Showing papers on "Kalman filter published in 1987"

Kalman Filtering with Real-time Applications

Abstract: "Kalman Filtering with Real-Time Applications" presents a thorough discussion of the mathematical theory and computational schemes of Kalman filtering. The filtering algorithms are derived via different approaches, including a direct method consisting of a series of elementary steps, and an indirect method based on innovation projection. Other topics include Kalman filtering for systems with correlated noise or colored noise, limiting Kalman filtering for time-invariant systems, extended Kalman filtering for nonlinear systems, interval Kalman filtering for uncertain systems, and wavelet Kalman filtering for multiresolution analysis of random signals. The last two topics are new additions to this third edition. Most filtering algorithms are illustrated by using simplified radar tracking examples. The style of the book is informal, and the mathematics is elementary but rigorous. The text is self-contained, suitable for self-study, and accessible to all readers with a minimum knowledge.

Application of Kalman filtering to track and vertex fitting

Abstract: Recently iterative procedures have been proposed for track and vertex fitting in counter experiments. We show that the proper theoretical framework for these procedures is the theory of linear filtering, in particular the Kalman filter. Using results from filtering theory we confirm and extend the previous results. We also discuss the detection of outliers and of secondary vertices.

Error modeling in stereo navigation

Abstract: In stereo navigation, a mobile robot estimates its position by tracking landmarks with on-board cameras. Previous systems for stereo navigation have suffered from poor accuracy, in part because they relied on scalar models of measurement error in triangulation. Using three-dimensional (3D) Gaussian distributions to model triangulation error is shown to lead to much better performance. How to compute the error model from image correspondences, estimate robot motion between frames, and update the global positions of the robot and the landmarks over time are discussed. Simulations show that, compared to scalar error models, the 3D Gaussian reduces the variance in robot position estimates and better distinguishes rotational from translational motion. A short indoor run with real images supported these conclusions and computed the final robot position to within two percent of distance and one degree of orientation. These results illustrate the importance of error modeling in stereo vision for this and other applications.

A Curvature-based Scheme for Improving Road Vehicle Guidance by Computer Vision

Abstract: An efficient method for guiding high speed land vehicles along roadways by computer vision has been developed and demonstrated with image sequence processing hardware in a real-time simulation loop 1 . The approach is tailored to a well structured highway environment with good lanemarkings. Contour correlation and high order world models are the basic elements of the method, realised in a special multi-microprocessor (on board) computer system. Perspec-tive projection and dynamical models (Kalman filter) are used in an integrated approach for the design of the visual feedback control system. By determining road curvature explicity from the visual input, previously encountered steady state errors in curves are eliminated. The performance of the system will be demonstrated by a video film. The operation of the image sequence processing system has been tested on a typical Autobahn-scene at velocities up to 100 km/h.

Tracking a Maneuvering Target Using Input Estimation

Abstract: The conventional Kalman tracking filter incurs mean tracking errors in the presence of a pilot-induced target maneuver. Chan,Hu, and Plant proposed a solution to this problem which used themean deviations of the residual innovation sequence to make corrections to the Kalman filter. This algorithm is further developedhere for the case of a one-dimensional Kalman filter, for which an Implementable closed-form recursive relation exists. Simulation results show that the Chan, Hu, and Plant method can accurately detect and correct an acceleration discontinuity under a variety of maneuver models and radar parameters. Also, the inclusion of thislogic into a multiple hypothesis tracking system is briefly outlined.

A speech enhancement method based on Kalman filtering

Abstract: In this paper, the problem of speech enhancement when only corrupted speech signal is available for processing is considered. For this, the Kalman filtering method is studied and compared with the Wiener filtering method. Its performance is found to be significantly better than the Wiener filtering method. A delayed-Kalman filtering method is also proposed which improves the speech enhancement performance of Kalman filter further.

