Showing papers on "Kalman filter published in 2000"

The unscented Kalman filter for nonlinear estimation

Abstract: This paper points out the flaws in using the extended Kalman filter (EKE) and introduces an improvement, the unscented Kalman filter (UKF), proposed by Julier and Uhlman (1997). A central and vital operation performed in the Kalman filter is the propagation of a Gaussian random variable (GRV) through the system dynamics. In the EKF the state distribution is approximated by a GRV, which is then propagated analytically through the first-order linearization of the nonlinear system. This can introduce large errors in the true posterior mean and covariance of the transformed GRV, which may lead to sub-optimal performance and sometimes divergence of the filter. The UKF addresses this problem by using a deterministic sampling approach. The state distribution is again approximated by a GRV, but is now represented using a minimal set of carefully chosen sample points. These sample points completely capture the true mean and covariance of the GRV, and when propagated through the true nonlinear system, captures the posterior mean and covariance accurately to the 3rd order (Taylor series expansion) for any nonlinearity. The EKF in contrast, only achieves first-order accuracy. Remarkably, the computational complexity of the UKF is the same order as that of the EKF. Julier and Uhlman demonstrated the substantial performance gains of the UKF in the context of state-estimation for nonlinear control. Machine learning problems were not considered. We extend the use of the UKF to a broader class of nonlinear estimation problems, including nonlinear system identification, training of neural networks, and dual estimation problems. In this paper, the algorithms are further developed and illustrated with a number of additional examples.

Time series analysis and its applications

Abstract: Characteristics of Time Series * Time Series Regression and ARIMA Models * Dynamic Linear Models and Kalman Filtering * Spectral Analysis and Its Applications.

Global Positioning Systems, Inertial Navigation, and Integration

Abstract: An updated guide to GNSS and INS, and solutions to real-world GPS/INS problems with Kalman filtering Written by recognized authorities in the field, this second edition of a landmark work provides engineers, computer scientists, and others with a working familiarity with the theory and contemporary applications of Global Navigation Satellite Systems (GNSS), Inertial Navigational Systems (INS), and Kalman filters. Throughout, the focus is on solving real-world problems, with an emphasis on the effective use of state-of-the-art integration techniques for those systems, especially the application of Kalman filtering. To that end, the authors explore the various subtleties, common failures, and inherent limitations of the theory as it applies to real-world situations, and provide numerous detailed application examples and practice problems, including GNSS-aided INS, modeling of gyros and accelerometers, and SBAS and GBAS. Drawing upon their many years of experience with GNSS, INS, and the Kalman filter, the authors present numerous design and implementation techniques not found in other professional references. This Second Edition has been updated to include: GNSS signal integrity with SBAS Mitigation of multipath, including results Ionospheric delay estimation with Kalman filters New MATLAB programs for satellite position determination using almanac and ephemeris data and ionospheric delay calculations from single and dual frequency data New algorithms for GEO with L1 /L5 frequencies and clock steering Implementation of mechanization equations in numerically stable algorithms To enhance comprehension of the subjects covered, the authors have included software in MATLAB, demonstrating the working of the GNSS, INS, and filter algorithms. In addition to showing the Kalman filter in action, the software also demonstrates various practical aspects of finite word length arithmetic and the need for alternative algorithms to preserve result accuracy.

Adaptive filtering and change detection

Abstract: INTRODUCTION Extended Summary. Applications. SIGNAL ESTIMATION On--Line Approaches. Off--Line Approaches. PARAMETER ESTIMATION Adaptive Filtering. Change Detection Based on Sliding Windows Change Detection Based on Filter Banks STATE ESTIMATION Kalman Filtering Change Detection Based on Likelihood Ratios Change Detection Based on Multiple Models Change Detection Based on Algebraical Consistency Tests THEORY Evaluation Theory Linear Estimation A. Signal models and notation B. Fault detection terminology

