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Showing papers on "Kalman filter published in 2001"


Proceedings Article
01 Jan 2001

3,169 citations


Book
Ruey S. Tsay1
15 Oct 2001
TL;DR: The author explains how the Markov Chain Monte Carlo Methods with Applications and Principal Component Analysis and Factor Models changed the way that conventional Monte Carlo methods were applied to time series analysis.
Abstract: Preface. Preface to First Edition. 1. Financial Time Series and Their Characteristics. 2. Linear Time Series Analysis and Its Applications. 3. Conditional Heteroscedastic Models. 4. Nonlinear Models and Their Applications. 5. High-Frequency Data Analysis and Market Microstructure. 6. Continuous-Time Models and Their Applications. 7. Extreme Values, Quantile Estimation, and Value at Risk. 8. Multivariate Time Series Analysis and Its Applications. 9. Principal Component Analysis and Factor Models. 10. Multivariate Volatility Models and Their Applications. 11. State-Space Models and Kalman Filter. 12. Markov Chain Monte Carlo Methods with Applications. Index.

2,766 citations


Book
16 Jan 2001
TL;DR: Kalman Filtering: Theory and Practice Using MATLAB, Fourth Edition is an ideal textbook in advanced undergraduate and beginning graduate courses in stochastic processes and Kalman filtering and appropriate for self-instruction or review by practicing engineers and scientists who want to learn more about this important topic.
Abstract: The definitive textbook and professional reference on Kalman Filtering fully updated, revised, and expanded This book contains the latest developments in the implementation and application of Kalman filtering. Authors Grewal and Andrews draw upon their decades of experience to offer an in-depth examination of the subtleties, common pitfalls, and limitations of estimation theory as it applies to real-world situations. They present many illustrative examples including adaptations for nonlinear filtering, global navigation satellite systems, the error modeling of gyros and accelerometers, inertial navigation systems, and freeway traffic control. Kalman Filtering: Theory and Practice Using MATLAB, Fourth Edition is an ideal textbook in advanced undergraduate and beginning graduate courses in stochastic processes and Kalman filtering. It is also appropriate for self-instruction or review by practicing engineers and scientists who want to learn more about this important topic.

2,303 citations


Book
08 Oct 2001
TL;DR: This book takes a nontraditional nonlinear approach and reflects the fact that most practical applications are nonlinear.
Abstract: From the Publisher: Kalman filtering is a well-established topic in the field of control and signal processing and represents by far the most refined method for the design of neural networks. This book takes a nontraditional nonlinear approach and reflects the fact that most practical applications are nonlinear. The book deals with important applications in such fields as control, financial forecasting, and idle speed control.

1,960 citations


Journal ArticleDOI
TL;DR: In this paper, an ensemble adjustment Kalman filter is proposed to estimate the probability distribution of the state of a model given a set of observations using Monte Carlo approximations to the nonlinear filter.
Abstract: A theory for estimating the probability distribution of the state of a model given a set of observations exists. This nonlinear filtering theory unifies the data assimilation and ensemble generation problem that have been key foci of prediction and predictability research for numerical weather and ocean prediction applications. A new algorithm, referred to as an ensemble adjustment Kalman filter, and the more traditional implementation of the ensemble Kalman filter in which “perturbed observations” are used, are derived as Monte Carlo approximations to the nonlinear filter. Both ensemble Kalman filter methods produce assimilations with small ensemble mean errors while providing reasonable measures of uncertainty in the assimilated variables. The ensemble methods can assimilate observations with a nonlinear relation to model state variables and can also use observations to estimate the value of imprecisely known model parameters. These ensemble filter methods are shown to have significant advantag...

