Showing papers on "Kalman filter published in 1994"

Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics

Abstract: A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The unbounded error growth found in the extended Kalman filter, which is caused by an overly simplified closure in the error covariance equation, is completely eliminated. Open boundaries can be handled as long as the ocean model is well posed. Well-known numerical instabilities associated with the error covariance equation are avoided because storage and evolution of the error covariance matrix itself are not needed. The results are also better than what is provided by the extended Kalman filter since there is no closure problem and the quality of the forecast error statistics therefore improves. The method should be feasible also for more sophisticated primitive equation models. The computational load for reasonable accuracy is only a fraction of what is required for the extended Kalman filter and is given by the storage of, say, 100 model states for an ensemble size of 100 and thus CPU requirements of the order of the cost of 100 model integrations. The proposed method can therefore be used with realistic nonlinear ocean models on large domains on existing computers, and it is also well suited for parallel computers and clusters of workstations where each processor integrates a few members of the ensemble.

On Gibbs sampling for state space models

Abstract: SUMMARY We show how to use the Gibbs sampler to carry out Bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time. Our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors. The states are generated efficiently using the Kalman filter. We illustrate our approach by several examples and empirically compare its performance to another Gibbs sampler where the states are generated one at a time. The empirical results suggest that our approach is both practical to implement and dominates the Gibbs sampler that generates the states one at a time.

Applied system identification

Abstract: 1. Introduction. 2. Time-Domain Models. 3. Frequency-Domain Models. 4. Frequency Response Functions. 5. System Realization. 6. Observer Identification. 7. Frequency Domain System ID. 8. Observer/Controller ID. 9. Recursive Techniques. Appendix A: Fundamental Matrix Algebra. Appendix B: Random Variables and Kalman Filter. Appendix C: Data Acquisition.

Data Augmentation and Dynamic Linear Models

Abstract: We define a subclass of dynamic linear models with unknown hyperparameters called d-inverse-gamma models. We then approximate the marginal p.d.f.s of the hyperparameter and the state vector by the data augmentation algorithm of Tanner/Wong. We prove that the regularity conditions for convergence hold. A sampling based scheme for practical implementation is discussed. Finally, we illustrate how to obtain an iterative importance sampling estimate of the model likelihood. (author's abstract)

Robust Multiple Car Tracking with Occlusion Reasoning

Abstract: In this work we address the problem of occlusion in tracking multiple 3D objects in a known environment and propose a new approach for tracking vehicles in road traffic scenes using an explicit occlusion reasoning step. We employ a contour tracker based on intensity and motion boundaries. The motion of the contour of the vehicles in the image is assumed to be well describable by an affine motion model with a translation and a change in scale. A vehicle contour is represented by closed cubic splines the position and motion of which is estimated along the image sequence. In order to employ linear Kalman Filters we decompose the estimation process into two filters: one for estimating the affine motion parameters and one for estimating the shape of the contours of the vehicles. Occlusion detection is performed by intersecting the depth ordered regions associated to the objects. The intersection part is then excluded in the motion and shape estimation. This procedure also improves the shape estimation in case of adjacent objects since occlusion detection is performed on slightly enlarged regions. In this way we obtain robust motion estimates and trajectories for vehicles even in the case of occlusions, as we show in some experiments with real world traffic scenes.

Neurocontrol of nonlinear dynamical systems with Kalman filter trained recurrent networks

Abstract: Although the potential of the powerful mapping and representational capabilities of recurrent network architectures is generally recognized by the neural network research community, recurrent neural networks have not been widely used for the control of nonlinear dynamical systems, possibly due to the relative ineffectiveness of simple gradient descent training algorithms. Developments in the use of parameter-based extended Kalman filter algorithms for training recurrent networks may provide a mechanism by which these architectures will prove to be of practical value. This paper presents a decoupled extended Kalman filter (DEKF) algorithm for training of recurrent networks with special emphasis on application to control problems. We demonstrate in simulation the application of the DEKF algorithm to a series of example control problems ranging from the well-known cart-pole and bioreactor benchmark problems to an automotive subsystem, engine idle speed control. These simulations suggest that recurrent controller networks trained by Kalman filter methods can combine the traditional features of state-space controllers and observers in a homogeneous architecture for nonlinear dynamical systems, while simultaneously exhibiting less sensitivity than do purely feedforward controller networks to changes in plant parameters and measurement noise. >

Robust Kalman filtering for uncertain discrete-time systems

Abstract: This paper is concerned with the problem of a Kalman filter design for uncertain discrete-time systems. The system under consideration is subjected to time-varying norm-bounded parameter uncertainty in both the state and output matrices. The problem addressed is the design of a linear filter such that the variance of the filtering error is guaranteed to be within a certain bound for all admissible uncertainties. Furthermore, the guaranteed cost can be optimized by appropriately searching a scaling design parameter. >

