a basic convergence result for particle filtering the basic nonlinear filtering problem for dynamical systems is considered approximating the optimal filter estimate by particle filter methods has become perhaps the most common and useful method in recent years many variants of particle filters have been suggested and there is an extensive literature on the theoretical aspects of the quality of the approximation still a clear cut result that the approximate solution for unbounded functions converges to the true optimal estimate as the number of particles tends to infinity seems to be lacking it is the purpose of this contribution to give such a basic convergence result for a rather general class of unbounded functions furthermore a general framework including many of the particle filter algorithms as special cases is given

a state predictor for continuous time stochastic systems abstract this work investigates the state prediction problem for nonlinear stochastic differential systems affected by multiplicative state noise this problem is relevant in many state estimation frameworks such as filtering of continuous discrete systems i e stochastic differential systems with discrete measurements and time delay systems a very common heuristic to achieve the state prediction exploits the numerical integration of the deterministic nonlinear equation associated to the noise free system unfortunately these methods provide the exact solution only for linear systems instead here we provide the exact state prediction for nonlinear system in terms of the series expansion of the expected value of the state conditioned to the value in a previous time instant obtained according to the carleman embedding technique the truncation of the infinite series allows to compute the prediction at future times with an arbitrary approximation simulations support the effectiveness of the proposed state prediction algorithm in comparison to the aforementioned heuristic method

adaptive ode solvers in extended kalman filtering algorithms this paper studies numerical methods that are used to treat ordinary differential equations arising in extended kalman filtering algorithms such problems are called the moment equations and constitute an important subclass of differential equations they all possess a number of specific properties that make the standard available software ineffective for some mathematical models in this area for instance we show that built in matlab ode solvers are not able to cope with a number of tests considered here in contrast the hybrid method developed by mazzoni 2007 exhibits much better performance on the same examples the latter means that specially designed numerical schemes are needed for efficient solution of the moment equations instead of the standard software designed for general systems of ordinary differential equations

discrete time solutions to the continuous time differential lyapunov equation with applications to kalman filtering prediction and filtering of continuous time stochastic processes often require a solver of a continuous time differential lyapunov equation cdle for example the time update in the kalman filter

parameter estimation algorithms for a set membership description of uncertainty abstract the problem of parameter estimation when the data are corrupted by unknown but bounded errors mainly consists in characterizing the minimal parameter set consistent with the measurements the model and the error description two different approaches are reviewed and compared in this paper the first one based on a recursive parameter ellipsoidal bounding algorithm the other on an orthotopic bounding set obtained by solving linear programming problems the original ellipsoidal algorithm modified for higher efficiency has been compared with the linear programming method although the orthotopic description may result in a more accurately defined parameter region it is time consuming when a large number of measurements is present conversely the ellipsodal bounding algorithm often provides a loose approximation to the parameter region but allows a fast data preprocessing producing a smaller number of constraints that can be subsequently fed to the linear programming algorithm a combined use of the two procedures is outlined and tested on simulated and real data the latter being relative to the tuning of an a d converter resulting in a remarkable reduction in the computing time

fuzzy filter design for ito stochastic systems with application to sensor fault detection the paper deals with the robust fault detection problem for takagi sugeno t s fuzzy ito stochastic systems our aim is to develop a robust fault detection approach to the t s fuzzy systems with brownian motion by using a general observer based fault detection filter as a residual generator the robust fault detection is formulated as a filtering problem attention is focused on the design of both the fuzzy rule independent and the fuzzy rule dependent fault detection filters guaranteeing a prescribed noise attenuation level in an hinfin sense sufficient conditions are proposed to guarantee the mean square asymptotic stability with an hinfin performance for the fault detection system the corresponding solvability conditions for the desired fuzzy rule independent and fuzzy rule dependent fault detection filters are also established finally a numerical example is provided to illustrate the effectiveness of the proposed theory

main component of soft tissue artifact of the upper limbs with respect to different functional daily life and sports movements soft tissue artifact sta is the main source of error in kinematic estimation of human movements based on skin markers our objective was to determine the components of marker displacements that best describe sta of the shoulder and arm i e clavicle scapula and humerus four participants performed arm flexion and rotation a daily life and a sports movement three pins with reflective markers were inserted into the clavicle scapula and humerus in addition up to seven skin markers were stuck on each segment sta was described with a modal approach individual marker displacements or marker cluster i e translations rotations homotheties and stretches relative to the local segment coordinate system defined by markers secured to the pins the modes were then ranked according to the percentage of total sta energy that they explained both individual skin marker displacements and marker cluster geometrical transformations were task location segment and subject specific however 85 of the total sta energy was systematically explained by the rigid transformations i e translations and rotations of the marker cluster in conclusion large joint dislocations and limited efficiency of least squares bone pose estimators are expected for the computation of upper limb joint kinematics from skin markers future developments shall consider the rigid transformations of marker clusters in the implementation of an sta model to reduce its effects on kinematics estimation