Rao-blackwellised particle filtering for dynamic Bayesian networks

Abstract: Particle filters (PFs) are powerful sampling-based inference/learning algorithms for dynamic Bayesian networks (DBNs). They allow us to treat, in a principled way, any type of probability distribution, nonlinearity and non-stationarity. They have appeared in several fields under such names as "condensation", "sequential Monte Carlo" and "survival of the fittest". In this paper, we show how we can exploit the structure of the DBN to increase the efficiency of particle filtering, using a technique known as Rao-Blackwellisation. Essentially, this samples some of the variables, and marginalizes out the rest exactly, using the Kalman filter, HMM filter, junction tree algorithm, or any other finite dimensional optimal filter. We show that Rao-Blackwellised particle filters (RBPFs) lead to more accurate estimates than standard PFs. We demonstrate RBPFs on two problems, namely non-stationary online regression with radial basis function networks and robot localization and map building. We also discuss other potential application areas and provide references to some finite dimensional optimal filters.

Robust Control and Filtering for Time-Delay Systems

Abstract: Robust control: robust stability robust stabilization robust H-infinity control guaranteed cost control passivity analysis and synthesis interconnected systems. Robust filtering: robust Kalman filtering robust H-infinity filtering interconnected systems. Appendices: some facts from matrix theory some algebraic inequalities stability theorems positive real systems LMI control software.

Mixture Kalman filters

Abstract: In treating dynamic systems, sequential Monte Carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling, importance sampling and weighted resampling to complete the on-line ‘filtering’ task. We propose a special sequential Monte Carlo method, the mixture Kalman filter, which uses a random mixture of the Gaussian distributions to approximate a target distribution. It is designed for on-line estimation and prediction of conditional and partial conditional dynamic linear models, which are themselves a class of widely used non-linear systems and also serve to approximate many others. Compared with a few available filtering methods including Monte Carlo methods, the gain in efficiency that is provided by the mixture Kalman filter can be very substantial. Another contribution of the paper is the formulation of many non-linear systems into conditional or partial conditional linear form, to which the mixture Kalman filter can be applied. Examples in target tracking and digital communications are given to demonstrate the procedures proposed.

Time series analysis of non‐Gaussian observations based on state space models from both classical and Bayesian perspectives

Abstract: The analysis of non-Gaussian time series by using state space models is considered from both classical and Bayesian perspectives. The treatment in both cases is based on simulation using importance sampling and antithetic variables; Markov chain Monte Carlo methods are not employed. Non-Gaussian disturbances for the state equation as well as for the observation equation are considered. Methods for estimating conditional and posterior means of functions of the state vector given the observations, and the mean-square errors of their estimates, are developed. These methods are extended to cover the estimation of conditional and posterior densities and distribution functions. The choice of importance sampling densities and antithetic variables is discussed. The techniques work well in practice and are computationally efficient. Their use is illustrated by applying them to a univariate discrete time series, a series with outliers and a volatility series.

Optical Flow Constraints on Deformable Models with Applications to Face Tracking

Abstract: Optical flow provides a constraint on the motion of a deformable model. We derive and solve a dynamic system incorporating flow as a hard constraint, producing a model-based least-squares optical flow solution. Our solution also ensures the constraint remains satisfied when combined with edge information, which helps combat tracking error accumulation. Constraint enforcement can be relaxed using a Kalman filter, which permits controlled constraint violations based on the noise present in the optical flow information, and enables optical flow and edge information to be combined more robustly and efficiently. We apply this framework to the estimation of face shape and motion using a 3D deformable face model. This model uses a small number of parameters to describe a rich variety of face shapes and facial expressions. We present experiments in extracting the shape and motion of a face from image sequences which validate the accuracy of the method. They also demonstrate that our treatment of optical flow as a hard constraint, as well as our use of a Kalman filter to reconcile these constraints with the uncertainty in the optical flow, are vital for improving the performance of our system.

