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Showing papers on "Kalman filter published in 2004"


Journal ArticleDOI
08 Nov 2004
TL;DR: The motivation, development, use, and implications of the UT are reviewed, which show it to be more accurate, easier to implement, and uses the same order of calculations as linearization.
Abstract: The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficulties arise from its use of linearization. To overcome this limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. It is more accurate, easier to implement, and uses the same order of calculations as linearization. This paper reviews the motivation, development, use, and implications of the UT.

6,098 citations


Book
31 Jan 2004
TL;DR: Part I Theoretical concepts: introduction suboptimal nonlinear filters a tutorial on particle filters Cramer-Rao bounds for nonlinear filtering and tracking applications: tracking a ballistic object bearings-only tracking range- only tracking bistatic radar tracking targets through blind Doppler terrain aided tracking detection and tracking of stealthy targets group and extended object tracking.
Abstract: Part I Theoretical concepts: introduction suboptimal nonlinear filters a tutorial on particle filters Cramer-Rao bounds for nonlinear filtering Part II Tracking applications: tracking a ballistic object bearings-only tracking range-only tracking bistatic radar tracking tracking targets through blind Doppler terrain aided tracking detection and tracking of stealthy targets group and extended object tracking

3,690 citations


Journal ArticleDOI
TL;DR: This work addresses the problem of performing Kalman filtering with intermittent observations by showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs.
Abstract: Motivated by navigation and tracking applications within sensor networks, we consider the problem of performing Kalman filtering with intermittent observations. When data travel along unreliable communication channels in a large, wireless, multihop sensor network, the effect of communication delays and loss of information in the control loop cannot be neglected. We address this problem starting from the discrete Kalman filtering formulation, and modeling the arrival of the observation as a random process. We study the statistical convergence properties of the estimation error covariance, showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs. We also give upper and lower bounds on this expected state error covariance.