1,660 citations


Proceedings Article
02 Aug 2001
TL;DR: Expectation Propagation approximates the belief states by only retaining expectations, such as mean and varitmce, and iterates until these expectations are consistent throughout the network, which makes it applicable to hybrid networks with discrete and continuous nodes.
Abstract: This paper presents a new deterministic approximation technique in Bayesian networks. This method, "Expectation Propagation," unifies two previous techniques: assumed-density filtering, an extension of the Kalman filter, and loopy belief propagation, an extension of belief propagation in Bayesian networks. Loopy belief propagation, because it propagates exact belief states, is useful for a limited class of belief networks, such as those which are purely discrete. Expectation Propagation approximates the belief states by only retaining expectations, such as mean and varitmce, and iterates until these expectations are consistent throughout the network. This makes it applicable to hybrid networks with discrete and continuous nodes. Experiments with Gaussian mixture models show Expectation Propagation to be donvincingly better than methods with similar computational cost: Laplace's method, variational Bayes, and Monte Carlo. Expectation Propagation also provides an efficient algorithm for training Bayes point machine classifiers.

1,514 citations


Journal ArticleDOI
TL;DR: In this article, an ensemble Kalman filter is proposed for the 4D assimilation of atmospheric data, which employs a Schur (elementwise) product of the covariances of the background error calculated from the ensemble and a correlation function having local support to filter the small (and noisy) background-error covariance associated with remote observations.
Abstract: An ensemble Kalman filter may be considered for the 4D assimilation of atmospheric data. In this paper, an efficient implementation of the analysis step of the filter is proposed. It employs a Schur (elementwise) product of the covariances of the background error calculated from the ensemble and a correlation function having local support to filter the small (and noisy) background-error covariances associated with remote observations. To solve the Kalman filter equations, the observations are organized into batches that are assimilated sequentially. For each batch, a Cholesky decomposition method is used to solve the system of linear equations. The ensemble of background fields is updated at each step of the sequential algorithm and, as more and more batches of observations are assimilated, evolves to eventually become the ensemble of analysis fields. A prototype sequential filter has been developed. Experiments are performed with a simulated observational network consisting of 542 radiosonde and 615 satellite-thickness profiles. Experimental results indicate that the quality of the analysis is almost independent of the number of batches (except when the ensemble is very small). This supports the use of a sequential algorithm. A parallel version of the algorithm is described and used to assimilate over 100 000 observations into a pair of 50-member ensembles. Its operation count is proportional to the number of observations, the number of analysis grid points, and the number of ensemble members. In view of the flexibility of the sequential filter and its encouraging performance on a NEC SX-4 computer, an application with a primitive equations model can now be envisioned.

1,444 citations


Journal ArticleDOI
TL;DR: The Ensemble Transform Kalman Filter (ET KF) as discussed by the authors is a suboptimal Kalman filter that uses ensemble transformation and a normalization to obtain the prediction error covariance matrix associated with a particular deployment of observational resources.
Abstract: A suboptimal Kalman filter called the ensemble transform Kalman filter (ET KF) is introduced. Like other Kalman filters, it provides a framework for assimilating observations and also for estimating the effect of observations on forecast error covariance. It differs from other ensemble Kalman filters in that it uses ensemble transformation and a normalization to rapidly obtain the prediction error covariance matrix associated with a particular deployment of observational resources. This rapidity enables it to quickly assess the ability of a large number of future feasible sequences of observational networks to reduce forecast error variance. The ET KF was used by the National Centers for Environmental Prediction in the Winter Storm Reconnaissance missions of 1999 and 2000 to determine where aircraft should deploy dropwindsondes in order to improve 24‐72-h forecasts over the continental United States. The ET KF may be applied to any well-constructed set of ensemble perturbations. The ET KF technique supercedes the ensemble transform (ET) targeting technique of Bishop and Toth. In the ET targeting formulation, the means by which observations reduced forecast error variance was not expressed mathematically. The mathematical representation of this process provided by the ET KF enables such things as the evaluation of the reduction in forecast error variance associated with individual flight tracks and assessments of the value of targeted observations that are distributed over significant time intervals. It also enables a serial targeting methodology whereby one can identify optimal observing sites given the location and error statistics of other observations. This allows the network designer to nonredundantly position targeted observations. Serial targeting can also be used to greatly reduce the computations required to identify optimal target sites. For these theoretical and practical reasons, the ET KF technique is more useful than the ET technique. The methodology is illustrated with observation system simulation experiments involving a barotropic numerical model of tropical cyclonelike vortices. These include preliminary empirical tests of ET KF predictions using ET KF, 3DVAR, and hybrid data assimilation schemes—the results of which look promising. To concisely describe the future feasible sequences of observations considered in adaptive sampling problems, an extension to Ide et al.’s unified notation for data assimilation is suggested.