Ground target tracking with variable structure IMM estimator

Abstract: In this paper we present the design of a Variable Structure Interacting Multiple Model (VS-IMM) estimator for tracking groups of ground targets on constrained paths using Moving Target Indicator (MTI) reports obtained from an airborne sensor. The targets are moving along a highway, with varying obscuration due to changing terrain conditions. In addition, the roads can branch, merge or cross-the scenario represents target convoys along a realistic road network with junctions, changing terrains, etc. Some of the targets may also move in an open field. This constrained motion estimation problem is handled using an IMM estimator with varying mode sets depending on the topography, The number of models in the IMM estimator, their types and their parameters are modified adaptively, in real-time, based on the estimated position of the target and the corresponding road/visibility conditions. This topography-based variable structure mechanism eliminates the need for carrying all the possible models throughout the entire tracking period as in the standard IMM estimator, significantly improving performance and reducing computational load. Data association is handled using an assignment algorithm. The estimator is designed to handle a very large number of ground targets simultaneously. A simulated scenario consisting of over one hundred targets is used to illustrate the selection of design parameters and the operation of the tracker. Performance measures are presented to contrast the benefits of the VS-IMM estimator over the Kalman filter and the standard IMM estimator, The VS-IMM estimator is then combined with multidimensional assignment to gain "time-depth." The additional benefit of using higher dimensional assignment algorithms for data association is also evaluated.

An Adaptive Ensemble Kalman Filter

Abstract: To the extent that model error is nonnegligible in numerical models of the atmosphere, it must be accounted for in 4D atmospheric data assimilation systems. In this study, a method of estimating and accounting for model error in the context of an ensemble Kalman filter technique is developed. The method involves parameterizing the model error and using innovations to estimate the model-error parameters. The estimation algorithm is based on a maximum likelihood approach and the study is performed in an idealized environment using a three-level, quasigeostrophic, T21 model and simulated observations and model error. The use of a limited number of ensemble members gives rise to a rank problem in the estimate of the covariance matrix of the innovations. The effect of this problem on the two terms of the log-likelihood function is that the variance term is underestimated, while the χ2 term is overestimated. To permit the use of relatively small ensembles, a number of strategies are developed to deal w...

Time Series and Cross-section Information in Affine Term-Structure Models

Abstract: In this article I provide an empirical analysis of the term structure of interest rates using the affine class of term-structure models introduced by Duffie and Kan. I estimate these models by combining time series and cross-section information in a theoretically consistent way. In the estimation I use a Kalman filter based on a discretization of the continuous-time factor process and allow for a general measurement-error structure. I provide evidence that a three-factor affine model with correlated factors is able to provide an adequate fit of the cross-section and the dynamics of the term structure. The three factors can be given the usual interpretation of level, steepness, and curvature.

Robust two-stage Kalman filters for systems with unknown inputs

Abstract: A method is developed for the state estimation of linear time-varying discrete systems with unknown inputs. By making use of the two-stage Kalman filtering technique and a proposed unknown inputs filtering technique, a robust two-stage Kalman filter which is unaffected by the unknown inputs can be readily derived and serves as an alternative to the Kitanidis' (1987) unbiased minimum-variance filter. The application of this new filter is illustrated by optimal filtering for systems with unknown inputs.

Multiple-model adaptive estimation using a residual correlation Kalman filter bank

Abstract: We propose a modified multiple model adaptive estimation (MMAE) algorithm that uses the time correlation of the Kalman filter residuals, in place of their scaled magnitude, to assign conditional probabilities for each of the modeled hypotheses. This modified algorithm, denoted the residual correlation Kalman filter bank (RCKFB), uses the magnitude of an estimate of the correlation of the residual with a slightly modified version of the usual MMAE hypothesis testing algorithm to assign the conditional probabilities to the various hypotheses that are modeled in the Kalman filter bank within the MMAE. This concept is used to detect flight control actuator failures, where the existence of a single frequency sinusoid (which is highly time correlated) in the residual of an elemental filter within an MMAE is indicative of that filter having the wrong actuator failure status hypothesis. This technique results in a delay in detecting the flight control actuator failure because several samples of the residual must be collected before the residual correlation can be estimated. However, it allows a significant reduction of the amplitude of the required system inputs for exciting the various system modes to enhance identifiability, to the point where they may possibly be subliminal, so as not to be objectionable to the pilot and passengers.

Mean shift and optimal prediction for efficient object tracking

Abstract: A new paradigm for the efficient color-based tracking of objects seen from a moving camera is presented. The proposed technique employs the mean shift analysis to derive the target candidate that is the most similar to a given target model, while the prediction of the next target location is computed with a Kalman filter. The dissimilarity between the target model and the target candidates is expressed by a metric based on the Bhattacharyya coefficient. The implementation of the new method achieves real-time performance, being appropriate for a large variety of objects with different color patterns. The resulting tracking, tested on various sequences, is robust to partial occlusion, significant clutter, target scale variations, rotations in depth, and changes in camera position.