efficient particle filtering via sparse kernel density estimation particle filters pfs are bayesian filters capable of modeling nonlinear non gaussian and nonstationary dynamical systems recent research in pfs has investigated ways to appropriately sample from the posterior distribution maintain multiple hypotheses and alleviate computational costs while preserving tracking accuracy to address these issues a novel utilization of the support vector data description svdd density estimation method within the particle filtering framework is presented the svdd density estimate can be integrated into a wide range of pfs to realize several benefits it yields a sparse representation of the posterior density that reduces the computational complexity of the pf the proposed approach also provides an analytical expression for the posterior distribution that can be used to identify its modes for maintaining multiple hypotheses and computing the map estimate and to directly sample from the posterior we present several experiments that demonstrate the advantages of incorporating a sparse kernel density estimate in a particle filter

visual object tracking via enhanced structural correlation filter in this study we aim to build a robust correlation based visual object tracking system the function of traditional correlation filters for visual tracking is to search the most likely position of target by circularly shifting the search image patch however the search image patch needs to be large enough to cover both the object and background which results in the algorithm being sensitive to changes in background to alleviate this problem we first propose an efficient object surrounding histogram model to suppress the background in this model we build a bayes classifier based on the initial given object and we then apply it to each pixel in subsequent frames with this model the original image can be enhanced in order to eliminate the impact of circular shifting moreover we develop a structural correlation filter that consists of both holistic and local object parts the multiple object parts are adaptively weighted and further aggregated to predict the relative motion from the last frame we conduct extensive experiments on frequently used benchmarks with 51 video sequences the experimental results show that the proposed algorithm achieves outstanding performance especially in terms of heavy occlusion and severe deformation

optimal estimation theory for dynamic systems with set membership uncertainty an overview in many problems such as linear and nonlinear regressions parameter and state estimation of dynamic systems state space and time series prediction interpolation smoothing and functions approximation one has to evaluate some unknown variable using available data the data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables typically the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory an interesting alternative approach referred to as set membership or unknown but bounded ubb error description has been investigated since the late 1960s in this approach uncertainty is described by an additive noise which is known only to have given integral typically l2 of l1 or componentwise l bounds in this paper we review the main results of this theory with special attention to the most recent advances obtained in the case of componentwise bounds

semiglobal uniform asymptotic stability of an easy to implement pll like sensorless observer for induction motors in this work stability properties of a novel and easy to implement sensorless observer for induction motors are investigated the considered solution is inspired by phase locked loop strategies and it takes advantage from the rotor flux derivatives to define a rotating vector to align with even if such variables are not directly measured input to state stability properties are proven for suitably defined electrical and magneto mechanical observation error subsystems time scale separation is then exploited to invoke singular perturbation arguments and guarantee boundedness of the observation errors trajectories finally the small gain theorem is adopted to prove semiglobal uniform asymptotic stability of the presented scheme some additional interesting properties are discussed beside the main stream of the proposed analysis simulations indicate the observer can be profitably exploited for induction machines speed sensorless control applications

efficient visual tracking using particle filter with incremental likelihood calculation in this paper we propose a particle filter that determines the weight of each particle employing the incremental likelihood calculation since there is usually a large overlap region between the two particles that are sequentially generated determining the weight of the particle has only a small time cost therefore the real time performance of the proposed tracker can be dramatically improved extensive experimental results for single object and multiple object tracking scenarios are presented to demonstrate the efficiency of the proposed approach finally an interesting color based active vision system is developed for a free floating space robot testbed to facilitate teleoperation

general two stage extended kalman filters a general two stage extended kalman filter gtsekf which extends the linear general two stage kalman filter to nonlinear systems is further proposed a new nonlinear two stage transformation is introduced to facilitate achieving this extension as in the linear one the gtsekf is derived mainly by applying the nonlinear two stage transformation to the well known extended kalman filter ekf and is shown to be equivalent to the ekf with a decoupled computing structure a nonlinear filter for estimating constant parameters in dynamic systems is presented to illustrate one application of the proposed gtsekf a literature example is also given to demonstrate the correctness and usefulness of the proposed results

c ondensation conditional density propagation forvisual tracking the problem of tracking curves in dense visual clutter is challenging kalman filtering is inadequate because it is based on gaussian densities which being unimo dal cannot represent simultaneous alternative hypotheses the condensation algorithm uses factored sampling previously applied to the interpretation of static images in which the probability distribution of possible interpretations is represented by a randomly generated set condensation uses learned dynamical models together with visual observations to propagate the random set over time the result is highly robust tracking of agile motion notwithstanding the use of stochastic methods the algorithm runs in near real time

assessment of the lower limb soft tissue artefact at marker cluster level with a high density marker set during walking the estimation of joint kinematics from skin markers is hindered by the soft tissue artefact sta a well known phenomenon although not fully characterized while most assessments of the sta have been performed based on the individual skin markers displacements recent assessments were based on the marker cluster geometrical transformations using e g principal component or modal analysis however these marker clusters were generally made of 4 6 markers and the current findings on the sta could have been biased by the limited number of skin makers analysed the objective of the present study was therefore to confirm them with a high density marker set i e 40 markers placed on the segments a larger number of modes than found in the literature was required to describe the sta nevertheless translations and rotations of the marker cluster remained the main sta modes archetypally the translation along the proximal distal and anterior posterior axes for the shank and the translation along the proximal distal axis and the rotation about the medial lateral axis for the thigh high correlations were also found between the knee flexion angle and the amplitude of these modes for the thigh whereas moderate ones were found for the shank these findings support the current re orientation of the sta compensation methods from bone pose estimators which typically address the non rigid components of the marker cluster to kinematic driven rigid component sta models