1,338 citations


Proceedings ArticleDOI
07 May 2001
TL;DR: The square-root unscented Kalman filter (SR-UKF) is introduced which is also O(L/sup 3/) for general state estimation and O( L/sup 2/) for parameter estimation and has the added benefit of numerical stability and guaranteed positive semi-definiteness of the state covariances.
Abstract: Over the last 20-30 years, the extended Kalman filter (EKF) has become the algorithm of choice in numerous nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system as well estimating parameters for nonlinear system identification (eg, learning the weights of a neural network). The EKF applies the standard linear Kalman filter methodology to a linearization of the true nonlinear system. This approach is sub-optimal, and can easily lead to divergence. Julier et al. (1997), proposed the unscented Kalman filter (UKF) as a derivative-free alternative to the extended Kalman filter in the framework of state estimation. This was extended to parameter estimation by Wan and Van der Merwe et al., (2000). The UKF consistently outperforms the EKF in terms of prediction and estimation error, at an equal computational complexity of (OL/sup 3/)/sup l/ for general state-space problems. When the EKF is applied to parameter estimation, the special form of the state-space equations allows for an O(L/sup 2/) implementation. This paper introduces the square-root unscented Kalman filter (SR-UKF) which is also O(L/sup 3/) for general state estimation and O(L/sup 2/) for parameter estimation (note the original formulation of the UKF for parameter-estimation was O(L/sup 3/)). In addition, the square-root forms have the added benefit of numerical stability and guaranteed positive semi-definiteness of the state covariances.

1,130 citations


Dissertation
01 Jan 2001
TL;DR: This thesis presents an approximation technique that can perform Bayesian inference faster and more accurately than previously possible, and is found to be convincingly better than rival approximation techniques: Monte Carlo, Laplace's method, and variational Bayes.
Abstract: One of the major obstacles to using Bayesian methods for pattern recognition has been its computational expense. This thesis presents an approximation technique that can perform Bayesian inference faster and more accurately than previously possible. This method, “Expectation Propagation,” unifies and generalizes two previous techniques: assumed-density filtering, an extension of the Kalman filter, and loopy belief propagation, an extension of belief propagation in Bayesian networks. The unification shows how both of these algorithms can be viewed as approximating the true posterior distribution with simpler distribution, which is close in the sense of KL-divergence. Expectation Propagation exploits the best of both algorithms: the generality of assumed-density filtering and the accuracy of loopy belief propagation. Loopy belief propagation, because it propagates exact belief states, is useful for limited types of belief networks, such as purely discrete networks. Expectation Propagation approximates the belief states with expectations, such as means and variances, giving it much wider scope. Expectation Propagation also extends belief propagation in the opposite direction—propagating richer belief states which incorporate correlations between variables. This framework is demonstrated in a variety of statistical models using synthetic and real-world data. On Gaussian mixture problems, Expectation Propagation is found, for the same amount of computation, to be convincingly better than rival approximation techniques: Monte Carlo, Laplace's method, and variational Bayes. For pattern recognition, Expectation Propagation provides an algorithm for training Bayes Point Machine classifiers that is faster and more accurate than any previously known. The resulting classifiers outperform Support Vector Machines on several standard datasets, in addition to having a comparable training time. Expectation Propagation can also be used to choose an appropriate feature set for classification, via Bayesian model selection. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