2,343 citations


Book
23 Apr 2004
TL;DR: In this paper, Kronecker Factorization and Levenberg-Marquardt method for least square estimation is used to estimate the probability of an error in a prior state estimate.
Abstract: LEAST SQUARES APPROXIMATION A Curve Fitting Example Linear Batch Estimation Linear Least Squares Weighted Least Squares Constrained Least Squares Linear Sequential Estimation Nonlinear Least Squares Estimation Basis Functions Advanced Topics Matrix Decompositions in Least Squares Kronecker Factorization and Least Squares Levenberg-Marquardt Method Projections in Least Squares Summary PROBABILITY CONCEPTS IN LEAST SQUARES Minimum Variance Estimation Estimation without a Prior State Estimates Estimation with a Prior State Estimates Unbiased Estimates Maximum Likelihood Estimation Cramer-Rao Inequality Nonuniqueness of the Weight Matrix Bayesian Estimation Advanced Topics Analysis of Covariance Errors Ridge Estimation Total Least Squares Summary REVIEW OF DYNAMICAL SYSTEMS Linear System Theory The State Space Approach Homogeneous Linear Dynamical Systems Forced Linear Dynamical Systems Linear State Variable Transformations Nonlinear Dynamical Systems Parametric Differentiation Observability Discrete-Time Systems Stability of Linear and Nonlinear Systems Attitude Kinematics and Rigid Body Dynamics Attitude Kinematics Rigid Body Dynamics Spacecraft Dynamics and Orbital Mechanics Spacecraft Dynamics Orbital Mechanics Aircraft Flight Dynamics Vibration Summary PARAMETER ESTIMATION: APPLICATIONS Global Positioning System Navigation Attitude Determination Vector Measurement Models Maximum Likelihood Estimation Optimal Quaternion Solution Information Matrix Analysis Orbit Determination Aircraft Parameter Identification Eigen-system Realization Algorithm Summary SEQUENTIAL STATE ESTIMATION A Simple First-Order Filter Example Full-Order Estimators Discrete-Time Estimators The Discrete-Time Kalman Filter Kalman Filter Derivation Stability and Joseph's Form Information Filter and Sequential Processing Steady-State Kalman Filter Correlated Measurement and Process Noise Orthogonality Principle The Continuous-Time Kalman Filter Kalman Filter Derivation in Continuous Time Kalman Filter Derivation from Discrete Time Stability Steady-State Kalman Filter Correlated Measurement and Process Noise The Continuous-Discrete Kalman Filter Extended Kalman Filter Advanced Topics Factorization Methods Colored-Noise Kalman Filtering Consistency of the Kalman Filter Adaptive Filtering Error Analysis Unscented Filtering Robust Filtering Summary BATCH STATE ESTIMATION Fixed-Interval Smoothing Discrete-Time Formulation Continuous-Time Formulation Nonlinear Smoothing Fixed-Point Smoothing Discrete-Time Formulation Continuous-Time Formulation Fixed-Lag Smoothing Discrete-Time Formulation Continuous-Time Formulation Advanced Topics Estimation/Control Duality Innovations Process Summary ESTIMATION OF DYNAMIC SYSTEMS: APPLICATIONS GPS Position Estimation GPS Coordinate Transformations Extended Kalman Filter Application to GPS Attitude Estimation Multiplicative Quaternion Formulation Discrete-Time Attitude Estimation Murrell's Version Farrenkopf's Steady-State Analysis Orbit Estimation Target Tracking of Aircraft The a-b Filter The a-b-g Filter Aircraft Parameter Estimation Smoothing with the Eigen-system Realization Algorithm Summary OPTIMAL CONTROL AND ESTIMATION THEORY Calculus of Variations Optimization with Differential Equation Constraints Pontryagin's Optimal Control Necessary Conditions Discrete-Time Control Linear Regulator Problems Continuous-Time Formulation Discrete-Time Formulation Linear Quadratic-Gaussian Controllers Continuous-Time Formulation Discrete-Time Formulation Loop Transfer Recovery Spacecraft Control Design Summary APPENDIX A MATRIX PROPERTIES Basic Definitions of Matrices Vectors Matrix Norms and Definiteness Matrix Decompositions Matrix Calculus APPENDIX B BASIC PROBABILITY CONCEPTS Functions of a Single Discrete-Valued Random Variable Functions of Discrete-Valued Random Variables Functions of Continuous Random Variables Gaussian Random Variables Chi-Square Random Variables Propagation of Functions through Various Models Linear Matrix Models Nonlinear Models APPENDIX C PARAMETER OPTIMIZATION METHODS C.1 Unconstrained Extrema C.2 Equality Constrained Extrema C.3 Nonlinear Unconstrained Optimization C.3.1 Some Geometrical Insights C.3.2 Methods of Gradients C.3.3 Second-Order (Gauss-Newton) Algorithm APPENDIX D COMPUTER SOFTWARE Index

1,205 citations


01 Jan 2004
TL;DR: This work has consistently shown that there are large performance benefits to be gained by applying Sigma-Point Kalman filters to areas where EKFs have been used as the de facto standard in the past, as well as in new areas where the use of the EKF is impossible.
Abstract: Probabilistic inference is the problem of estimating the hidden variables (states or parameters) of a system in an optimal and consistent fashion as a set of noisy or incomplete observations of the system becomes available online. The optimal solution to this problem is given by the recursive Bayesian estimation algorithm which recursively updates the posterior density of the system state as new observations arrive. This posterior density constitutes the complete solution to the probabilistic inference problem, and allows us to calculate any “optimal” estimate of the state. Unfortunately, for most real-world problems, the optimal Bayesian recursion is intractable and approximate solutions must be used. Within the space of approximate solutions, the extended Kalman filter (EKF) has become one of the most widely used algorithms with applications in state, parameter and dual estimation. Unfortunately, the EKF is based on a sub-optimal implementation of the recursive Bayesian estimation framework applied to Gaussian random variables. This can seriously affect the accuracy or even lead to divergence of any inference system that is based on the EKF or that uses the EKF as a component part. Recently a number of related novel, more accurate and theoretically better motivated algorithmic alternatives to the EKF have surfaced in the literature, with specific application to state estimation for automatic control. We have extended these algorithms, all based on derivativeless deterministic sampling based approximations of the relevant Gaussian statistics, to a family of algorithms called Sigma-Point Kalman Filters (SPKF). Furthermore, we successfully expanded the use of this group of algorithms (SPKFs) within the general field of probabilistic inference and machine learning, both as stand-alone filters and as subcomponents of more powerful sequential Monte Carlo methods (particle filters). We have consistently shown that there are large performance benefits to be gained by applying Sigma-Point Kalman filters to areas where EKFs have been used as the de facto standard in the past, as well as in new areas where the use of the EKF is impossible.