A new class of dynamic methods for the identification of origin-destination flows

Abstract: A new systems dynamics approach for the identification of origin-destination (O-D) flows in a traffic system is presented. It is the basic idea of this approach that traffic flow through a facility is treated as a dynamic process in which the sequences of short-time exit flow counts depend by causal relationships upon the time-variable sequences of entrance flow volumes. In that way enough information can be obtained from the counts at the entrances and the exits to obtain unique and bias-free estimates for the unknown O-D flows without further a priori information. Four different methods were developed: an ordinary least squares estimator involving cross-correlation matrices, a constrained optimization method, a simple recursive estimation formula and estimation by Kalman filtering. The methods need only moderate computational effort and are particularly useful for tracking time-variable O-D patterns for on-line identification and control purposes. An analysis of the accuracy of the estimates and a discussion of the convergence properties of the methods are given. Finally, a comparison with some conventional static estimation procedures is carried out using synthetic as well as real data from several intersections. These tests demonstrated that the presented dynamic methods are highly superior to conventional techniques and produce more accurate results.

Kalman filtering, smoothing, and recursive robot arm forward and inverse dynamics

Abstract: The inverse and forward dynamics problems for multilink serial manipulators are solved by using recursive techniques from linear filtering and smoothing theory. The pivotal step is to cast the system dynamics and kinematics as a two-point boundary-value problem. Solution of this problem leads to filtering and smoothing techniques similar to the equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing. The solutions prescribe an inward filtering recursion to compute a sequence of constraint moments and forces followed by an outward recursion to determine a corresponding sequence of angular and linear accelerations. An inward recursion refers to a sequential technique that starts at the tip of the terminal link and proceeds inwardly through all of the links until it reaches the base. Similarly, an outward recursion starts at the base and propagates out toward the tip. The recursive solutions are O(N), in the sense that the number of required computations only grows linearly with the number of links. A technique is provided to compute the relative angular accelerations at all of the joints from the applied external joint moments (and vice versa). It also provides an approach to evaluate recursively the composite multilink system inertia matrix and its inverse. The main contribution is to establish the equivalence between the filtering and smoothing techniques arising in state estimation theory and the methods of recursive robot dynamics. The filtering and smoothing architecture is very easy to understand and implement. This provides for a better understanding of robot dynamics. While the focus is not on exploring computational efficiency, some initial results in that direction are obtained. This is done by comparing performance with other recursive methods for a planar chain example. The analytical foundation is laid for the potential use of filtering and smoothing techniques in robot dynamics and control.

Fault Diagnosis in Dynamic Systems via State Estimation - a Survey

Abstract: This paper gives a survey on methods for the detection and localization of sensor and component faults of uncertain dynamic systems. In contrast to the commonly used techniques of hardware redundancy these methods make use of analytical redundancy and, thereby, allow to detect and localize faults with the aid of a digital computer. They comprise single, multiple or hierarchical state estimation using Luenberger observers or Kalman filters. An issue of particular relevance is the consideration of parameter uncertainties or parameter variations of the process. Several proposals are discussed to reduce the effects of parameter variations. Moreover, results from computer simulations and a practical technical application to the control of an inverted pendulum are reported.

Decentralized Filtering and Redundancy Management for Multisensor Navigation

Abstract: Failure detection and redundancy management is discussed for avionics applications of integrated navigation involving coordinated use of multiple simultaneous sensor subsystems such as GPS, JTIDS, TACAN, VOR/DME, ILS, an inertial navigation system (INS), and possibly even Doppler AHRS. A brief high level survey is provided to assess the status of those techniques and methodologies advertized as already available for handling the challenging real-time failure detection, redundancy management, and Kalman filtering aspects of these systems with differing availabilities, differing reliabilities, differing accuracies, and differing information content/sampling rates. Following the status review, a new failure detection/redundancy management approach is developed based on voter/monitoring at both the raw data and at the filtered-data level, as well as using additional inputs from hardware built-in-testing (BIT) and from specialized tests for subsequent failure isolation in the case of ambiguous indications. The technique developed involves use of Gaussian confidence regions to reasonably account for the inherent differences in accuracy between the various sensor subsystems. Online estimates of covariances from the Kalman filter are to be used for this purpose (when available). A technique is provided for quantitatively evaluating both the probability of detecting failed component subsystems and the probability of false alarm to be incurred, which is then to be traded off as the basis for rational selection of the thresholds used in the automated decision process. Moreover, the redundancy management procedure is demonstrated to be amenable to pilot or navigation operator prompting and override, if necessary.