Optimal guaranteed cost control and filtering for uncertain linear systems

Abstract: The paper presents results on the design of robust state feedback controllers and steady-state robust state estimators for a class of uncertain linear systems with norm bounded uncertainty. The state feedback results extend the linear quadratic regulator to the case in which the underlying system is dependent on uncertain parameters. The state estimation results extend the steady-state Kalman filter to the case in which the underlying system is also uncertain. >

A state-space approach to adaptive RLS filtering

Abstract: Adaptive filtering algorithms fall into four main groups: recursive least squares (RLS) algorithms and the corresponding fast versions; QR- and inverse QR-least squares algorithms; least squares lattice (LSL) and QR decomposition-based least squares lattice (QRD-LSL) algorithms; and gradient-based algorithms such as the least-mean square (LMS) algorithm. Our purpose in this article is to present yet another approach, for the sake of achieving two important goals. The first one is to show how several different variants of the recursive least-squares algorithm can be directly related to the widely studied Kalman filtering problem of estimation and control. Our second important goal is to present all the different versions of the RLS algorithm in computationally convenient square-root forms: a prearray of numbers has to be triangularized by a rotation, or a sequence of elementary rotations, in order to yield a postarray of numbers. The quantities needed to form the next prearray can then be read off from the entries of the postarray, and the procedure can be repeated; the explicit forms of the rotation matrices are not needed in most cases. >

Towards model-based recognition of human movements in image sequences

Abstract: The interpretation of the movements of articulated bodies in image sequences is one of the most challenging problems in computer vision. In this contribution, we introduce a model-based approach for the recognition of pedestrians. We represent the human body by a 3D-model consisting of cylinders, whereas for modelling the movement of walking we use data from medical motion studies. The estimation of model parameters in consecutive images is done by applying a Kalman filter. Experimental results are shown for synthetic as well as for real image data.

Advanced data assimilation in strongly nonlinear dynamical systems

Abstract: Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

Chapter 50 State-space models

Abstract: This chapter reviews the usefulness of the Kalman filter for parameter estimation and inference about unobserved variables in linear dynamic systems. Applications include exact maximum likelihood estimation of regressions with ARMA disturbances, time-varying parameters, missing observations, forming an inference about the public's expectations about inflation, and specification of business cycle dynamics. The chapter also reviews models of changes in regime and develops the parallel between such models and linear state-space models. The chapter concludes with a brief discussion of alternative approaches to nonlinear filtering.

Longitudinal Data with Serial Correlation : A State-Space Approach

Abstract: This monograph is written for students at the graduate level in biostatistics, statistics or other disciplines that collect longitudinal data. It concentrates on the state space approach that provides a convenient way to compute likelihoods using the Kalman filter.

Multiscale recursive estimation, data fusion, and regularization

Abstract: We describe a framework for modeling stochastic phenomena at multiple scales and for their efficient estimation or reconstruction given partial and/or noisy measurements which may also be at several scales. In particular multiscale signal representations lead naturally to pyramidal or tree-like data structures in which each level in the tree corresponds to a particular scale of representation. A class of multiscale dynamic models evolving on dyadic trees is introduced. The main focus of this paper is on the description, analysis, and application of an extremely efficient optimal estimation algorithm for this class of models. This algorithm consists of a fine-to-coarse filtering sweep, followed by a coarse-to-fine smoothing step, corresponding to the dyadic tree generalization of Kalman filtering and Rauch-Tung-Striebel smoothing. The Kalman filtering sweep consists of the recursive application of three steps: a measurement update step, a fine-to-coarse prediction step, and a fusion step. We illustrate the use of our methodology for the fusion of multiresolution data and for the efficient solution of "fractal regularizations" of ill-posed signal and image processing problems encountered. >

An efficient method for contour tracking using active shape models

Abstract: There has been considerable research interest recently, in the areas of real time contour tracking and active shape models. This paper demonstrates how dynamic filtering can be used in combination with a modal-based flexible shape model to track an articulated non-rigid body in motion. The results show the method being used to track the silhouette of a walking pedestrian in real time. The active shape model used was generated automatically from real image data and incorporates variability in shape due to orientation as well as object flexibility. A Kalman filter is used to control spatial scale for feature search over successive frames. Iterative refinement allows accurate contour localisation where feasible. The shape model incorporates knowledge of the likely shape of the contour and speeds up tracking by reducing the number of system parameters. A further increase in speed is obtained by filtering the shape parameters independently. >