On foot navigation: continuous step calibration using both complementary recursive prediction and adaptive Kalman filtering

Abstract: Keywords: topotraj Reference TOPO-CONF-2000-007 Record created on 2004-12-16, modified on 2016-08-08

Detecting and tracking eyes by using their physiological properties, dynamics, and appearance

Abstract: Reliable detection and tracking of eyes is an important requirement for attentive user interfaces. In this paper, we present a methodology for detecting eyes robustly in indoor environments in real-time. We exploit the physiological properties and appearance of eyes as well as head/eye motion dynamics. Infrared lighting is used to capture the physiological properties of eyes, Kalman trackers are used to model eye/head dynamics, and a probabilistic based appearance model is used to represent eye appearance. By combining three separate modalities, with specific enhancements within each modality, our approach allows eyes to be treated as robust features that can be used for other higher-level processing.

Adaptive joint detection and decoding in flat-fading channels via mixture Kalman filtering

Abstract: A novel adaptive Bayesian receiver for signal detection and decoding in fading channels with known channel statistics is developed; it is based on the sequential Monte Carlo methodology that has emerged in the field of statistics. The basic idea is to treat the transmitted signals as "missing data" and to sequentially impute multiple samples of them based on the observed signals. The imputed signal sequences, together with their importance weights, provide a way to approximate the Bayesian estimate of the transmitted signals and the channel states. Adaptive receiver algorithms for both uncoded and convolutionally coded systems are developed. The proposed techniques can easily handle the non-Gaussian ambient channel noise. It is shown through simulations that the proposed sequential Monte Carlo receivers achieve near-bound performance in fading channels for both uncoded and coded systems, without the use of any training/pilot symbols or decision feedback. Moreover, the proposed receiver structure exhibits massive parallelism and is ideally suited for high-speed parallel implementation using the very large scale integration (VLSI) systolic array technology.

On the parametrization and design of an extended Kalman filter frequency tracker

Abstract: The problem of estimating the frequency of a harmonic signal embedded in broad-band noise is considered. The paper focuses on the extended Kalman filter frequency tracker, which is the application of the extended Kalman filter (EKF) framework to the frequency estimation problem. The EKF frequency tracker recently proposed in the literature is characterized by a vector of three design parameters {q,r,/spl epsi/}, whose role and tuning is still a controversial and unclear issue. In this paper it is shown that a wise parametrization of the extended Kalman frequency tracker is characterized by just one parameter: the /spl epsi/ must be set to zero to achieve the basic property of unbiasedness in a noise-free setting; the performances of the tracker are not influenced independently by q and r; and what really matters is the ratio /spl lambda/=r/q only. The proposed simplification of the extended Kalman filter frequency tracker allows an easier and more transparent tuning of its tracking behavior.

Bayesian estimation and Kalman filtering: a unified framework for mobile robot localization

Abstract: Decision and estimation theory are closely related topics in applied probability. In this paper, Bayesian hypothesis testing is combined with Kalman filtering to merge two different approaches to map-based mobile robot localization; namely Markov localization and pose tracking. A robot carries proprioceptive sensors that monitor its motion and allow it to estimate its trajectory as it moves away from a known location. A single Kalman filter is used for tracking the pose displacements of the robot between different areas. The robot is also equipped with exteroceptive sensors that seek for landmarks in the environment. Simple feature extraction algorithms process the incoming signals and suggest potential corresponding locations on the map. Bayesian hypothesis testing is applied in order to combine the continuous Kalman filter displacement estimates with the discrete landmark pose measurement events. Within this framework, also known as multiple hypothesis tracking, multimodal probability distribution functions can be represented and this inherent limitation of the Kalman filter is overcome.