hessian matrix distribution for bayesian policy gradient reinforcement learning bayesian policy gradient algorithms have been recently proposed for modeling the policy gradient of the performance measure in reinforcement learning as a gaussian process these methods were known to reduce the variance and the number of samples needed to obtain accurate gradient estimates in comparison to the conventional monte carlo policy gradient algorithms in this paper we propose an improvement over previous bayesian frameworks for the policy gradient we use the hessian matrix distribution as a learning rate schedule to improve the performance of the bayesian policy gradient algorithm in terms of the variance and the number of samples as in computing the policy gradient distributions the bayesian quadrature method is used to estimate the hessian matrix distributions we prove that the posterior mean of the hessian distribution estimate is symmetric one of the important properties of the hessian matrix moreover we prove that with an appropriate choice of kernel the computational complexity of hessian distribution estimate is equal to that of the policy gradient distribution estimates using simulations we show encouraging experimental results comparing the proposed algorithm to the bayesian policy gradient and the bayesian policy natural gradient algorithms described in ghavamzadeh and engel 10

soft tissue artifact distribution on lower limbs during treadmill gait influence of skin markers location on cluster design segment poses and joint kinematics estimated from skin markers are highly affected by soft tissue artifact sta and its rigid motion component starm while four marker clusters could decrease the sta non rigid motion during gait activity other data such as marker location or starm patterns would be crucial to compensate for sta in clinical gait analysis the present study proposed 1 to devise a comprehensive average map illustrating the spatial distribution of sta for the lower limb during treadmill gait and 2 to analyze starm from four marker clusters assigned to areas extracted from spatial distribution all experiments were realized using a stereophotogrammetric system to track the skin markers and a bi plane fluoroscopic system to track the knee prosthesis computation of the spatial distribution of sta was realized on 19 subjects using 80 markers apposed on the lower limb three different areas were extracted from the distribution map of the thigh the marker displacement reached a maximum of 24 9 mm and 15 3 mm in the proximal areas of thigh and shank respectively starm was larger on thigh than the shank with rms error in cluster orientations between 1 2 and 8 1 the translation rms errors were also large 3 0 mm to 16 2 mm no marker cluster correctly compensated for starm however the coefficient of multiple correlations exhibited excellent scores between skin and bone kinematics as well as for starm between subjects these correlations highlight dependencies between starm and the kinematic components this study provides new insights for modeling starm for gait activity

structure selection for bounded parameter models consistency conditions and selection criterion strong consistency conditions for structure selection in bounded parameter models are studied a certain robust selection criterion based on the volume of the exact parameter bounding polytope is proposed for linear regression models the effectiveness of the polytope volume criterion is demonstrated on a model nonlinear in its variables but linear in its parameters its strong consistency is proved for a large class of noise distributions the usual assumptions on the noise namely independence constant variance or martingale difference properties need not be made but asymptotic independence is assumed

accurate numerical implementation of the continuous discrete extended kalman filter this paper addresses an accurate and effective implementation of the continuous discrete extended kalman filtering method the technique under discussion is grounded in numerical solution of the moment differential equations to predict the state mean of the stochastic dynamical system and the corresponding error covariance matrix here we apply an efficient embedded runge kutta pair possessing superior stability and many other attractive features including automatic global error control in order to improve performance of the complex computational procedure consisting of the extended kalman filter and the underlying adaptive ode solver thus we introduce a new continuous discrete adaptive extended kalman filter and show its advantage over the standard variant on two test examples in practice this technique allows for much longer sampling intervals without any loss of accuracy and that improves the applied potential of the extended kalman filtering method significantly

a chaotic iterative algorithm based on linearized bregman iteration for image deblurring in this paper we propose a new chaotic iterative algorithm for image deblurring the algorithm is based on generalized inverse iteration and linearized bregman iteration for the basis pursuit problem min u r n u 1 au f numerical experiments show that the chaotic algorithm for image restoration is effective and efficient

on the value of information in system identification bounded noise case assuming instantaneous bounds on the noise system parameter identification is formulated as membership set estimation problem sequential algorithms are constructed to estimate the membership sets of the parameters which are consistent with the measurements and the noise constraints the important new feature of the proposed algorithms is their ability to ignore redundant data the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm the convergence properties and the notion of identifiability in the set theoretic context are also studied

various ways to compute the continuous discrete extended kalman filter the extended kalman filter ekf is a very popular tool dealing with state estimation its continuous discrete version cd ekf estimates the state trajectory of continuous time nonlinear models whose internal state is described by a stochastic differential equation and which is observed through a noisy nonlinear form of the sampled state the prediction step of the cd ekf leads to solve a differential equation that cannot be generally solved in a closed form this technical note presents an overview of the numerical methods including recent works usually implemented to approximate this filter comparisons of theses methods on two different nonlinear models are finally presented the first one is the van der pol oscillator which is widely used as a benchmark the second one is a neuronal population model this more original model is used to simulate eeg activity of the cortex experiments showed better stability properties of implementations for which the positivity of the prediction matrix is guaranteed

