Showing papers on "Alpha beta filter published in 2003"
09 Jul 2003
TL;DR: Numerical results show that the proposed methodology to estimate n, based on an extended Kalman filter coupled with a change detection mechanism, shows both high accuracy as well as prompt reactivity to changes in the network occupancy status.
Abstract: Throughput performance of the IEEE 802.11 distributed coordination function (DCF) is very sensitive to the number n of competing stations. The contribute of this paper is threefold. First, we show that n can be expressed as function of the collision probability encountered on the channel; hence, it can be estimated based on run-time measurements. Second, we show that the estimation of n, based on exponential smoothing of the measured collision probability (specifically, an ARMA filter), results to be a biased estimation, with poor performance in terms of accuracy/tracking trade-offs. Third, we propose a methodology to estimate n, based on an extended Kalman filter coupled with a change detection mechanism. This approach shows both high accuracy as well as prompt reactivity to changes in the network occupancy status. Numerical results show that, although devised in the assumption of saturated terminals, our proposed approach results effective also in non-saturated conditions, and specifically in tracking the average number of competing terminals.
490 citations
04 Jun 2003
TL;DR: An empirical study comparing the performance of unscented and extended Kalman filtering for improving human head and hand tracking, represented with quaternions, which are critical for correct viewing perspectives in virtual reality.
Abstract: The unscented Kalman filter is a superior alternative to the extended Kalman filter for a variety of estimation and control problems. However, its effectiveness for improving human motion tracking for virtual reality applications in the presence of noisy data has been unexplored. In this paper, we present an empirical study comparing the performance of unscented and extended Kalman filtering for improving human head and hand tracking. Specifically, we examine human head and hand orientation motion signals, represented with quaternions, which are critical for correct viewing perspectives in virtual reality. Our experimental results and analysis indicate that unscented Kalman filtering performs equivalently with extended Kalman filtering. However, the additional computational overhead of the unscented Kalman filter and quasi-linear nature of the quaternion dynamics lead to the conclusion that the extended Kalman filter is a better choice for estimating quaternion motion in virtual reality applications.
340 citations
TL;DR: Two reduced-order input estimators built upon a state functional observer are proposed, the first is an extension of a state/input estimator, while the second is based on adaptive observer design technique.
243 citations
TL;DR: In this paper, the authors examined the use of three adaptive filtering techniques, i.e., adaptive Kalman filter covariance, multiple model adaptive estimation and adaptive estimation, to test the dynamic alignment of the inertial sensor errors.
Abstract: GPS and low-cost INS sensors are widely used for positioning and attitude determination applications. Low-cost inertial sensors exhibit large errors that can be compensated using position and velocity updates from GPS. Combining both sensors using a Kalman filter provides high-accuracy, real-time navigation. A conventional Kalman filter relies on the correct definition of the measurement and process noise matrices, which are generally defined a priori and remain fixed throughout the processing run. Adaptive Kalman filtering techniques use the residual sequences to adapt the stochastic properties of the filter on line to correspond to the temporal dependence of the errors involved. This paper examines the use of three adaptive filtering techniques. These are artificially scaling the predicted Kalman filter covariance, the Adaptive Kalman Filter and Multiple Model Adaptive Estimation. The algorithms are tested with the GPS and inertial data simulation software. A trajectory taken from a real marine trial is used to test the dynamic alignment of the inertial sensor errors. Results show that on line estimation of the stochastic properties of the inertial system can significantly improve the speed of the dynamic alignment and potentially improve the overall navigation accuracy and integrity.
231 citations
08 Jul 2003
TL;DR: In this article, an Unscented Kalman filter was proposed for real-time estimation of a rigid body orientation from measurements of acceleration, angular velocity and magnetic field strength.
Abstract: This paper describes a Kalman filter for the real-time estimation of a rigid body orientation from mea- surements of acceleration, angular velocity and magnetic field strength. A quaternion representation of the orienta- tion is computationally effective and avoids problems with singularities. The nonlinear relationship between estimated Orientation and expected measurement prevent the usage of a classical Kalman filter: This problem is solved by an Un- scented Kalman filter which allows nonlinear process and measurement models and is more accurate and less costly than the common Extended Kalman filter: Several exten- sions to the original Unscented Kalman filter are necessary to treat the inherent properties of unit quaternions. Results with simulated and measured data are discussed.
223 citations
22 May 2003
TL;DR: Novel algorithms for predictive tracking of user position and orientation based on double exponential smoothing are presented, which are faster, easier to implement, and perform equivalently to the Kalman and extended Kalman filtering predictors.