A gyro-free quaternion-based attitude determination system suitable for implementation using low cost sensors

Abstract: Attitude determination systems that use inexpensive sensors and are based on computationally efficient and robust algorithms are indispensable for real-time vehicle navigation, guidance and control applications. This paper describes an attitude determination system that is based on two vector measurements of non-zero, non-colinear vectors. The algorithm is based on a quaternion formulation of Wahba's (1966) problem, whereby the error quaternion (q/sub e/) becomes the observed state and can be cast into a standard linear measurement equation. Using the Earth's magnetic field and gravity as the two measured quantities, a low-cost attitude determination system is proposed. An iterated least-squares solution to the attitude determination problem is tested on simulated static cases, and shown to be globally convergent. A time-varying Kalman filter implementation of the same formulation is tested on simulated data and experimental data from a maneuvering aircraft. The time-varying Kalman filter implementation of this algorithm is exercised on simulated and real data collected from an inexpensive triad of accelerometers and magnetometers. The accelerometers in conjunction with the derivative of GPS velocity provided a measure of the gravitation field vector and the magnetometers measured the Earth's magnetic field vector. Tracking errors on experimental data are shown to be less than 1 degree mean and standard deviation of approximately 11 degrees in yaw, and 3 degrees in pitch and roll. Best case performance of the system during maneuvering is shown to improve standard deviations to approximately 3 degrees in yaw, and 1.5 degrees in pitch and roll.

Collective localization: a distributed Kalman filter approach to localization of groups of mobile robots

Abstract: This paper presents a new approach to the cooperative localization problem, namely collective localization. A group of M robots is viewed as a single system composed of robots that carry, in general, different sensors and have different positioning capabilities. A single Kalman filter is formulated to estimate the position and orientation of all the members of the group. This centralized schema is capable of fusing information provided by the sensors distributed on the individual robots while accommodating independencies and interdependencies among the collected data. In order to allow for distributed processing, the equations of the centralized Kalman filter are treated so that this filter can be decomposed in M modified Kalman filters each running on a separate robot. The collective localization algorithm is applied to a group of 3 robots and the improvement in localization accuracy is presented.

Learning and classification of complex dynamics

Abstract: Standard, exact techniques based on likelihood maximization are available for learning auto-regressive process models of dynamical processes. The uncertainty of observations obtained from real sensors means that dynamics can be observed only approximately. Learning can still be achieved via "EM-K"-expectation-maximization (EM) based on Kalman filtering. This cannot handle more complex dynamics, however, involving multiple classes of motion. A problem arises also in the case of dynamical processes observed visually: background clutter arising for example, in camouflage, produces non-Gaussian observation noise. Even with a single dynamical class, non-Gaussian observations put the learning problem beyond the scope of EM-K. For those cases, we show here how "EM-C"-based on the CONDENSATION algorithm which propagates random "particle-sets," can solve the learning problem. Here, learning in clutter is studied experimentally using visual observations of a hand moving over a desktop. The resulting learned dynamical model is shown to have considerable predictive value: when used as a prior for estimation of motion, the burden of computation in visual observation is significantly reduced. Multiclass dynamics are studied via visually observed juggling; plausible dynamical models have been found to emerge from the learning process, and accurate classification of motion has resulted. In practice, EM-C learning is computationally burdensome and the paper concludes with some discussion of computational complexity.

On tempo tracking: Tempogram Representation and Kalman filtering

Abstract: We formulate tempo tracking in a Bayesian framework where a tempo tracker is modeled as a stochastic dynamical system. The tempo is modeled as a hidden state variable of the system and is estimated by a Kalman filter. The Kalman filter operates on a Tempogram, a wavelet-like multiscale expansion of a real performance. An important advantage of our approach is that it is possible to formulate both off-line or real-time algorithms. The simulation results on a systematically collected set of MIDI piano performances of Yesterday and Michelle by the Beatles shows accurate tracking of approximately 90% of the beats.

Distributed Multi-Robot Localization

Abstract: This paper presents a new approach to the cooperative localization problem, namely distributed multi-robot localization. A group of M robots is viewed as a single system composed of robots that carry, in general, different sensors and have different positioning capabilities. A single Kalman filter is formulated to estimate the position and orientation of all the members of the group. This centralized schema is capable of fusing information provided by the sensors distributed on the individual robots while accommodating independencies and interdependencies among the collected data. In order to allow for distributed processing, the equations of the centralized Kalman filter are treated so that this filter can be decomposed into M modified Kalman filters each running on a separate robot. The distributed localization algorithm is applied to a group of 3 robots and the improvement in localization accuracy is presented.