a model of the soft tissue artefact rigid component when using stereophotogrammetry and skin markers the reconstruction of skeletal movement is affected by soft tissue artefact sta this may be described by considering a marker cluster as a deformable shape undergoing a geometric transformation formed by a non rigid change in size and shape and a rigid component translation and rotation displacements a modal decomposition of the sta relative to an appropriately identified basis allows the separation of these components this study proposes a mathematical model of the sta that embeds only its rigid component and estimates the relevant six mode amplitudes as linear functions of selected proximal and distal joint rotations during the analysed task this model was successfully calibrated for thigh and shank using simultaneously recorded pin and skin marker data of running volunteers the root mean square difference between measured and model estimated sta rigid component was 1 1 0 8 mm median inter quartile range over 3 subjects 5 trials 33 markers coordinates and it was mostly due to the wobbling not included in the model knee joint kinematics was estimated using reference pin marker data and skin marker data both raw and compensated with the model estimated sta sta compensation decreased inaccuracy on average from 6 to 1 for flexion extension from 43 to 18 for the other two rotations and from 69 to 25 for the linear displacements thus the proposed mathematical model provides an sta estimate which can be effectively used within optimal bone pose and joint kinematics estimators for artefact compensation and for simulations aimed at their comparative assessments

multiple object tracking with partial occlusion handling using salient feature points abstract handling occlusion has been a challenging task in object tracking in this paper we propose a multiple object tracking method in the presence of partial occlusion using salient feature points we first extract the prominent feature points from each target object and then use a particle filter based approach to track the feature points in image sequences based on various attributes such as location velocity and other descriptors we then detect and revise the feature points that have been tracked incorrectly the main idea is that even if some feature points are not successfully tracked due to occlusion or poor imaging condition the other correctly tracked features can collectively perform the corrections on their behalf finally we track the objects using the correctly tracked feature points through a hough like approach and the object bounding boxes are updated using the relative locations of these feature points experimental results demonstrate that our method is proficient in providing accurate human tracking as well as appropriate occlusion handling compared to the existing methods

identification and application of bounded parameter models abstract the place of parameter bounding algorithms in identification methodology is discussed such algorithms provide a radical alternative to the computation of parameter point estimates and covariances instead of p d f or mean and covariance for the noise and prior parameter estimates they require bounds in an essentially deterministic model formulation the paper is a preliminary review of some standard tasks namely experiment design testing for outliers toleranced prediction and worst case control design in the context of parameter bounding identification computational requirements of these tasks are examined and the limitations of existing parameter bounding algorithms are noted

progressive match expansion via coherent subspace constraint in this paper a quasi dense matching algorithm called progressive match expansion via coherent subspace pecs is proposed our algorithm starts from a set of sparse seeds and iteratively expands potential matches in the region around the seeds until no more matches could be found the main difference from previous methods is that our method computes a coherent non rigid transformation to relate the matching pixels instead of using local planar affine model to approximate the real scene surface within the expanding region the points in the expanding region are treated as a whole and all the matches satisfying the transformation are found at once first dense sift descriptors are extracted and a subspace encoding the feature similarity between two point sets is computed this embedding pulls two points closer if they have similar features and makes the non rigid transformation learning more robust second a coherent non rigid transformation in the subspace is computed to move one point set towards the other and the spatially aligned two points denote a match the proposed model is robust to scenes with non smooth surface and experiment results reveal the good performance in both 2d image matching and 3d reconstruction

an active contour model and its algorithms with local and global gaussian distribution fitting energies in this paper we propose an active contour model and its corresponding algorithms with detailed implementation for image segmentation in the proposed model the local and global region fitting energies are described by the combination of the local and global gaussian distributions with different means and variances respectively in this combination we increase a weighting coefficient by which we can adjust the ratio between the local and global region fitting energies then we present an algorithm for implementing the proposed model directly considering that in practice the selection of the weighting coefficient is troublesome we present a modified algorithm in order to overcome this problem and increase the flexibility by adaptively updating the weighting coefficient and the time step with the contour evolution this algorithm is less sensitive to the initialization of the contour and can speed up the convergence rate besides it is robust to the noise and can be used to extract the desired objects experiment results demonstrate that the proposed model and its algorithms are effective with application to both the synthetic and real world images