Optimal waveform selection for tracking systems

Abstract: Investigates adaptive waveform selection schemes where selection is based on overall target tracking system performance. Optimal receiver assumptions allow the inclusion of transmitted waveform specification parameters in the tracking subsystem defining equations. The authors give explicit expressions for two one-step ahead optimization problems for a single target in white Gaussian noise when the tracker is a conventional Kalman filter. These problems may be solved to yield the most improvement possible in tracking performance for each new transmitted pulse. In cases where target motion is restricted to one dimension, closed-form solutions to the local (one step ahead) waveform optimization problem have been obtained. The optimal waveform selection algorithms in the paper may be included with conventional Kalman filtering equations to form an enhanced Kalman tracker. Simulation examples are presented to illustrate the potential of the waveform selection schemes for the optimal utilization of the capabilities of modern digital waveform generators, including multiple waveform classes. The extension of the basic waveform optimization scheme to more complex tracking scenarios is also discussed. >

A comparison of position estimation techniques using occupancy grids

Abstract: A mobile robot requires perception of its local environment for both sensor based locomotion and for position estimation. Occupancy grids, based on ultrasonic range data, provide a robust description of the local environment for locomotion. Unfortunately, current techniques for position estimation based on occupancy grids are both unreliable and computationally expensive. This paper reports on experiments with four techniques for position estimation using occupancy grids. A world modeling technique based on combining global and local occupancy grids is described. Techniques are described for extracting line segments from an occupancy grid based on a Hough transform. The use of an extended Kalman filter for position estimation is then adapted to this framework. Four matching techniques are presented for obtaining the innovation vector required by the Kalman filter equations. Experimental results show that matching of segments extracted from the both the local and global occupancy grids gives results which are superior to a direct matching of grids, or to a mixed matching of segments to grids. >

Estimation, Prediction, and Interpolation for Nonstationary Series with the Kalman Filter

Abstract: We show how our definition of the likelihood of an autoregressive integrated moving average (ARIMA) model with missing observations, alternative to that of Kohn and Ansley and based on the usual assumptions made in estimation of and forecasting with ARIMA models, permits a direct and standard state-space representation of the nonstationary (original) data, so that the ordinary Kalman filter and fixed point smoother can be efficiently used for estimation, forecasting, and interpolation. In this way, the problem of estimating missing values in nonstationary series is considerably simplified. The results are extended to regression models with ARIMA errors, and a computer program is available from the authors.

A General Framework for Developing Sequential Fisheries Models

Abstract: A sequential fisheries model relates observed data to the biological dynamics of an underlying stock. Either model component, dynamic or observational, can be subject to statistical variation. Current fisheries literature includes models with (1) variable dynamics and no observation error, (2) deterministic dynamics and observations subject to measurement error, and (3) combined dynamic and measurement variability. This paper presents a general framework for developing sequential fishery models and estimating model parameters from available data. The framework encompasses most traditional stock assessment models and suggests new, potentially useful extensions. It generalizes the conventional definition of state space model to include nonlinear equations with nonnormal error. The paper rigorously compares two paradigms (KF: Kalman filter, EV: errors in variables) used for parameter estimation. Each paradigm is formulated in both frequentist and Bayes contexts, where Bayes is shown to be most appropriate fo...

Posterior Odds Testing for a Unit Root with Data-Based Model Selection

Abstract: The Kalman filter is used to derive updating equations for the Bayesian data density in discrete time linear regression models with stochastic regressors. The implied “Bayes model” has time varying parameters and conditionally heterogeneous error variances. A σ-finite Bayes model measure is given and used to produce a new-model-selection criterion (PIC) and objective posterior odds tests for sharp null hypotheses like the presence of a unit root. This extends earlier work by Phillips and Ploberger [18]. Autoregressive-moving average (ARMA) models are considered, and a general test of trend-stationarity versus difference stationarity is developed in ARMA models that allow for automatic order selection of the stochastic regressors and the degree of the deterministic trend. The tests are completely consistent in that both type I and type II errors tend to zero as the sample size tends to infinity. Simulation results and an empirical application are reported. The simulations show that the PIC works very well and is generally superior to the Schwarz BIC criterion, even in stationary systems. Empirical application of our methods to the Nelson-Plosser [11] series show that three series (unemployment, industrial production, and the money stock) are level- or trend-stationary. The other eleven series are found to be stochastically nonstationary.