1,036 citations


Journal ArticleDOI
01 Jun 2001
TL;DR: Addresses real-time implementation of the simultaneous localization and map-building (SLAM) algorithm and presents optimal algorithms that consider the special form of the matrices and a new compressed filler that can significantly reduce the computation requirements when working in local areas or with high frequency external sensors.
Abstract: Addresses real-time implementation of the simultaneous localization and map-building (SLAM) algorithm. It presents optimal algorithms that consider the special form of the matrices and a new compressed filler that can significantly reduce the computation requirements when working in local areas or with high frequency external sensors. It is shown that by extending the standard Kalman filter models the information gained in a local area can be maintained with a cost /spl sim/O(N/sub a//sup 2/), where N/sub a/ is the number of landmarks in the local area, and then transferred to the overall map in only one iteration at full SLAM computational cost. Additional simplifications are also presented that are very close to optimal when an appropriate map representation is used. Finally the algorithms are validated with experimental results obtained with a standard vehicle running in a completely unstructured outdoor environment.

Book
01 Dec 2001
TL;DR: This text is a practical guide to building Kalman filters and shows how the filtering equations can be applied to real-life problems and spends a great deal of time setting up a problem before the Kalman filter is actually formulated to give the reader an intuitive feel for the problem being addressed.
Abstract: This text is a practical guide to building Kalman filters and shows how the filtering equations can be applied to real-life problems Numerous examples are presented in detail, showing the many ways in which Kalman filters can be designed Computer code written in FORTRAN, MATLAB[registered], and True BASIC accompanies all of the examples so that the interested reader can verify concepts and explore issues beyond the scope of the text Sometimes mistakes are introduced intentionally to the initial filter designs to show the reader what happens when the filter is not working properly The text spends a great deal of time setting up a problem before the Kalman filter is actually formulated to give the reader an intuitive feel for the problem being addressed Real problems are seldom presented in the form of differential equations and they usually do not have unique solutions Therefore, the authors illustrate several different filtering approaches for tackling a problem Readers will gain experience in software and performance tradeoffs for determining the best filtering approach for the application at hand The second edition has two new chapters and an additional appendix In the first new chapter, a recursive digital filter known as the fading memory filter is introduced and it is shown that for some radar tracking applications the fading memory filter can yield similar performance to a Kalman filter at far less computational cost A second new chapter presents techniques for improving Kalman filter performance Included is a practical method for preprocessing measurement data when there are too many measurements for the filter to utilize in a given amount of time The chapter also contains practical methods for making the Kalman filter adaptive A new appendix has been added which serves as a central location and summary for the text's most important concepts and formulas MATLAB is a registered trademark of The MathWorks, Inc

Proceedings ArticleDOI
29 Oct 2001
TL;DR: An extended Kalman filter for real-time estimation of rigid body orientation using the newly developed MARG (magnetic, angular rate, and gravity) sensors, which eliminates the long-standing problem of singularities associated with attitude estimation.
Abstract: Presents an extended Kalman filter for real-time estimation of rigid body orientation using the newly developed MARG (magnetic, angular rate, and gravity) sensors. Each MARG sensor contains a three-axis magnetometer, a three-axis angular rate sensor, and a three-axis accelerometer. The filter represents rotations using quaternions rather than Euler angles, which eliminates the long-standing problem of singularities associated with attitude estimation. A process model for rigid body angular motions and angular rate measurements is defined. The process model converts angular rates into quaternion rates, which are integrated to obtain quaternions. The Gauss-Newton iteration algorithm is utilized to find the best quaternion that relates the measured accelerations and earth magnetic field in the body coordinate frame to calculated values in the earth coordinate frame. The best quaternion is used as part of the measurements for the Kalman filter. As a result of this approach, the measurement equations of the Kalman filter become linear, and the computational requirements are significantly reduced, making it possible to estimate orientation in real time. Extensive testing of the filter with synthetic data and actual sensor data proved it to be satisfactory. Test cases included the presence of large initial errors as well as high noise levels. In all cases the filter was able to converge and accurately track rotational motions.

Journal ArticleDOI
TL;DR: This work derives sufficient conditions for the stability of moving horizon state estimation with linear models subject to constraints on the estimate, and discusses smoothing strategies for moving horizon estimation.