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

optimal solution of the two stage kalman estimator the two stage kalman estimator was originally proposed to reduce the computational complexity of the augmented state kalman filter it was also applied to the tracking of maneuvering targets by treating the target acceleration as a bias term except in certain restrictive conditions the conventional two stage estimators are suboptimal in the sense that they are not equivalent to the augmented state filter in this paper the authors propose a new two stage kalman estimator i e new structure which is an extension of friedland s estimator and is optimal in general conditions in addition we provide some analytic results to demonstrate the computational advantages of two stage estimators over augmented ones

speed and rotor flux estimation of induction machines using a two stage extended kalman filter this paper presents an effective implementation of an extended kalman filter used for the estimation of both rotor flux and rotor velocity of an induction motor an algorithm proposed by hsieh and chen in hsieh c s chen f c 1999 optimal solution of the two stage kalman estimator ieee transactions on automatic control 44 1 194 199 for linear parameter estimation is extended to non linear estimation where parameters such as the velocity of an induction machine are present in the transition matrix and in the augmented state space compared to a straightforward implementation of an extended kalman filter our modified optimal two stage kalman estimator reduces the number of arithmetic operations by 25 allowing higher sampling rate or the use of a cheaper microcontroller

numerical methods for stochastic differential equations stochastic differential equations sde s play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability a general strategy for developing accurate and efficient schemes for solving stochastic equations is outlined here high order numerical methods are developed for the integration of stochastic differential equations with strong solutions we demonstrate the accuracy of the resulting integration schemes by computing the errors in approximate solutions for sde s which have known exact solutions

an intensive restraint topology adaptive snake model and its application in tracking dynamic image sequence the aim of this work is to propose an improved intensive restraint topology adaptive snake model for detecting and tracking target contours with complex topological morphology from dynamic gray scale image sequences the image is discretized by orthogonal equidistant grid lines and snake nodes are constrained to move only from one grid vertex to another along grid lines thus the computation is much simpler than those of other t snakes since complicated calculation of intersection points of snake curve and grid lines is not required topological transformation is implemented through splitting snake nodes as well as automatically detecting and eliminating topological collision an adaptive weighted expansion energy term is introduced into snake s energy function driving the model to pass across the region with non uniform intensity distribution inside the target region the required manual interaction is reduced to only select a random point within the target region in the first frame of the image sequence for subsequent frames the detection result in the previous frame is regarded as the initial model in the current frame through experiments on simulated image data and clinical x ray coronary angiographic sequences the model s topological flexibility and lower computation cost compared with other t snakes are demonstrated also the sensitivity of the model to weights of the energy terms and grid size as well as the initial plan of the model is discussed based on experimental results

extension of friedland s separate bias estimation to randomly time varying bias of nonlinear systems by extending b friedland s 1969 separate bias estimation algorithm for linear systems to nonlinear systems and combining the result with the suboptimal fading extended kalman filter proposed by d h zhou 1990 and by d h zhou et al a pseudo separate bias estimation algorithm for randomly time varying bias of a class of nonlinear time varying stochastic systems is obtained a simulation example is presented to illustrate the effectiveness of the algorithm

object tracking from image sequences using adaptive models in fuzzy particle filter this paper describes a vision based system for tracking objects from image sequences the proposed system has the standard architecture with a particle filter which is a popular algorithm to track objects in real time many tracking algorithms have a great difficulty in tracking objects robustly by reason of complex background and rapid changes under a real complex environment such as a traffic road to make a robust algorithm for object tracking we propose the method that uses the adaptive autoregressive model as a state transition model and the adaptive appearance mixture model as an observation model but in case of changing the state of a tracked object suddenly the adaptive models may not make the optimal parameters for accurate states at current time because the noise variance of the adaptive models in this case is larger than that in normal case it has an effect on the accuracy of an object tracking algorithm thus we propose a fuzzy particle filter to overcome problems from the occurrence of the unexpected improper variances due to several causes in this paper as the process noises and the observation noises in a fuzzy particle filter are considered as fuzzy variables by using the possibility theory a fuzzy particle filter with fuzzy noises is used to manage uncertainty in various noise models also we make possibility measure as using the fuzzy relation equation which is defined by these fuzzy variables and then the states are estimated by using a fuzzy expected value operator also because the proposed algorithm applies several functions to improve the accuracy of tracking an object the performance of tracking speed deteriorates to resolve this problem to some extent we consider the fact that a fuzzy particle filter has a little bit of an effect on the number of particles consequently we propose the method which can adjust the number of particles by using the result from a measurement step in order to improve the speed for an object tracking in the proposed algorithm the experiments of this paper show that the proposed method is efficient and has many advantages for an object tracking in real environments

soft tissue artifact compensation by linear 3d interpolation and approximation methods several compensation methods estimate bone pose from a cluster of skin mounted makers each influenced by soft tissue artifact sta in this study linear 3d interpolation and approximation methods affine mapping kriging and radial basis function rbf and the conventional singular value decomposition svd method were examined to determine their suitability for sta compensation the ability of these four methods to estimate knee angles and displacements was compared using simulated gait data with and without added sta the knee angle and the displacement estimates of all four methods were similar with root mean square errors rmses near 1 5 degrees and 4mm respectively the 3d interpolation and approximation methods were more complicated to implement than the conventional svd method however these non standard methods provided additional geometric homothety stretch and time functions that model the deformation of the cluster of markers this additional information may be useful to model and compensate the sta

hard frequency domain model error bounds from least squares like identification techniques the problem of deriving so called hard error bounds for estimated transfer functions is addressed a hard bound is one that is sure to be satisfied i e the true system nyquist plot will be confined with certainty to a given region provided that the underlying assumptions are satisfied by blending a priori knowledge and information obtained from measured data it is shown how the uncertainty of transfer function estimates can be quantified the emphasis is on errors due to model mismatch the effects of unmodeled dynamics can be considered as bounded disturbances hence techniques from set membership identification can be applied to this problem the approach taken corresponds to weighted least squares estimation and provides hard frequency domain transfer function error bounds the main assumptions used in the current contribution are that the measurement errors are bounded that the true system is indeed linear with a certain degree of stability and that there is some knowledge about the shape of the true frequency response