1,116 citations


Journal ArticleDOI
TL;DR: It is shown that when represented in the information form, map posteriors are dominated by a small number of links that tie together nearby features in the map, which is developed into a sparse variant of the EIF, called the sparse extended information filter (SEIF).
Abstract: In this paper we describe a scalable algorithm for the simultaneous mapping and localization (SLAM) problem. SLAM is the problem of acquiring a map of a static environment with a mobile robot. The vast majority of SLAM algorithms are based on the extended Kalman filter (EKF). In this paper we advocate an algorithm that relies on the dual of the EKF, the extended information filter (EIF). We show that when represented in the information form, map posteriors are dominated by a small number of links that tie together nearby features in the map. This insight is developed into a sparse variant of the EIF, called the sparse extended information filter (SEIF). SEIFs represent maps by graphical networks of features that are locally interconnected, where links represent relative information between pairs of nearby features, as well as information about the robot’s pose relative to the map. We show that all essential update equations in SEIFs can be executed in constant time, irrespective of the size of the map. We...

716 citations


Journal ArticleDOI
01 Oct 2004-Tellus A
TL;DR: A new, local formulation of the ensemble Kalman filter approach for atmospheric data assimilation based on the hypothesis that, when the Earth’s surface is divided up into local regions of moderate size, vectors of the forecast uncertainties in such regions tend to lie in a subspace of much lower dimension than that of the full atmospheric state vector of such a region.
Abstract: In this paper, we introduce a new, local formulation of the ensemble Kalman filter approach for atmospheric data assimilation. Our scheme is based on the hypothesis that, when the Earth’s surface is divided up into local regions of moderate size, vectors of the forecast uncertainties in such regions tend to lie in a subspace of much lower dimension than that of the full atmospheric state vector of such a region. Ensemble Kalman filters, in general, take the analysis resulting from the data assimilation to lie in the same subspace as the expected forecast error. Under our hypothesis the dimension of the subspace corresponding to local regions is low. This is used in our scheme to allow operations only on relatively low-dimensional matrices. The data assimilation analysis is performed locally in a manner allowing massively parallel computation to be exploited. The local analyses are then used to construct global states for advancement to the next forecast time. One advantage, which may take on more importance as ever-increasing amounts of remotely-sensed satellite data become available, is the favorable scaling of the computational cost of our method with increasing data size, as compared to other methods that assimilate data sequentially. The method, its potential advantages, properties, and implementation requirements are illustrated by numerical experiments on the Lorenz-96 model. It is found that accurate analysis can be achieved at a cost which is very modest compared to that of a full global ensemble Kalman filter.

700 citations


Journal ArticleDOI
TL;DR: A general multi-sensor optimal information fusion decentralized Kalman filter with a two-layer fusion structure is given for discrete time linear stochastic control systems with multiple sensors and correlated noises.

692 citations


Journal ArticleDOI
TL;DR: In this article, a particle representation of the filtering distributions, and their evolution through time using sequential importance sampling and resampling ideas are developed for performing smoothing computations in general state-space models.
Abstract: We develop methods for performing smoothing computations in general state-space models. The methods rely on a particle representation of the filtering distributions, and their evolution through time using sequential importance sampling and resampling ideas. In particular, novel techniques are presented for generation of sample realizations of historical state sequences. This is carried out in a forward-filtering backward-smoothing procedure that can be viewed as the nonlinear, non-Gaussian counterpart of standard Kalman filter-based simulation smoothers in the linear Gaussian case. Convergence in the mean squared error sense of the smoothed trajectories is proved, showing the validity of our proposed method. The methods are tested in a substantial application for the processing of speech signals represented by a time-varying autoregression and parameterized in terms of time-varying partial correlation coefficients, comparing the results of our algorithm with those from a simple smoother based on the filte...