Journal ArticleDOI
TL;DR: In this paper, two commonly used measurement fusion methods for Kalman-filter-based multisensor data fusion are analyzed. And the authors show that they are functionally equivalent if the sensors used for data fusion, with different and independent noise characteristics, have identical measurement matrices.
Abstract: Currently there exist two commonly used measurement fusion methods for Kalman-filter-based multisensor data fusion. The first (Method I) simply merges the multisensor data through the observation vector of the Kalman filter, whereas the second (Method II) combines the multisensor data based on a minimum-mean-square-error criterion. This paper, based on an analysis of the fused state estimate covariances of the two measurement fusion methods, shows that the two measurement fusion methods are functionally equivalent if the sensors used for data fusion, with different and independent noise characteristics, have identical measurement matrices. Also presented are simulation results on state estimation using the two measurement fusion methods, followed by the analysis of the computational advantages of each method.

Journal ArticleDOI
01 Oct 2001
TL;DR: The algorithm exploits nonholonomic constraints that govern the motion of a vehicle on a surface to obtain velocity observation measurements which aid in the estimation of the alignment of the IMU as well as the forward velocity of the vehicle.
Abstract: This paper presents a new method for improving the accuracy of inertial measurement units (IMUs) mounted on land vehicles. The algorithm exploits nonholonomic constraints that govern the motion of a vehicle on a surface to obtain velocity observation measurements which aid in the estimation of the alignment of the IMU as well as the forward velocity of the vehicle. It is shown that this can be achieved without any external sensing provided that certain observability conditions are met. A theoretical analysis is provided together with a comparison of experimental results between a nonlinear implementation of the algorithm and an IMU/GPS navigation system. This comparison demonstrates the effectiveness of the algorithm. The real time implementation is also addressed through a multiple observation inertial aiding algorithm based on the information filter. The results show that the use of these constraints and vehicle speed guarantees the observability of the velocity and the attitude of the inertial unit, and hence bounds the errors associated with these states. The strategies proposed provides a tighter navigation loop which can sustain outages of GPS for a greater amount of time as compared to when the inertial unit is used with standard integration algorithms.

Journal ArticleDOI
TL;DR: It is shown that, under certain stabilizability and detectability conditions, the steady-state filters are stable and that, for quadratically-stable models, the filters guarantee a bounded error variance.
Abstract: Develops a framework for state-space estimation when the parameters of the underlying linear model are subject to uncertainties. Compared with existing robust filters, the proposed filters perform regularization rather than deregularization. It is shown that, under certain stabilizability and detectability conditions, the steady-state filters are stable and that, for quadratically-stable models, the filters guarantee a bounded error variance. Moreover, the resulting filter structures are similar to various (time- and measurement-update, prediction, and information) forms of the Kalman filter, albeit ones that operate on corrected parameters rather than on the given nominal parameters. Simulation results and comparisons with /spl Hscr//sub /spl infin// guaranteed-cost, and set-valued state estimation filters are provided.

Journal ArticleDOI
01 Oct 2001
TL;DR: The method uses multi-hypothesis Kalman filter based pose tracking combined with a probabilistic formulation of hypothesis correctness to generate and track Gaussian pose hypotheses online and generates movement commands for the platform to enhance the gathering of information for the pose estimation process.
Abstract: We present a probabilistic approach for mobile robot localization using an incomplete topological world model. The method, called the multi-hypothesis localization (MHL), uses multi-hypothesis Kalman filter based pose tracking combined with a probabilistic formulation of hypothesis correctness to generate and track Gaussian pose hypotheses online. Apart from a lower computational complexity, this approach has the advantage over traditional grid based methods that incomplete and topological world model information can be utilized. Furthermore, the method generates movement commands for the platform to enhance the gathering of information for the pose estimation process. Extensive experiments are presented from two different environments, a typical office environment and an old hospital building.