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

accuracy of single plane fluoroscopy in determining relative position and orientation of total knee replacement components abstract the accuracy of estimating the relative pose between knee replacement components in terms of clinical motion is important in the study of knee joint kinematics the objective of this study was to determine the accuracy of the single plane fluoroscopy method in calculating the relative pose between the femoral component and the tibial component along knee motion axes while the components were in motion relative to one another the kinematics of total knee replacement components were determined in vitro using two simultaneous methods single plane fluoroscopic shape matching and an optoelectronic motion tracking system the largest mean differences in relative pose between the two methods for any testing condition were 2 1 0 3 and 1 1 in extension abduction and internal rotation respectively and 1 3 0 9 and 1 9 mm in anterior distal and lateral translations respectively for the optimized position of the components during dynamic trials the limits of agreement between which 95 of differences can be expected to fall were 2 9 to 4 5 in flexion 0 9 to 1 5 in abduction 2 4 to 2 1 in external rotation 2 0 to 3 9 mm in anterior posterior translation 2 2 to 0 4 mm in distal proximal translation and 7 2 to 8 6 mm in medial lateral translation these mean accuracy values and limits of agreement can be used to determine whether the shape matching approach using single plane fluoroscopic images is sufficiently accurate for an intended motion tracking application

technical communique stochastic stability of the unscented kalman filter with intermittent observations in this paper the stochastic stability of the discrete time unscented kalman filter for general nonlinear stochastic systems with intermittent observations is proposed it is shown that the estimation error remains bounded if the system satisfies some assumptions and the statistical convergence property of the estimation error covariance is studied showing the existence of a critical value for the arrival rate of the observations an upper bound on this expected state error covariance is given a numerical example is given to illustrate the effectiveness of the techniques developed

set membership identification of systems with parametric and nonparametric uncertainty a method for parameter set estimation in which the system model is assumed to contain both parametric and nonparametric uncertainty is presented in the disturbance free case the parameter set estimate is guaranteed to contain the parameter set of the true plant in the presence of stochastic disturbances the parameter set estimate obtained from finite data records is shown to have the property that it contains the true plant parameter set with probability one as the data length tends to infinity

multiresolution gray scale and rotation invariant texture classification with local binary patterns presents a theoretically very simple yet efficient multiresolution approach to gray scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions the method is based on recognizing that certain local binary patterns termed uniform are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature we derive a generalized gray scale and rotation invariant operator presentation that allows for detecting the uniform patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis the proposed approach is very robust in terms of gray scale variations since the operator is by definition invariant against any monotonic transformation of the gray scale another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table experimental results demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns

a novel approach to filter design for t s fuzzy discrete time systems with time varying delay in this paper the problem of l2 l filtering for a class of discrete time takagi sugeno t s fuzzy time varying delay systems is studied our attention is focused on the design of full and reduced order filters that guarantee the filtering error system to be asymptotically stable with a prescribed h performance sufficient conditions for the obtained filtering error system are proposed by applying an input output approach and a two term approximation method which is employed to approximate the time varying delay the corresponding full and reduced order filter design is cast into a convex optimization problem which can be efficiently solved by standard numerical algorithms finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

asymptotically convergent modified recursive least squares with data dependent updating and forgetting factor for systems with bounded noise continual updating of estimates required by most recursive estimation schemes often involves redundant usage of information and may result in system instabilities in the presence of bounded output disturbances an algorithm which eliminates these difficulties is investigated based on a set theoretic assumption the algorithm yields modified least squares estimates with a forgetting factor it updates the estimates selectively depending on whether the observed data contain sufficient information the information evaluation required at each step involves very simple computations in addition the parameter estimates are shown to converge asymptotically at an exponential rate to a region around the true parameter

kalman filtering for continuous time uncertain systems with markovian jumping parameters studies the problem of kalman filtering for a class of uncertain linear continuous time systems with markovian jumping parameters the system under consideration is subjected to time varying norm bounded parameter uncertainties in the state and measurement equations stochastic quadratic stability of the above system is analyzed a state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties which is in terms of solutions of two sets of coupled algebraic riccati equations

