that the two sided correlation transformation tct has a smaller subspace fitting error than the coherent signal subspace method csm it is also shown that unlike csm the tct algorithm can generate unbiased estimates of the directions of arrival regardless of the bandwidth of the signals the capability of the tct and csm methods for resolving two closely spaced sources is compared the resolution threshold for the new technique is much smaller than that for csm

multiaspect target identification with wave based matched pursuits and continuous hidden markov models multiaspect target identification is effected by fusing the features extracted from multiple scattered waveforms these waveforms are characteristic of viewing the target from a sequence of distinct orientations classification is performed in the maximum likelihood sense which we show under reasonable assumptions can be implemented via a hidden markov model hmm we utilize a continuous hmm paradigm and compare its performance to its discrete counterpart the feature parsing is performed via wave based matched pursuits algorithm performance is assessed by considering measured acoustic scattering data from five similar submerged elastic targets

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

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

wavefield modeling and array processing i spatial sampling we introduce the concept of wavefield modeling and study its relationship to array professing and direction finding we show how the output of an array can be written as the product of a wavefield independent sampling matrix and an array independent coefficient vector using this decomposition we derive the conditions under which the array output may be linearly interpolated to give the array output of a different array within a desired accuracy we proceed to show under what conditions the array output may be linearly interpolated to give the value of the wavefield over a continuous manifold as a result we also derive conditions under which the array manifold may be linearly transformed between frequencies finally we treat the case where the sources are known to be limited to specific possibly disjoint angular sectors of arbitrary shape and show how the sampling matrix can in this case be replaced by a modified sampling matrix of lower rank this result yields a straightforward extension of the formalism presented in this paper to the ease of limited angular sectors in two companion papers we use wavefield modeling to derive practical algorithms and bounds on the performance of arrays

double calibration an accurate reliable and easy to use method for 3d scapular motion analysis the most recent non invasive methods for the recording of scapular motion are based on an acromion marker am set and a single calibration sc of the scapula in a resting position however this method fails to accurately measure scapular kinematics above 90 of arm elevation due to soft tissue artifacts of the skin and muscles covering the acromion the aim of this study was to evaluate the accuracy and inter trial and inter session repeatability of a double calibration method dc in comparison with sc the sc and dc data were measured with an optoelectronic system during arm flexion and abduction at different angles of elevation 0 180 they were compared with palpation of the scapula using a scapula locator dc data was not significantly different from palpation for 5 6 axes of rotation tested y x and z in abduction and flexion where as sc showed significant differences for 5 6 axes the root mean square errors ranged from 2 96 to 4 48 for dc and from 6 to 9 19 for sc the inter trial repeatability was good to excellent for sc and dc the inter session repeatability was moderate to excellent for sc and moderate to good for dc coupling am and dc is an easy to use method which yields accurate and reliable measurements of scapular kinematics for the complete range of arm motion it can be applied to the measurement of shoulder motion in many fields sports orthopaedics and rehabilitation especially when large ranges of arm motion are required

reduced complexity maximum likelihood direction of arrival estimation based on spatial aliasing spatial aliasing is an undesirable phenomenon that prevents the unique determination of the direction of arrival doa of impinging signals in array signal processing however the characteristics of spatial aliasing that generates ambiguous doas can be also used to reduce the computational complexity in maximum likelihood ml doa estimation this paper proposes a structural method to dramatically reduce the computational complexity of the ml doa estimation using the spatial aliasing generated by a nested array structure with a doubly scaled aper ture an ml full grid search is computationally simplified by the highly compressed searching range and the small number of candidate values to be searched which are derived based on spatial aliasing performance analyses based on the theoretical bounds and computational complexity with computer simulations show that the proposed method requires an extremely reduced computational load compared to the conventional ml doa estimation with a uniform linear array ula while achieving the performance enhancement in the estimation accuracy due to the enlarged array aperture

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

wavefield modeling and array processing ii algorithms for pt i see ibid vol 42 no 10 p 2549 1994 we present several novel algorithms for array processing as well as extensions of existing methods based on this approach we first consider the problem of localization of wideband sources via coherent processing and show how wavefield modeling enables us to derive expressions for the frequency transformation focusing matrices this method is extended to three dimensions and to sector processing we then develop computationally efficient implementations of music and root music for the narrowband and the coherent and incoherent wideband cases as well as a natural extension of root music to any 2 d array in addition wavefield modeling allows us for the first time to extend root music to 3 d arrays and wavefields we also present a low complexity variant of root music for direction finding within a limited angular sector finally we derive a low dimensional sufficient statistic and reduced rank processing schemes for the case of oversampled arrays and or limited angular sector scenarios

coherent wide band esprit method for directions of arrival estimation of multiple wide band sources a strategy extending the coherent signal subspace method csm is proposed for estimating directions of arrival of multiple wideband sources the proposed method coherent wideband esprit extends the esprit algorithm to a framework based on the csm a simulation example is provided to illustrate the effectiveness of the proposed method