Abstract: We present novel algorithms for predictive tracking of user position and orientation based on double exponential smoothing. These algorithms, when compared against Kalman and extended Kalman filter-based predictors with derivative free measurement models, run approximately 135 times faster with equivalent prediction performance and simpler implementations. This paper describes these algorithms in detail along with the Kalman and extended Kalman Filter predictors tested against. In addition, we describe the details of a predictor experiment and present empirical results supporting the validity of our claims that these predictors are faster, easier to implement, and perform equivalently to the Kalman and extended Kalman filtering predictors.
176 citations
04 Jun 2003
TL;DR: A comparison study of performances and characteristics of three advanced state observers, including the high-gain observers, the sliding-mode observers and the extended state observers shows that, over all, the extendedstate observer is much superior in dealing with dynamic uncertainties, disturbances and sensor noise.
Abstract: This paper presents a comparison study of performances and characteristics of three advanced state observers, including the high-gain observers, the sliding-mode observers and the extended state observers. These observers were originally proposed to address the dependence of the classical observers, such as the Kalman filter and the Luenberger observer, on the accurate mathematical representation of the plant. The results show that, over all, the extended state observer is much superior in dealing with dynamic uncertainties, disturbances and sensor noise. Several novel nonlinear gain functions are proposed to address the difficulty in dealing with unknown initial conditions. Simulation and experimental results are provided.
176 citations
TL;DR: A practical model observer for the signal-detection task is reviewed and an alternative is the ideal linear observer constrained to a small set of channels: the channelized-Hotelling observer.
Abstract: Image quality can be objectively defined according to how well an observer can perform a task of practical interest given the image. We review a practical model observer for the signal-detection task. The ideal observer for this task is a function of the image probability distributions, which are multidimensional and complicated. This observer is often too difficult to derive or estimate. An alternative to the ideal observer is the ideal linear observer, which can still be unmanageable. Our alternative is the ideal linear observer constrained to a small set of channels: the channelized-Hotelling observer.
159 citations
TL;DR: Performance comparisons show that the KPF is an improvement over Condensation, while the UPF has a much higher computational cost for equal tracking error.
158 citations
TL;DR: A new observer is developed to determine range information (and, hence, the three-dimensional (3-D) coordinates) of an object feature moving with affine motion dynamics (or the more general Ricatti motion dynamics) with known motion parameters.
Abstract: In this note, a new observer is developed to determine range information (and, hence, the three-dimensional (3-D) coordinates) of an object feature moving with affine motion dynamics (or the more general Ricatti motion dynamics) with known motion parameters. The unmeasurable range information is determined from a single camera provided an observability condition is satisfied that has physical significance. To develop the observer, the perspective system is expressed in terms of the nonlinear feature dynamics. The structure of the proposed observer is inspired by recent disturbance observer results. The proposed technique facilitates a Lyapunov-based analysis that is less complex than the sliding-mode based analysis derived for recent observer designs. The analysis demonstrates that the 3-D task-space coordinates of the feature point can be asymptotically identified. Simulation results are provided that illustrate the performance of the observer in the presence of noise.
150 citations
10 Nov 2003
TL;DR: This paper extends the sparse extended information filter to handle data association problems and report real-world results, obtained with an outdoor vehicle, that performs favorably when compared to the extended Kalman filter solution from which it is derived.
Abstract: In [Thrun, S., et al., 2001], we proposed the sparse extended information filter for efficiently solving the simultaneous localization and mapping (SLAM) problem. In this paper, we extend this algorithm to handle data association problems and report real-world results, obtained with an outdoor vehicle. We find that our approach performs favorably when compared to the extended Kalman filter solution from which it is derived.
TL;DR: In this paper, a performance comparison between a Kalman filter and the interacting multiple model (IMM) estimator is carried out for single-target tracking, and it is shown that above a certain maneuvering index an IMM estimator was preferred over a KF to track the target motion.
Abstract: In this paper, a performance comparison between a Kalman filter and the interacting multiple model (IMM) estimator is carried out for single-target tracking. In a number of target tracking problems of various sizes, ranging from single-target tracking to tracking of about a thousand aircraft for air traffic control, it has been shown that the IMM estimator performs significantly better than a Kalman filter. In spite of these studies and many others, the condition under which an IMM estimator is desirable over a single model Kalman filter versus an IMM estimator are quantified here in terms of the target maneuvering index, which is a function of target motion uncertainty, measurement uncertainty, and sensor revisit interval. Using simulation studies, it is shown that above a certain maneuvering index an IMM estimator is preferred over a Kalman filter to track the target motion. These limits should serve as a guideline in choosing the more versatile, but somewhat costlier, IMM estimator over a simpler Kalman filter.