generalized mathematical representation of the soft tissue artefact abstract while reconstructing skeletal movement using stereophotogrammetry the relative movement between a skin marker and the underlying bone is regarded as an artefact soft tissue artefact sta similarly the consequent pose size and shape variations that affect a cluster of markers associated with a bony segment or any arbitrary change of configuration in the marker local positions as representative of the skin envelope shape variation may also be looked upon as an sta bone pose estimators able to compensate for these artefacts must embed relevant a priori knowledge in the form of an sta mathematical model prior to tackling this modeling exercise an appropriate definition and mathematical representation of the sta time histories must be accomplished relevant appropriateness is based on the degree of approximation of the sta reconstruction and on the number of parameters involved the objective of this study was to propose a generalized mathematical representation of the sta which would be applicable for most plausible definitions of it to this purpose a modal approach was used that most importantly allows for the splitting of a given sta into additive components modes for each sta definition these modes may be ranked according to the contribution that each of them gives to the reconstruction of the sta in this way the sta definition leading to the minimum number of modes and therefore of parameters that provides an adequate approximation for further purposes can be selected allowing a trade off between complexity and effectiveness of the sta model using information available in the literature and data provided by an ex vivo experiment it is shown that the modes corresponding to the different sta definitions individual marker displacements marker cluster geometrical transformations and skin envelope shape variations can be ranked and selected leading respectively to a large moderate or low number of parameters embedded in the sta mathematical representation

parameter identification in the presence of non parametric dynamic uncertainty abstract this paper provides identification laws which yield monotonic parameter error reduction in the absence of external noise inputs but in the presence of non parametric dynamic uncertainty unmodelled dynamics this paper considers two non parametric uncertainty sets motivated by robust control the weighted ball in h and the weighted ball in the induced l2 norm the non parametric uncertainty produces signals which corrupt the signals used in identification this paper shows that the corruption is non conservatively bounded in an l2 sense this l2 bound is then compared with the signal energy with the result used to enable disable the parameter adjustment of a gradient least squares adjustment mechanism it is proved that the resulting parameter adjustment yields non increasing parameter errors with strictly decreasing parameter errors whenever the parameter errors are distinguishable from zero given the system input and output histories

asymptotic properties of set membership identification algorithms this paper addresses the asymptotic worst case properties of set membership identification smid algorithms we first present a set membership identification algorithm which can be used with a model structure consisting of parametric and nonparametric uncertainty as well as output additive disturbances this algorithm is then studied in the context of asymptotic worst case behavior we derive lower bounds on the worst case achievable identification error measured by the volume as well as the sum of sidelengths of the identified ellipsoidal uncertainty sets we then show that there exist inputs which can shrink the uncertainty sets to these lower bounds

bone orientation and position estimation errors using cosserat point elements and least squares methods application to gait the aim of this study was to analyze the accuracy of bone pose estimation based on sub clusters of three skin markers characterized by triangular cosserat point elements tcpes and to evaluate the capability of four instantaneous physical parameters which can be measured non invasively in vivo to identify the most accurate tcpes moreover tcpe pose estimations were compared with the estimations of two least squares minimization methods applied to the cluster of all markers using rigid body rbls and homogeneous deformation hdls assumptions analysis was performed on previously collected in vivo treadmill gait data composed of simultaneous measurements of the gold standard bone pose by bi plane fluoroscopy tracking the subjects knee prosthesis and a stereophotogrammetric system tracking skin markers affected by soft tissue artifact femur orientation and position errors estimated from skin marker clusters were computed for 18 subjects using clusters of up to 35 markers results based on gold standard data revealed that instantaneous subsets of tcpes exist which estimate the femur pose with reasonable accuracy median root mean square error during stance swing 1 4 2 8deg for orientation 1 5 4 2mm for position a non invasive and instantaneous criteria to select accurate tcpes for pose estimation 4 8 7 3deg 5 8 12 3mm was compared with rbls 4 3 6 6deg 6 9 16 6mm and hdls 4 6 7 6deg 6 7 12 5mm accounting for homogeneous deformation using hdls or selected tcpes yielded more accurate position estimations than rbls method which conversely yielded more accurate orientation estimations further investigation is required to devise effective criteria for cluster selection that could represent a significant improvement in bone pose estimation accuracy

utilization of modified polar coordinates for bearings only tracking previous studies have shown that the cartesian coordinate extended kalman filter exhibits unstable behavior characteristics when utilized for bearings only target motion analysis tma in contrast formulating the tma estimation problem in modified polar mp coordinates leads to an extended kalman filter which is both stable and asymptotically unbiased exact state equations for the mp filter are derived without imposing any restrictions on own ship motion thus prediction accuracy inherent in the traditional cartesian formulation is completely preserved in addition these equations reveal that mp coordinates are well suited for bearings only tma because they automatically decouple observable and unobservable components of the estimated state vector such decoupling is shown to prevent covariance matrix ill conditioning which is the primary cause of filter instability further investigation also confirms that the mp state estimates are asymptotically unbiased realistic simulation data are presented to support these findings and to compare algorithm performance with respect to the cramer rao lower bound ideal as well as the cartesian and pseudolinear filters

new developments in state estimation for nonlinear systems based on an interpolation formula accurate state estimators for nonlinear systems can be derived the estimators do not require derivative information which makes them simple to implement

optimal multistage kalman estimators an optimal multistage kalman estimator omske is proposed as a generalization of the optimal two stage kalman estimator for the reduction of the computational burden of the kalman estimator ke for discrete time linear time varying systems with triangular transition matrices this new filer is obtained by applying a multistage u v transformation to decouple the covariances of the ke it is shown analytically that the computational complexity of the omske is less than that of the ke and is minimum when the system transition matrix has the maximum stage number