588 citations


Journal ArticleDOI
08 Nov 2004
TL;DR: Generic importance sampling mechanisms for data fusion are introduced and it is shown how each of the three cues can be modeled by an appropriate data likelihood function, and how the intermittent cues are best handled by generating proposal distributions from their likelihood functions.
Abstract: The effectiveness of probabilistic tracking of objects in image sequences has been revolutionized by the development of particle filtering. Whereas Kalman filters are restricted to Gaussian distributions, particle filters can propagate more general distributions, albeit only approximately. This is of particular benefit in visual tracking because of the inherent ambiguity of the visual world that stems from its richness and complexity. One important advantage of the particle filtering framework is that it allows the information from different measurement sources to be fused in a principled manner. Although this fact has been acknowledged before, it has not been fully exploited within a visual tracking context. Here we introduce generic importance sampling mechanisms for data fusion and discuss them for fusing color with either stereo sound, for teleconferencing, or with motion, for surveillance with a still camera. We show how each of the three cues can be modeled by an appropriate data likelihood function, and how the intermittent cues (sound or motion) are best handled by generating proposal distributions from their likelihood functions. Finally, the effective fusion of the cues by particle filtering is demonstrated on real teleconference and surveillance data.

561 citations


BookDOI
01 May 2004
TL;DR: In this paper, the authors present an overview of the literature on adaptive filtering for speech processing and its application in the context of noise control. But their focus is on the use of lowpass filters.
Abstract: List of Figures.List of Tables.Preface.Acknowledgments.Abbreviations and Acronyms.Part I: Basics.1 Introduction.1.1 Some History.1.2 Overview of the Book.2 Acoustic Echo and Noise Control Systems.2.1 Notation.2.2 Applications.3 Fundamentals.3.1 Signals.3.2 Acoustic Echoes.3.3 Standards.Part II: Algorithms.4 Error Criteria and Cost Functions.4.1 Error Criteria for Adaptive Filters.4.2 Error Criteria for Filter Design.4.3 Error Criteria for Speech Processing and Control Purposes.5 Wiener Filter.5.1 Time-Domain Solution.5.2 Frequency-Domain Solution.6 Linear Prediction.6.1 Normal Equations.6.2 Levinson{Durbin Recursion.7 Algorithms for Adaptive Filters.7.1 The Normalized Least Mean Square Algorithm.7.2 The Affine Projection Algorithm.7.3 The Recursive Least Squares Algorithm.7.4 The Kalman Algorithm.Part III: Acoustic Echo and Noise Control.8 Traditional Methods for Stabilization of Electroacoustic Loops.8.1 Adaptive Line Enhancement.8.2 Frequency Shift.8.3 Controlled Attenuation.9 Echo Cancellation.9.1 Processing Structures.9.2 Stereophonic and Multichannel Echo Cancellation.10 Residual Echo and Noise Suppression.10.1 Basics.10.2 Suppression of Residual Echoes.10.3 Suppression of Background Noise.10.4 Combining Background Noise and Residual Echo Suppression.11 Beamforming.11.1 Basics.11.2 Characteristics of Microphone Arrays.11.3 Fixed Beamforming.11.4 Adaptive Beamforming.Part IV: Control and Implementation Issues.12 System Control-Basic Aspects.12.1 Convergence versus Divergence Speed.12.2 System Levels for Control Design.13 Control of Echo Cancellation Systems.13.1 Pseudooptimal Control Parameters for the NLMS Algorithm.13.2 Pseudooptimal Control Parameters for the Affine Projection Algorithm.13.3 Summary of Pseudooptimal Control Parameters.13.4 Detection and Estimation Methods.13.5 Detector Overview and Combined Control Methods.14 Control of Noise and Echo Suppression Systems.14.1 Estimation of Spectral Power Density of Background Noise.14.2 Musical Noise.14.3 Control of Filter Characteristics.15 Control for Beamforming.15.1 Practical Problems.15.2 Stepsize Control.16 Implementation Issues.16.1 Quantization Errors.16.2 Number Representation Errors.16.3 Arithmetical Errors.16.4 Fixed Point versus Floating Point.16.5 Quantization of Filter Taps.Part V: Outlook and Appendixes.17 Outlook.Appendix A: Subband Impulse Responses.A.1 Consequences for Subband Echo Cancellation.A.2 Transformation.A.3 Concluding Remarks.Appendix B: Filterbank Design.B.1 Conditions for Approximately Perfect Reconstruction.B.2 Filter Design Using a Product Approach.B.3 Design of Prototype Lowpass Filters.B.4 Analysis of Prototype Filters and the Filterbank System.References.Index.