Triangulation-based fusion of sonar data with application in robot pose tracking

Abstract: In this paper a sensor fusion scheme, called triangulation-based fusion (TBF) of sonar data, is presented. This algorithm delivers stable natural point landmarks, which appear in practically all indoor environments, i.e., vertical edges like door posts, table legs, and so forth. The landmark precision is in most cases within centimeters. The TBF algorithm is implemented as a voting scheme, which groups sonar measurements that are likely to have hit the same object in the environment. The algorithm has low complexity and is sufficiently fast for most mobile robot applications. As a case study, we apply the TBF algorithm to robot pose tracking. The pose tracker is implemented as a classic extended Kalman filter, which use odometry readings for the prediction step and TBF data for measurement updates. The TBF data is matched to pre-recorded reference maps of landmarks in order to measure the robot pose. In corridors, complementary TBF data measurements from the walls are used to improve the orientation and position estimate. Experiments demonstrate that the pose tracker is robust enough for handling kilometer distances in a large scale indoor environment containing a sufficiently dense landmark set.

Data Assimilation into a Primitive-Equation Model with a Parallel Ensemble Kalman Filter

Abstract: Data assimilation experiments are performed using an ensemble Kalman filter (EnKF) implemented for a two-layer spectral shallow water model at triangular truncation T100 representing an abstract planet covered by a strongly stratified fluid. Advantage is taken of the inherent parallelism in the EnKF by running each ensemble member on a different processor of a parallel computer. The Kalman filter update step is parallelized by letting each processor handle the observations from a limited region. The algorithm is applied to the assimilation of synthetic altimetry data in the context of an imperfect model and known representation-error statistics. The effect of finite ensemble size on the residual errors is investigated and the error estimates obtained with the EnKF are compared to the actual errors.

An extended complex Kalman filter for frequency measurement of distorted signals

Abstract: The design of an extended complex Kalman filter for the measurement of power system frequency has been presented in this paper. The design principles and the validity of the model have been outlined. A complex model has been developed to track a distorted signal that belongs to a power system. The model inherently takes care of the frequency measurement along with the amplitude and phase of the signals. The theory has been applied to standard test signals representing the worst-case measurement and network conditions in a typical power system. The proposed algorithm is suitable for real-time applications where the measurement noise and other disturbances are high. The complex quantities can be conveniently handled using a floating point processor. Comparison of the results of the proposed method with those obtained from a real extended Kalman filter reveals the superior performance of the former method.

Time Varying Beta Risk: An Analysis of Alternative Modelling Techniques

Abstract: This paper investigates the performance of three different approaches to modelling time-variation in conditional asset betas: GARCH models, the extended market model of Schwert and Seguin (1990) and the Kalman Filter algorithm. Using daily UK industry returns, we find the simple market model beta to be as efficient as the more complicated GARCH type models. However, the Kalman Filter algorithm incorporating a random walk parameterisation dominates all other models under the mean-square error criterion. Finally, we provide strong evidence that a combination of the methods under investigation may lead to considerably more powerful estimators of the time-variation in conditional beta.

Fault detection and identification in a mobile robot using multiple model estimation and neural network

Abstract: We propose a method to detect and identify faults in wheeled mobile robots. The idea behind the method is to use adaptive estimation to predict the outcome of several faults, and to learn them collectively as a failure pattern. Models of the system behavior under each type of fault are embedded in multiple parallel Kalman filter (KF) estimators. Each KF is tuned to a particular fault and predicts, using its embedded model, the expected values for the sensor readings. The residual, the difference between the predicted readings (based on certain assumptions for the system model and the sensor models) and the actual sensor readings, is used as an indicator of how well each filter is performing. A backpropagation neural network processes this set of residuals as a pattern and decides which fault has occurred, that is, which filter is better tuned to the correct state of the mobile robot. The technique has been implemented on a physical robot and results from experiments are discussed.