Proceedings ArticleDOI
21 May 2001
TL;DR: In this article, the authors analyzed the properties of the full covariance simultaneous localization and map building problem (SLAM) and showed that even for the special case of a stationary vehicle (with no process noise) which uses a range-bearing sensor and has non-zero angular uncertainty, the SLAM algorithm always yields an inconsistent map.
Abstract: The paper analyzes the properties of the full covariance simultaneous localization and map building problem (SLAM). We prove that, even for the special case of a stationary vehicle (with no process noise) which uses a range-bearing sensor and has non-zero angular uncertainty, the full covariance SLAM algorithm always yields an inconsistent map. We also show, through simulations, that these conclusions appear to extend to a moving vehicle with process noise. However, these inconsistencies only become apparent after several hundred beacon updates.

Proceedings ArticleDOI
Yong Rui1, Yunqiang Chen1
08 Dec 2001
TL;DR: The UPF uses the unscented Kalman filter to generate sophisticated proposal distributions that seamlessly integrate the current observation, thus greatly improving the tracking performance, and is applied in audio and visual tracking.
Abstract: Tracking objects involves the modeling of non-linear non-Gaussian systems. On one hand, variants of Kalman filters are limited by their Gaussian assumptions. On the other hand, conventional particle filter, e.g., CONDENSATION, uses transition prior as the proposal distribution. The transition prior does not take into account current observation data, and many particles can therefore be wasted in low likelihood area. To overcome these difficulties, unscented particle filter (UPF) has recently been proposed in the field of filtering theory. In this paper, we introduce the UPF framework into audio and visual tracking. The UPF uses the unscented Kalman filter to generate sophisticated proposal distributions that seamlessly integrate the current observation, thus greatly improving the tracking performance. To evaluate the efficacy of the UPF framework, we apply it in two real-world tracking applications. One is the audio-based speaker localization, and the other is the vision-based human tracking. The experimental results are compared against those of the widely used CONDENSATION approach and have demonstrated superior tracking performance.

Proceedings ArticleDOI
16 Sep 2001
TL;DR: The pose of the hand model is estimated with an Unscented Kalman filter (UKF), which minimizes the geometric error between the profiles and edges extracted from the images, and permits higher frame rates than more sophisticated estimation methods such as particle filtering.
Abstract: This paper presents a practical technique for model-based 3D hand tracking. An anatomically accurate hand model is built from truncated quadrics. This allows for the generation of 2D profiles of the model using elegant tools from projective geometry, and for an efficient method to handle self-occlusion. The pose of the hand model is estimated with an Unscented Kalman filter (UKF), which minimizes the geometric error between the profiles and edges extracted from the images. The use of the UKF permits higher frame rates than more sophisticated estimation methods such as particle filtering, whilst providing higher accuracy than the extended Kalman filter The system is easily scalable from single to multiple views, and from rigid to articulated models. First experiments on real data using one and two cameras demonstrate the quality of the proposed method for tracking a 7 DOF hand model.

Journal ArticleDOI
TL;DR: In this article, a new adaptive robust filtering method based on the robust M (maximumlikelihood type) estimation is proposed, which can not only resist the influence of outlying kinematic model errors, but also control the effects of measurement outliers.
Abstract: The Kalman filter has been applied extensively in the area of kinematic geodetic positioning. The reliability of the linear filtering results, however, is reduced when the kinematic model noise is not accurately modeled in filtering or the measurement noises at any measurement epoch are not normally distributed. A new adaptively robust filtering is proposed based on the robust M (maximum-likelihood-type) estimation. It consists in weighting the influence of the updated parameters in accordance with the magnitude of discrepancy between the updated parameters and the robust estimates obtained from the kinematic measurements and in weighting individual measurements at each discrete epoch. The new procedure is different from functional model-error compensation; it changes the covariance matrix or equivalently changes the weight matrix of the predicted parameters to cover the model errors. A general estimator for an adaptively robust filter is developed, which includes the estimators of the classical Kalman filter, adaptive Kalman filter, robust filter, sequential least-squares adjustment and robust sequential adjustment. The procedure can not only resist the influence of outlying kinematic model errors, but also controls the effects of measurement outliers. In addition to the robustness, the feasibility of implementing the new filter is achieved by using the equivalent weights of the measurements and the predicted state parameters. A numerical example is given to demonstrate the ideas involved.