Journal ArticleDOI
14 Jun 2004
TL;DR: A real time motion-tracking system using a Kalman-based fusion algorithm to obtain dynamic orientations and further positions of segments of the subject's body and the results validated the effectiveness of the proposed method.
Abstract: A basic requirement in virtual environments is the tracking of objects, especially humans. A real time motion-tracking system was presented and evaluated in this paper. System sensors were built using tri-axis microelectromechanical accelerometers, rate gyros, and magnetometers. A Kalman-based fusion algorithm was applied to obtain dynamic orientations and further positions of segments of the subject's body. The system with the proposed algorithm was evaluated via dynamically measuring Euler orientation and comparing with other two conventional methods. An arm motion experiment was demonstrated using the developed system and algorithm. The results validated the effectiveness of the proposed method.

Journal ArticleDOI
TL;DR: This work uses the Bayes' rule Chapman-Kolmogorov paradigm with a linear state equation and point process observation models to derive adaptive filters appropriate for estimation from neural spike trains and suggests a practical approach for constructing filtering algorithms to track neural receptive field dynamics on a millisecond timescale.
Abstract: Neural receptive fields are dynamic in that with experience, neurons change their spiking responses to relevant stimuli. To understand how neural systems adapt their representations of biological information, analyses of receptive field plasticity from experimental measurements are crucial. Adaptive signal processing, the well-established engineering discipline for characterizing the temporal evolution of system parameters, suggests a framework for studying the plasticity of receptive fields. We use the Bayes' rule Chapman-Kolmogorov paradigm with a linear state equation and point process observation models to derive adaptive filters appropriate for estimation from neural spike trains. We derive point process filter analogues of the Kalman filter, recursive least squares, and steepest-descent algorithms and describe the properties of these new filters. We illustrate our algorithms in two simulated data examples. The first is a study of slow and rapid evolution of spatial receptive fields in hippocampal neurons. The second is an adaptive decoding study in which a signal is decoded from ensemble neural spiking activity as the receptive fields of the neurons in the ensemble evolve. Our results provide a paradigm for adaptive estimation for point process observations and suggest a practical approach for constructing filtering algorithms to track neural receptive field dynamics on a millisecond timescale.

Proceedings ArticleDOI
01 Jan 2004
TL;DR: A throughput region that guarantees the convergence of the error covariance matrix is found by solving a feasibility problem of a linear matrix inequality and an unstable throughput region such that the state estimation error of the Kalman filter is unbounded.
Abstract: We study the Kalman filtering problem when part or all of the observation measurements are lost in a random fashion. We formulate the Kalman filtering problem with partial observation losses and derive the Kalman filter updates with partial observation measurements. We show that with these partial measurements the Kalman filter and its error covariance matrix iteration become stochastic, since they now depend on the random packet arrivals of the sensor measurements, which can be lost or delayed when transmitted over a communication network. The communication network needs to provide a sufficient throughput for each of the sensor measurements in order to guarantee the stability of the Kalman filter, where the throughput captures the rate of the sensor measurements correctly received. We investigate the statistical convergence properties of the error covariance matrix iteration as a function of the throughput of the sensor measurements. A throughput region that guarantees the convergence of the error covariance matrix is found by solving a feasibility problem of a linear matrix inequality. We also find an unstable throughput region such that the state estimation error of the Kalman filter is unbounded. The expected error covariance matrix is bounded both from above and from below. The results are illustrated with some simple numerical examples.