technical communique two stage kalman estimator with unknown exogenous inputs this paper presents a two stage estimator for bias and state filtering in discrete time stochastic linear systems affected by unknown inputs or disturbances we show that the state estimate can be expressed as x k k x k k b k kb k k where x k k is a bias free state estimate and b k k the optimal estimate of constant bias the proposed two stage estimator is based on an alternate derivation of the unbiased minimum variance estimator with unknown exogenous inputs developed by darouach and zasadzinski 1997 automatica 33 717 719

a new continuous discrete particle filter for continuous discrete nonlinear systems abstract the continuous discrete version of particle filter cd pf for continuous discrete nonlinear systems is proposed in this paper firstly the continuous discrete extended kalman filter cd ekf and the cd pf are described in detail then some comparisons of these two methods are carried out the simulation results show that the performance of the cd pf is better than that of the cd ekf then higher order stochastic runge kutta schemes are proposed to improve the stability and precision of the filter furthermore the cd pf is applied to nonlinear systems with nongaussian noise finally some simulations are provided to illustrate the effectiveness of the proposed filter

mean shift mode seeking and clustering mean shift a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed in the paper this generalization makes some k means like clustering algorithms its special cases it is shown that mean shift is a mode seeking process on the surface constructed with a shadow kernal for gaussian kernels mean shift is a gradient mapping convergence is studied for mean shift iterations cluster analysis if treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data applications in clustering and hough transform are demonstrated mean shift is also considered as an evolutionary strategy that performs multistart global optimization

state estimation incorporating infrequent delayed and integral measurements this paper investigates the problem of state estimation incorporating infrequent delayed and integral measurements in chemical process there often exist two types of measurements on one hand the measurements for process variables such as flow rates and pressures are sampled frequently and are available nearly instantaneously on the other hand the measurements for quality variables such as concentration are sampled infrequently and are available with a delay due to long analysis time involved moreover due to the interval time taken by chemical sample collection the measurements for some quality variables have another important characteristic it is a function of the states of the compositions over a period of time this paper formulates the process with infrequent delayed and integral measurements as an equivalent variable dimension system whose measurements are both delay and integration free based on the new model a variable dimension unscented kalman filter vd ukf is proposed to estimate the states furthermore the stability of the proposed vd ukf is analyzed compared with the existing results the proposed stability condition is significantly relaxed and the invertibility condition of jacobian matrices is no longer needed finally a simulation example demonstrates the effectiveness of the proposed method

assessment of intersegmental coordination of rats during walking at different speeds application of continuous relative phase abstract the present study investigated the feasibility and reliability of continuous relative phase crp and deviation phase dp to assess intersegmental hind limb coordination pattern and coordination variability in rats during walking twenty six adult rats walked at 8 m min 12 m min and 16 m min while two dimensional kinematics were recorded segment angles and segment angular velocities of the paw shank and thigh on the left hind limb were extracted from 15 strides and crp was calculated for the paw shank and shank thigh coupling the effect of walking speed on the time point average curve of the crp acrp and dp and on the mean acrp and mean dp was established by statistical parametric mapping spm and a one way anova for repeated measures absolute and relative reliability were assessed by measurement error and intra class correlation coefficient the spm analysis revealed time dependent differences in the effect of speed thus the crp of the paw shank coupling decreased with increasing speed during most of the gait cycle while the crp of the shank thigh coupling was decreased during the swing phase the session to session reliability was fair to good for the coordination measure and poor for the variability measure

optimal and suboptimal separate bias kalman estimators for a stochastic bias addresses two issues concerning the separate bias kalman estimator the first of these issues deals with the derivation of the optimal estimator for the general case in which the bias vector is stochastic in nature and the second issue deals with defining a suitable suboptimal realization of the generalized estimator

rigid and non rigid geometrical transformations of a marker cluster and their impact on bone pose estimation when stereophotogrammetry and skin markers are used bone pose estimation is jeopardised by the soft tissue artefact sta at marker cluster level this can be represented using a modal series of rigid rt translation and rotation and non rigid nrt homothety and scaling geometrical transformations the nrt has been found to be smaller than the rt and claimed to have a limited impact on bone pose estimation this study aims to investigate this matter and comparatively assessing the propagation of both sta components to bone pose estimate using different numbers of markers twelve skin markers distributed over the anterior aspect of a thigh were considered and sta time functions were generated for each of them as plausibly occurs during walking using an ad hoc model and represented through the geometrical transformations using marker clusters made of four to 12 markers affected by these stas and a procrustes superimposition approach bone pose and the relevant accuracy were estimated this was done also for a selected four marker cluster affected by stas randomly simulated by modifying the original sta nrt component so that its energy fell in the range 30 90 of total sta energy the pose error which slightly decreased while increasing the number of markers in the marker cluster was independent from the nrt amplitude and was always null when the rt component was removed it was thus demonstrated that only the rt component impacts pose estimation accuracy and should thus be accounted for when designing algorithms aimed at compensating for sta