Journal ArticleDOI
01 Oct 2001
TL;DR: A distributed, real-time computing platform for tracking multiple interacting persons in motion using a multiview implementation, where each view is first independently processed on a dedicated processor to combat the negative effects of occlusion and articulated motion.
Abstract: We propose a distributed, real-time computing platform for tracking multiple interacting persons in motion. To combat the negative effects of occlusion and articulated motion we use a multiview implementation, where each view is first independently processed on a dedicated processor. This monocular processing uses a predictor-corrector filter to weigh reprojections of three-dimensional (3-D) position estimates, obtained by the central processor, against observations of measurable image motion. The corrected state vectors from each view provide input observations to a Bayesian belief network, in the central processor, with a dynamic, multidimensional topology that varies as a function of scene content and feature confidence. The Bayesian net fuses independent observations from multiple cameras by iteratively resolving independency relationships and confidence levels within the graph, thereby producing the most likely vector of 3-D state estimates given the available data. To maintain temporal continuity, we follow the network with a layer of Kalman filtering that updates the 3-D state estimates. We demonstrate the efficacy of the proposed system using a multiview sequence of several people in motion. Our experiments suggest that, when compared with data fusion based on averaging, the proposed technique yields a noticeable improvement in tracking accuracy.

Proceedings ArticleDOI
13 Mar 2001
TL;DR: A novel framework enables accurate augmented reality (AR) registration with integrated inertial gyroscope and vision tracking technologies that combines the low-frequency stability of vision sensors with the high-frequency tracking of Gyroscope sensors, hence achieving stable static and dynamic six-degree-of-freedom pose tracking.
Abstract: A novel framework enables accurate augmented reality (AR) registration with integrated inertial gyroscope and vision tracking technologies. The framework includes a two-channel complementary motion filter that combines the low-frequency stability of vision sensors with the high-frequency tracking of gyroscope sensors, hence achieving stable static and dynamic six-degree-of-freedom pose tracking. Our implementation uses an extended Kalman filter (EKF). Quantitative analysis and experimental results show that the fusion method achieves dramatic improvements in tracking stability and robustness over either sensor alone. We also demonstrate a new fiducial design and detection system in our example AR annotation systems that illustrate the behavior and benefits of the new tracking method.

Patent
14 May 2001
TL;DR: In this paper, an inertial processing unit (430) coupled to one or more motion sensors (410) determines a first position estimate based on the corresponding signals from the motion sensors.
Abstract: A navigation system (400, 500) for mounting on a human. The navigation system (400, 500) includes one or more motion sensors for sensing motion of the human and outputting one or more corresponding motion signals. An inertial processing unit (430) coupled to one or more of motion sensors (410) determines a first position estimate based on one or more of the corresponding signals from the motion sensors. A distance traveled is determined by a motion classifier (420) coupled to one or more of the motion sensors (410), where the distance estimate is based on one or more of the corresponding motion signals processed in one or more motion models. A Kalman filter (440) is also integrated into the system, where the Kalman filter (440) receives the first position estimate and the distance estimate and provides corrective feedback signals to the inertial processor (430) for the first position estimate. In an additional embodiment, input from a position indicator (510), such as a GPS, provides a third position estimate, and where the Kalman filter (440) provides correction to the first position estimate, the distance estimate and parameters of the motion model being used.