TL;DR: Under the approximation of uncorrelatedness among the local models, the global filter is shown to be minimum variance and the proposed state estimator is demonstrated on a vehicle tracking problem and a backing up truck–trailer example.
21 May 2003
TL;DR: In this article, the authors adopted a one-dimensional vertical motion model with unknown ballistic coefficient, derived and analyzed the posterior Cramer-Rao lower bounds (CRLBs) for this problem, and compared the error performance of three nonlinear filters against the theoretical CRLBs.
Abstract: Tracking of a ballistic re-entry object from radar observations is a highly complex problem in nonlinear filtering. The paper adopts a one-dimensional vertical motion model with unknown ballistic coefficient, derives and analyses the posterior Cramer-Rao lower bounds (CRLBs) for this problem, and compares the error performance of three nonlinear filters against the theoretical CRLBs. The considered nonlinear filters include the extended Kalman filter, the unscented Kalman filter and the bootstrap (particle) filter. Taking into account the computational and statistical performance, the unscented Kalman filter is found to be the preferred choice for this application.
03 Dec 2003
TL;DR: The use of the Gauss-Newton method, particularly the reduced-order implementation introduced in the paper, significantly simplifies the Kalman filter design, and reduces computational requirements.
Abstract: This paper presents an improved Kalman filter for real-time tracking of human body motions. An earlier version of the filter was presented at IROS 2001. Since then, the filter has been substantially improved. Real-time tracking of rigid body orientation is accomplished using the MARG (magnetic, angular rate, and gravity) sensors. A MARG sensor measures the three-dimensional local magnetic field, three-dimensional angular rate, and three-dimensional acceleration. A Kalman filter is designed to process measurements provided by the MARG sensors, and to produce real-time orientation represented in quaternions. There are many design decisions as related to choice of state vectors, output equations, process model, etc. The filter design presented in this paper utilizes the Gauss-Newton method for parameter optimization in conjunction with Kalman filtering. The use of the Gauss-Newton method, particularly the reduced-order implementation introduced in the paper, significantly simplifies the Kalman filter design, and reduces computational requirements.
TL;DR: In this paper, an extension of the sequential importance sampling filter (SIR) is proposed to estimate the system parameters and to predict the evolution of the system with a remarkably better accuracy than the EnKF.
Abstract: . The quality of the prediction of dynamical system evolution is determined by the accuracy to which initial conditions and forcing are known. Availability of future observations permits reducing the effects of errors in assessment the external model parameters by means of a filtering algorithm. Usually, uncertainties in specifying internal model parameters describing the inner system dynamics are neglected. Since they are characterized by strongly non-Gaussian distributions (parameters are positive, as a rule), traditional Kalman filtering schemes are badly suited to reducing the contribution of this type of uncertainties to the forecast errors. An extension of the Sequential Importance Resampling filter (SIR) is proposed to this aim. The filter is verified against the Ensemble Kalman filter (EnKF) in application to the stochastic Lorenz system. It is shown that the SIR is capable of estimating the system parameters and to predict the evolution of the system with a remarkably better accuracy than the EnKF. This highlights a severe drawback of any Kalman filtering scheme: due to utilizing only first two statistical moments in the analysis step it is unable to deal with probability density functions badly approximated by the normal distribution.
TL;DR: In this article, the extended Kalman filter converges locally for a broad class of nonlinear systems if the initial estimation error of the filter is not too large, and the error goes to zero exponentially as time goes to infinity.
Abstract: We demonstrate that the extended Kalman filter converges locally for a broad class of nonlinear systems If the initial estimation error of the filter is not too large then the error goes to zero exponentially as time goes to infinity To demonstrate this, we require that the system be C 2 and uniformly observable with bounded second partial derivatives
TL;DR: This book is the first one aimed to be a textbook for this field, but it is very hard to write a book for readers with such different backgrounds, as the author of this book has emphasized computer modeling.