01 Dec 2004
TL;DR: In this article, a probabilistic framework called Sigma-Point Kalman Filters (SPKF) was applied to the problem domain addressed by the extended Kalman Filter (EKF).
Abstract: A probabilistic framework, called Sigma-point Kalman Filters (SPKF) was applied to the problem domain addressed by the extended Kalman Filter (EKF). SPKF methods are superior to the standard EKF based estimation approaches, as an SPKF achieves second-order or higher accuracy. The SPKF has also been applied to the integrated navigation problem as it relates to unmanned aerial vehicle (UAV) autonomy. The SPKF-based sensor latency compensation technique is used to demonstrate the lagged GPS measurements.

Proceedings ArticleDOI
13 Jun 2004
TL;DR: This work demonstrates the flexibility and effectiveness of using the Kalman Filter as a solution for managing trade-offs between precision of results and resources in satisfying stream queries.
Abstract: To answer user queries efficiently, a stream management system must handle continuous, high-volume, possibly noisy, and time-varying data streams. One major research area in stream management seeks to allocate resources (such as network bandwidth and memory) to query plans, either to minimize resource usage under a precision requirement, or to maximize precision of results under resource constraints. To date, many solutions have been proposed; however, most solutions are ad hoc with hard-coded heuristics to generate query plans. In contrast, we perceive stream resource management as fundamentally a filtering problem, in which the objective is to filter out as much data as possible to conserve resources, provided that the precision standards can be met. We select the Kalman Filter as a general and adaptive filtering solution for conserving resources. The Kalman Filter has the ability to adapt to various stream characteristics, sensor noise, and time variance. Furthermore, we realize a significant performance boost by switching from traditional methods of caching static data (which can soon become stale) to our method of caching dynamic procedures that can predict data reliably at the server without the clients' involvement. In this work we focus on minimization of communication overhead for both synthetic and real-world streams. Through examples and empirical studies, we demonstrate the flexibility and effectiveness of using the Kalman Filter as a solution for managing trade-offs between precision of results and resources in satisfying stream queries.

Journal ArticleDOI
TL;DR: It is shown that the inclusion of information about the time-continuous nature of the underlying trajectories can improve parameter estimation considerably and two approaches, which take into account both the errors-in-variables problem and the problem of complex cost functions, are described in detail.
Abstract: We review the problem of estimating parameters and unobserved trajectory components from noisy time series measurements of continuous nonlinear dynamical systems. It is first shown that in parameter estimation techniques that do not take the measurement errors explicitly into account, like regression approaches, noisy measurements can produce inaccurate parameter estimates. Another problem is that for chaotic systems the cost functions that have to be minimized to estimate states and parameters are so complex that common optimization routines may fail. We show that the inclusion of information about the time-continuous nature of the underlying trajectories can improve parameter estimation considerably. Two approaches, which take into account both the errors-in-variables problem and the problem of complex cost functions, are described in detail: shooting approaches and recursive estimation techniques. Both are demonstrated on numerical examples.

Book ChapterDOI
01 Jun 2004
TL;DR: This book offers a step by step approach to the analysis of the salient features in time series such as the trend, seasonal, and irregular components.
Abstract: The paper presents a broad general review of the state space approach to time series analysis. It begins with an introduction to the linear Gaussian state space model. Applications to problems in practical time series analysis are considered. The state space approach is briefly compared with the Box–Jenkins approach. The Kalman filter and smoother and the simulation smoother are described. Missing observations, forecasting and initialisation are considered. A representation of a multivariate series as a univariate series is displayed. The construction and maximisation of the likelihood function are discussed. An application to real data is presented. The treatment is extended to non-Gaussian and nonlinear state space models. A simulation technique based on importance sampling is described for analysing these models. The use of antithetic variables in the simulation is considered. Bayesian analysis of the models is developed based on an extension of the importance sampling technique. Classical and Bayesian methods are applied to a real time series.