Journal ArticleDOI
TL;DR: The objective of this paper is to report on the application and performance of an alternative neural computing algorithm which involves ‘sequential or dynamic learning’ of the traffic flow process and to recommend the simple dynamic network as the overall recommendation for any future application.
Abstract: Accurate short-term traffic flow forecasting has become a crucial step in the overall goal of better road network management. Previous research [H. Kirby, M. Dougherty, S. Watson, Should we use neural networks or statistical models for short term motorway traffic forecasting, International Journal of Forecasting 13 (1997) 43–50.] has demonstrated that a straightforward application of neural networks can be used to forecast traffic flows along a motorway link. The objective of this paper is to report on the application and performance of an alternative neural computing algorithm which involves ‘sequential or dynamic learning’ of the traffic flow process. Our initial work [H. Chen, S. Clark, M.S. Dougherty, S.M. Grant-Muller, Investigation of network performance prediction, Report on Dynamic Neural Network and Performance Indicator development, Institute for Transport Studies, University of Leeds Technical Note 418, 1998 (unpublished)] was based on simulated data (generated using a Hermite polynomial with random noise) that had a profile similar to that of traffic flows in real data. This indicated the potential suitability of dynamic neural networks with traffic flow data. Using the Kalman filter type network an initial application with M25 motorway flow data suggested that a percentage absolute error (PAE) of approximately 9.5% could be achieved for a network with five hidden units (compared with 11% for the static neural network model). Three different neural networks were trained with all the data (containing an unknown number of incidents) and secondly using data wholly obtained around incidents. Results showed that from the three different models, the ‘simple dynamic model’ with the first five units fixed (and subsequent hidden units distributed amongst these) had the best forecasting performance. Comparisons were also made of the networks’ performance on data obtained around incidents. More detailed analysis of how the performance of the three networks changed through a single day (including an incident) showed that the simple dynamic model again outperformed the other two networks in all time periods. The use of ‘piecewise’ models (i.e. where a different model is selected according to traffic flow conditions) for data obtained around incidents highlighted good performance again by the simple dynamic network. This outperformed the standard Kalman filter neural network for a medium-sized network and is our overall recommendation for any future application.

Journal ArticleDOI
TL;DR: It is shown that theKalman filtering track fusion formula with feedback is, like the track fusion without feedback, exactly equivalent to the corresponding centralized Kalman filtering formula.

Journal ArticleDOI
TL;DR: In this paper, a subspace approach is proposed for predictive control without using the traditional dynamic model such as the state-space, input-output transfer function or step response model, which simplifies the design procedure of the predictive controllers.

Patent
08 Jan 2001
TL;DR: In this paper, a Kalman filter is used to generate a calibration curve for the rate of heading sensor bias drift with temperature change, and the bias drift rate calibration curve is then used to estimate a vehicle bias periodically while the vehicle is moving.
Abstract: The present invention solves the problems of the prior art by providing methods for compensating for temperature-dependent drift of bias in a vehicle heading sensor of a dead reckoning vehicle positioning system. Specifically, the invention uses a Kalman filter to generate a calibration curve for the rate of heading sensor bias drift with temperature change. The Kalman filter calculates coefficients for a model of heading sensor bias drift rate versus temperature at each point where the vehicle is stationary. The bias drift rate calibration curve is then used to estimate a heading sensor bias periodically while the vehicle is moving. The invention further provides a method for using an aging time for temperature sensor bias drift rate to force convergence of the error variance matrix of the Kalman filter. The invention further provides vehicle navigational systems that utilize the methods of the present invention.

Journal ArticleDOI
TL;DR: In this article, a new technique based upon the use of block-Kriging and of Kalman filtering to combine, optimally in a Bayesian sense, areal precipitation fields estimated from meteorological radar to point measurements of precipitation such as are provided by a network of rain-gauges.
Abstract: . The paper introduces a new technique based upon the use of block-Kriging and of Kalman filtering to combine, optimally in a Bayesian sense, areal precipitation fields estimated from meteorological radar to point measurements of precipitation such as are provided by a network of rain-gauges. The theoretical development is followed by a numerical example, in which an error field with a large bias and a noise to signal ratio of 30% is added to a known random field, to demonstrate the potentiality of the proposed algorithm. The results analysed on a sample of 1000 realisations, show that the final estimates are totally unbiased and the noise variance reduced substantially. Moreover, a case study on the upper Reno river in Italy demonstrates the improvements in rainfall spatial distribution obtainable by means of the proposed radar conditioning technique. Keywords: Rainfall, meteorological radar, Bayesian technique, block-Kriging, Kalman filtering