Abstract: DEVICES, AND STRUCTURES By S.E. Lyshevshi, CRC Press, 2002. This book is the first of the CRC Press “Nanoand Microscience, Engineering, Technology, and Medicine Series,” of which the author of this book is also the editor. This book could be a textbook of a semester course on microelectro mechanical systems (MEMS) and nanoelectromechanical systems (NEMS). The objective is to cover the topic from basic theory to the design and development of structures of practical devices and systems. The idea of MEMS and NEMS is to utilize and further extend the technology of integrated circuits (VLSI) to nanometer structures of mechanical and biological devices for potential applications in molecular biology and medicine. MEMS and NEMS (nanotechnology) are hot topics in the future development of electronics. The interest is not limited to electrical engineers. In fact, many scientists and researchers are interested in developing MEMS and NEMS for biological and medical applications. Thus, this field has attracted researchers from many different fields. Many new books are coming out. This book seems to be the first one aimed to be a textbook for this field, but it is very hard to write a book for readers with such different backgrounds. The author of this book has emphasized computer modeling, mostly due to his research interest in this field. It would be good to provide coverage on biological and medical MEMS, for example, by reporting a few gen or DNA-related cases. Furthermore, the mathematical modeling in term of a large number of nonlinear coupled differential equations, as used in many places in the book, does not appear to have any practical value to the actual physical structures.
TL;DR: A new methodology for online tuning of model parameters in a two-phase flow model by taking into account measured data is presented, and important model parameters are tuned using the ensemble Kalman filter.
13 Jul 2003
TL;DR: In this article, the authors explored the practical application of the Kalman filter to the analysis of harmonic levels in power systems and investigated the merits and limitations of different possible implementations and the effect of fundamental frequency variation.
Abstract: This paper explores the practical application of the Kalman filter to the analysis of harmonic levels in power systems. The merits and limitations of different possible implementations are investigated and the effect of fundamental frequency variation is examined. The tuning of the Kalman filter for desired dynamic response is discussed and an adaptive tuning algorithm derived for the improved convergence of nonlinear models. The effectiveness of the resulting schemes are tested under a variety of typical power system operating conditions.
09 Dec 2003
TL;DR: The block triangular structure is exploited by recursively designing observers that take the state estimates obtained by the observers for the "previous" blocks into account, and the estimation error of the resulting overall observer converges to zero within finite time.
Abstract: In this note we consider the state estimation problem for nonlinear systems. In a first step we outline the design of an observer for single output nonlinear systems in observer normal form. The estimate of this observer converges to the exact system state within predefined finite time. This observer is then used in the design of a finite time convergent observer for multiple output systems that are given in block triangular observer normal form. Specifically, the block triangular structure is exploited by recursively designing observers that take the state estimates obtained by the observers for the "previous" blocks into account. As shown the estimation error of the resulting overall observer converges to zero within finite time. The outlined approach is exemplified considering the state estimation of a eights order two link elastic robot.
TL;DR: In this article, the GPS composite clock is implemented using the Kalman filter for the estimation of the difference between two clocks, and it is shown that the non-observability of the clock time readings is controlled by the so-called "transparent variations" that do not interfere with the estimation algorithm.
Abstract: The Kalman filter is a very useful tool of estimation theory, successfully adopted in a wide variety of problems. As a recursive and optimal estimation technique, the Kalman filter seems to be the correct tool also for building precise timescales, and various attempts have been made in the past giving rise, for example, to the TA(NIST) timescale. Despite the promising expectations, a completely satisfactory implementation has never been found, due to the intrinsic non-observability of the clock time readings, which makes the clock estimation problem underdetermined. However, the case of the Kalman filter applied to the estimation of the difference between two clocks is different. In this case the problem is observable and the Kalman filter has proved to be a powerful tool. A new proposal with interesting results, concerning the definition of an independent timescale, came with the GPS composite clock, which is based on the Kalman filter and has been in use since 1990 in the GPS system. In the composite clock the indefinite growth of the covariance matrix due to the non-observability is controlled by the so-called `transparent variations'—squeezing operations on the covariance matrix that do not interfere with the estimation algorithm. A useful quantity, the implicit ensemble mean, is defined and the `corrected clocks' (physical clocks minus their predicted bias) are shown to be observable with respect to this quantity. We have implemented the full composite clock and we discuss some of its advantages and criticalities. More recently, the Kalman filter is generating new interest, and a few groups are proposing new implementations. This paper gives an overview of what has been done and of what is currently under investigation, pointing out the peculiar advantages and the open questions in the application of this attractive technique to the generation of a timescale.
TL;DR: In this paper, the observer/Kalman filter identification method is applied to the problem of online system identification of accurate, locally linear, aircraft dynamic models of nonlinear aircraft, without user imposed a priori assumptions about model structure or model order.