Journal ArticleDOI
TL;DR: In this article, the authors provide an application-independent analysis of the performance of the common Kalman filter variants in a non-linear system with uncorrelated uncertainties, which is the original formulation of the KF.
Abstract: The Kalman filter is a well-known recursive state estimator for linear systems. In practice, the algorithm is often used for non-linear systems by linearizing the system's process and measurement models. Different ways of linearizing the models lead to different filters. In some applications, these ‘Kalman filter variants’ seem to perform well, while for other applications they are useless. When choosing a filter for a new application, the literature gives us little to rely on. This paper tries to bridge the gap between the theoretical derivation of a Kalman filter variant and its performance in practice when applied to a non-linear system, by providing an application-independent analysis of the performances of the common Kalman filter variants. Correlated uncertainties can be dealt with by augmenting the state vector, this is the original formulation of the KF (Kalman 1960). Expressed in this new state vector, the process and measurement models are of the form (1) and (2) with uncorrelated uncertainties...

Journal ArticleDOI
TL;DR: The filtering problem under consideration can effectively be solved if there are positive definite solutions to a couple of algebraic Riccati-like inequalities or linear matrix inequalities and the set of desired robust filters is characterized in terms of some free parameters.
Abstract: This paper deals with a new filtering problem for linear uncertain discrete-time stochastic systems with randomly varying sensor delay. The norm-bounded parameter uncertainties enter into the system matrix of the state space model. The system measurements are subject to randomly varying sensor delays, which often occur in information transmissions through networks. The problem addressed is the design of a linear filter such that, for all admissible parameter uncertainties and all probabilistic sensor delays, the error state of the filtering process is mean square bounded, and the steady-state variance of the estimation error for each state is not more than the individual prescribed upper bound. We show that the filtering problem under consideration can effectively be solved if there are positive definite solutions to a couple of algebraic Riccati-like inequalities or linear matrix inequalities. We also characterize the set of desired robust filters in terms of some free parameters. An illustrative numerical example is used to demonstrate the usefulness and flexibility of the proposed design approach.

ReportDOI
01 Jan 2004
TL;DR: This work investigates the determinant of the Cramer Rao Lower Bound and compute it in the 2D and 3D cases, characterizing the global minima in the 1D case and proposing motion coordination algorithms that steer the mobile sensor network to an optimal deployment.
Abstract: : This work studies optimal sensor placement and motion coordination strategies for mobile sensor networks. For a target tracking application with range sensors, we investigate the determinant of the Cramer-Rao Lower Bound and compute it in the 2D and 3D cases. We characterize the global minima of the 2D case. We propose and characterize motion coordination algorithms that steer the mobile sensor network to an optimal deployment and that are amenable to a decentralized implementation. Finally, our numerical simulations illustrate how the proposed motion coordination algorithms lead to the improved performance of an extended Kalman filter in a target tracking scenario.

Journal ArticleDOI
TL;DR: A novel time-varying weather and load model for solving the short-term electric load-forecasting problem using moving window of current values of weather data as well as recent past history of load and weather data is presented.

Journal ArticleDOI
08 Nov 2004
TL;DR: An overview of the PDA technique and its application for different target tracking scenarios is presented and a sliding window parameter estimator using the Pda approach for tracking the state of a maneuvering target using measurements from an electrooptical sensor is presented.
Abstract: In tracking targets with less-than-unity probability of detection in the presence of false alarms (FAs), data association-deciding which of the received multiple measurements to use to update each track-is crucial. Most algorithms that make a hard decision on the origin of the true measurement begin to fail as the FA rate increases or with low observable (low probability of target detection) maneuvering targets. Instead of using only one measurement among the received ones and discarding the others, an alternative approach is to use all of the validated measurements with different weights (probabilities), known as probabilistic data association (PDA). This paper presents an overview of the PDA technique and its application for different target tracking scenarios. First, it describes the use of the PDA technique for tracking low observable targets with passive sonar measurements. This target motion analysis is an application of the PDA technique, in conjunction with the maximum-likelihood approach, for target motion parameter estimation via a batch procedure. Then, the PDA technique for tracking highly maneuvering targets and for radar resource management is illustrated with recursive state estimation using the interacting multiple model estimator combined with PDA. Finally, a sliding window (which can also expand and contract) parameter estimator using the PDA approach for tracking the state of a maneuvering target using measurements from an electrooptical sensor is presented.