Robust Recursive Estimation in the Presence of Heavy-Tailed Observation Noise

Abstract: Under the usual assumptions of normality, the recursive estimator known as the Kalman filter gives excellent results and has found an extremely broad field of application--not only for estimating the state of a stochastic dynamic system, but also for estimating model parameters as well as detecting abrupt changes in the states or the parameters. It is well known, however, that significantly nonnormal noise, and particularly the presence of outliers, severely degrades the performance of the Kalman filter. This results in poor state estimates, nonwhite residuals and invalid inference. A first-order approximation is derived for the conditional prior distribution of the state of a discrete-time stochastic linear dynamic system in the presence of $\varepsilon$-contaminated normal observation noise. This distribution is then used to derive a first-order approximation of the conditional mean (minimum-variance) estimator. If the observation noise distribution can be represented as a member of the $\varepsilon$-contaminated normal neighborhood, then the conditional prior is also, to first order, an analogous perturbation from a normal distribution whose first two moments are given by the Kalman filter. Moreover, the perturbation is itself of a special form, combining distributions whose parameters are given by banks of parallel Kalman filters and optimal smoothers.

Federated Kalman filter simulation results

Abstract: This paper describes federated filter applications to integrated, fault-tolerant navigation systems, with emphasis on real-time implementation issues and numerical simulation results. The federated filter is a near-optimal estimator for decentralized, multi-sensor data fusion. Its decentralized estimation archi- tecture is based on theoretically sound information-sharing principles. A federated filter consists of one or more sensor- dedicated local filters, generally operating in parallel, plus a master combining filter. The master filter periodically com- bines (fuses) the local filter solutions to form the best total solution. Fusion generally occurs at a reduced rate, relative to the local measurement rates. The method can provide sig- nificant improvements in data throughput, fault tolerance, and system modularity. Numerical simulation results are pre- sented for an example multi-sensor navigation system. These results demonstrate federated filter performance characteristics in terms of estimation accuracy, fault-tolerance, and computation speed. This work was supported by the Defense Small Business Innovation

Development of track to track fusion algorithms

Abstract: This paper describes techniques for track level fusion of surveillance data that are applicable to existing and near term tactical surveillance systems The linear optimal fused estimate is a convex combination of remote estimates with weights being the estimation confidences (covariances) The covariance based algorithm is most applicable where the track estimate is generated by a Kalman filter based tracking system When track covariance is not available, such as in /spl alpha/-/spl beta/ tracking systems, an estimated covariance can be used for track fusion In addition, track fusion also requires accounting for the cross covariance between tracks Various approaches to estimating the auto covariances and the cross covariances are examined, and the performance is evaluated through computer simulations

Multiscale systems, Kalman filters, and Riccati equations

Abstract: An algorithm analogous to the Rauch-Tung-Striebel algorithm/spl minus/consisting of a fine-to-coarse Kalman filter-like sweep followed by a coarse-to-fine smoothing step/spl minus/was developed previously by the authors (ibid. vol.39, no.3, p.464-78 (1994)). In this paper they present a detailed system-theoretic analysis of this filter and of the new scale-recursive Riccati equation associated with it. While this analysis is similar in spirit to that for standard Kalman filters, the structure of the dyadic tree leads to several significant differences. In particular, the structure of the Kalman filter error dynamics leads to the formulation of an ML version of the filtering equation and to a corresponding smoothing algorithm based on triangularizing the Hamiltonian for the smoothing problem. In addition, the notion of stability for dynamics requires some care as do the concepts of reachability and observability. Using these system-theoretic constructs, the stability and steady-state behavior of the fine-to-coarse Kalman filter and its Riccati equation are analysed. >

Tracking the direction of arrival of multiple moving targets

Abstract: The authors focus on the problem of tracking the direction-of-arrival (DOA) of multiple moving targets. The targets are assumed to be moving with constant accelerations subject to minor random perturbations and emitting narrow band signals that impinge on an array of passive sensors. Estimates of the DOA vector of the targets are obtained from the sensor data based on the maximum likelihood (ML) principle in such a way that the association between the estimates made at different time points is maintained. At each stage, the current ML estimates of DOA are treated as measurements and refined via a Kalman filter; tracking is accomplished without the need to perform unduly heavy computations. An efficient strategy for dealing with closely spaced targets is also presented. Finally, the performance of the tracking algorithm is illustrated via computer simulations. >

Sensorless control of reluctance machines at arbitrary operating conditions including standstill

Abstract: Reluctance machines with three-phase stator windings and damperless rotors are usually operated in a closed-loop rotor-oriented control. The necessary position encoder reduces robustness considerably. In order to replace this sensor by a position-detecting algorithm based on electrical measurements, two methods are presented, well-suited to low velocity (INFORM model) and high velocity (EMF model), respectively. Based on this information, a Kalman filter yields estimates of the machine state. A rotor-oriented controller enables highly dynamic operation even at standstill. Measurements verify the good static and dynamic properties of the drive in speed-controlled mode. >