Abstract: The observer/Kalman filter identification method is applied to the problem of online system identification of accurate, locally linear, aircraft dynamic models of nonlinear aircraft. It is a time-domain technique that identifies a discrete input-output mapping from known input and output data samples, without user imposed a priori assumptions about model structure or model order. The basic formulation of observer/Kalman filter identification specific to the aircraft problem is developed and implemented in a nonlinear, six-degree-of-freedom simulation of an AV-8B Harrier. A similar simulation of a generic uninhabited combat aerial vehicle is also used. Numerical examples are presented, consisting of longitudinal and lateral/directional successive online identifications at different nonperfect trim conditions, identification with sensor noise on multiple channels, and identification with discrete gusts. Accuracy of the identified linear system models to the nonlinear plant is quantified with comparison of eigenvalues, the Vinnicombe gap metric, and time history matching. Results demonstrate that the observer/Kalman filter identification method is suitable for aircraft online identification of locally linear aircraft models and is generally insensitive to moderate intensity Gaussian white sensor noise and for light to moderate intensity discrete gusts.
08 Jul 2003
TL;DR: In this paper, an alternative linearization of range rate that is not a function of the position elements is derived, which can improve a tracking system's velocity estimates without risk to its position estimates.
Abstract: Radar range rate measurements are not always used in target tracking filters because they are highly nonlinear in Cartesian space. A linear approxi- mation of range rate composed of its partial derivatives with respect to the track state vector is sometimes used in the measurement equation of an Extended Kalman filter. Unfortunately, this naive linearization can de- grade the filter's position estimates. The origins of this phenomenon are investigated and found to lie in the functional relationship induced by the linearization between the position elements of the track state vec- tor and the range rate innovation. An alternative lin- earization of range rate that is not a function of the position elements is derived. It is shown that the new linearization improves position estimate for some tra- jectories. An ordinary Kalman filter's gains are com- pared to those of the usual and alternative extended Kalman filters analytically and via simulation. The results show that the alternative linearization leads to a filter having the same position gains as an ordinary Kalman filter, and an additional gain on the track's radial velocity. This new extended Kalman filter can improve a tracking system's velocity estimates without risk to its position estimates.
TL;DR: In this paper, a new method to assimilate data into a model and estimate the state of a nonlinear dynamical system is suggested. And the performance of this new method of state estimation is compared with that of the extended Kalman filter, largely owing to it taking into account the nonlinearity of the system.
TL;DR: In this article, a study of three timescales formed from a Kalman filter operating on a model of a clock ensemble is presented, and an optimality property is proved for the reduced Kalman scale.
Abstract: This is a study of three timescales formed from a Kalman filter operating on a model of a clock ensemble. The raw Kalman scale is unstable at short averaging times. The Kalman-plus-weights and reduced Kalman scales are stable at all averaging times. An optimality property is proved for the reduced Kalman scale.
08 Jul 2003
TL;DR: In this article, Rao-Blackwellisation is used to calculate tractable integrations in the unscented Kalman filter, which leads to a re-duction in the quasi-Monte Carlo variance, and a decrease in the computational complexity by considering a common tracking problem.
Abstract: The Unscented Kalman Filter oflers sign$- cant improvements in the estimation of non-linear discrete- time models in comparison to the Extended Kalman Fil- ter 1121. In this paper we use a technique introduced by Casella and Robert (2), known as Rao-Blackwellisation, to calculate the tractable integrations that are found in the Unscented Kalman Filter: We show that this leads to a re- duction in the quasi-Monte Carlo variance, and a decrease in the computational complexity by considering a common tracking problem.
TL;DR: A nonlinear observer, with the feedback gain weighted by the sensitivity of the output with respect to the state, is developed for systems with nonlinear output map.
TL;DR: In this paper, a combined observer is synthesized to estimate plant uncertainties and disturbances, which enables robust state estimation for uncertain dynamical systems and simultaneously, provides full-stateto the perturbation observer under output feedback conditions.
Abstract: A combined observer is synthesized bv unifying the conventional linear state estimator and the perturbation observer to estimate plant uncertainties and disturbances. It enables robust state estimation for uncertain dynamical systems and simultaneously, provides full-stateto the perturbation observer under output feedback conditions. The proposed combined observer is very practical since it is given as a recursive discrete-time form with minimal tuning parameters, and it requires no knowledge of the plant uncertainty. A coupled estimation error dynamics is derived, and the related technical issues such as stability and noise sensitivity are addressed. The combined observer setting is also extended to stochastic systems, and the discrete Kalman filter is reformulated by including the perturbation estimate update process. Numerical examples and experimental results validate the proposed schemes.