Journal ArticleDOI
TL;DR: A switching Kalman filter model for the real-time inference of hand kinematics from a population of motor cortical neurons is presented, which generalizes previous encoding and decoding methods, addresses the non-Gaussian nature of firing rates, and can cope with crudely sorted neural data common in on-line prosthetic applications.
Abstract: We present a switching Kalman filter model for the real-time inference of hand kinematics from a population of motor cortical neurons. Firing rates are modeled as a Gaussian mixture where the mean of each Gaussian component is a linear function of hand kinematics. A "hidden state" models the probability of each mixture component and evolves over time in a Markov chain. The model generalizes previous encoding and decoding methods, addresses the non-Gaussian nature of firing rates, and can cope with crudely sorted neural data common in on-line prosthetic applications.

09 Jun 2004
TL;DR: The improved state estimation performance of the SPKF is demonstrated by applying it to the problem of loosely coupled GPS/INS integration and an approximate 30% error reduction in both attitude and position estimates relative to the baseline EKF implementation is demonstrated.
Abstract: Core to integrated navigation systems is the concept of fusing noisy observations from GPS, Inertial Measurement Units (IMU), and other available sensors. The current industry standard and most widely used algorithm for this purpose is the extended Kalman filter (EKF) [6]. The EKF combines the sensor measurements with predictions coming from a model of vehicle motion (either dynamic or kinematic), in order to generate an estimate of the current navigational state (position, velocity, and attitude). This paper points out the inherent shortcomings in using the EKF and presents, as an alternative, a family of improved derivativeless nonlinear Kalman filters called sigma-point Kalman filters (SPKF). We demonstrate the improved state estimation performance of the SPKF by applying it to the problem of loosely coupled GPS/INS integration. A novel method to account for latency in the GPS updates is also developed for the SPKF (such latency compensation is typically inaccurate or not practical with the EKF). A UAV (rotor-craft) test platform is used to demonstrate the results. Performance metrics indicate an approximate 30% error reduction in both attitude and position estimates relative to the baseline EKF implementation.

Journal ArticleDOI
TL;DR: A state estimation algorithm is proposed that fuses data from rate gyros and accelerometers to give long-term drift free attitude estimates and can be used for a rigid body performing any kind of rotations.

Journal ArticleDOI
TL;DR: This paper describes the implementation of an intelligent navigation system, based on the integrated use of the global positioning system (GPS) and several inertial navigation system (INS) sensors, for autonomous underwater vehicle (AUV) applications and highlights the use of fuzzy logic techniques to the adaptation of the initial statistical assumption.

Proceedings ArticleDOI
14 Jun 2004
TL;DR: In this paper, the unscented Kalman filter has been proposed to solve non-linear problems in the extended Kalman filters, and an empirical analysis has been conducted to evaluate the performance of unscenting Kalman filtering.
Abstract: An integrated navigation information system must know continuously the current position with a good precision. The required performance of the positioning module is achieved by using a cluster of heterogeneous sensors whose measurements are fused. The most popular data fusion method for positioning problems is the extended Kalman filter. The extended Kalman filter is a variation of the Kalman filter used to solve non-linear problems. Recently, an improvement to the extended Kalman filter has been proposed, the unscented Kalman filter. This paper describes an empirical analysis evaluating the performances of the unscented Kalman filter and comparing them with the extended Kalman filter's performances.

Journal ArticleDOI
01 Aug 2004-Tellus A
TL;DR: This paper shows that the ensemble approach makes possible an additional benefit: the timing of observations, whether they occur at the assimilation time or at some earlier or later time, can be effectively accounted for at low computational expense.
Abstract: Ensemble Kalman filteringwas developed as away to assimilate observed data to track the current state in a computational model. In this paper we showthat the ensemble approach makes possible an additional benefit: the timing of observations, whether they occur at the assimilation time or at some earlier or later time, can be effectively accounted for at low computational expense. In the case of linear dynamics, the technique is equivalent to instantaneously assimilating data as they are measured. The results of numerical tests of the technique on a simple model problem are shown.

Proceedings ArticleDOI
16 Aug 2004
TL;DR: A probabilistic framework, called Sigma-point Kalman Filters (SPKF) was applied to the problem domain addressed by the extended Kalman Filter, and the SPKF-based sensor latency compensation technique is used to demonstrate the lagged GPS measurements.