A Chi-square test for fault-detection in Kalman filters

Abstract: A test for real-time detection of soft failures in navigation systems using Kalman filters has been proposed by Kerr. The test is based on the overlap between the confidence regions associated with two estimates, one obtained from a Kalman filter using on-line measurements, and the other based solely on a priori information. An alternate computational technique is presented which is based on constructing a chi-square test statistic from the difference between the two estimates and comparing it to a precomputed threshold. The chi-square test avoids the iterative computations required by the two-ellipsoid method for dimensions of two and higher.

Robust Preprocessing for Kalman Filtering of Glint Noise

Abstract: The non-Gaussian character of glint noise is demonstrated by exploratory data analysis. This non-Gaussian behavior is characterized by outliers in the form of glint spikes. Since glint noise is processed by an angle-tracking Kalman filter, and since the latter is quite nonrobust, strategies are proposed to minimize the effect of these glint spikes. One of the strategies, which involves robust preprocessing of the data, is pursued in detail. Finally, some results of a planar missile simulation are presented that clearly demonstrate the merits of the robust preprocessing strategy.

Recursive identification of bilinear systems

Abstract: Methods of identifying bilinear systems from recorded input-output data are discussed in this article A short survey of the existing literature on the topic is given ‘Standard’ methods from linear systems identification, such as least squares, extended least squares, recursive prediction error and instrumental variable methods are transferred to bilinear, input-output model structures and tested in simulation Special attention is paid to problems of stabilizing the model predictor, and it is shown how a time-varying Kalman filter and associated parameter estimation algorithm can deal with this problem

Passive Position Location Estimation Using the Extended Kalman Filter

Abstract: Several papers have been published recently using the method ofleast squares for passive position location estimation. While the Kalman filter is mentioned as an alternative approach in most ofthese papers, none of the papers actually compare the performanceof the Kalman filter with the method of least squares. In this paper,the performances of the extended Kalman filter and the iteratedextended Kalman filter are compared with the method of leastsquares. Monte Carlo results are given showing how the a prioricovariance matrix influences the accuracy of the extended Kalmanfilter.

An Efficient Dynamic State Estimation Algorithm including Bad Data Processing

Abstract: This paper presents a comparison between the performance of dynamic and tracking estimators, in power systems operating under quasi-static conditions, concerning their characteristics of forecasting and filtering. From this comparison a new dynamic estimator which incorporates the main advantages of the previous estimators is proposed. Also, a new scheme of detection and identification of bad data properly built for dynamic algorithms is presented. Numerical results showing the performance of the new algorithm under different operational conditions are discussed.

Advances in Econometrics: Applications of the Kalman filter in econometrics

Abstract: Introduction From the point of view of econometric modelling, the Kalman filter is of very little interest. It is simply a statistical algorithm that enables certain computations to be carried out for a model cast in state space form. The crucial point for the econometrician to understand is that the state space form opens up the possibility of formulating models that are much wider and richer than those normally considered. Furthermore, it often allows the setting up of models that have a more natural interpretation and provide more useful information on the nature of underlying economic processes. This second point can be illustrated clearly at the simplest level of a pure time series model. Indeed, the aim of this chapter will be to show how the state space form can be used to provide a framework for modelling economic time series that is in many ways preferable to the more conventional approach based on ARIMA processes. The proposed framework links up closely with that of dynamic econometric models, and the resulting model selection methodology is much more akin to that of econometrics. Perhaps the clearest indication of the closeness of these links is that the starting point for the proposed framework is regression rather than the theory of stationary stochastic processes. The state space form allows unobserved components to be incorporated into a model, and the Kalman filter provides the means of estimating them. The specification of these components must, to some extent, depend on a priori considerations, and since the components presumably have an economic interpretation, the model is a structural one; see Engle (1978). In the reduced form the information on individual unobserved components is not explicitly available since the disturbances that generate the various unobserved components are amalgamated into a single disturbance term. In the case of a linear univariate structural time series model, the reduced form is an ARIMA process.

Mass property estimation for control of asymmetrical satellites

Abstract: Real-time algorithms that estimate the mass-property parameters commonly used in spacecraft control laws are developed based upon a stochastic estimation viewpoint. The elements of the inverse inertia matrix and the center-of-mass location vector are estimated from noisy measurements of the angular velocity using a secondorder filter, while estimates of the mass reciprocal are generated from noisy linear velocity measurements using a Kalman filter. Simulation results show that the rate of convergence of each estimate depends strongly upon the particular maneuver being performed, but that the mass properties can be estimated to within 1% error.

Kalman filtering approaches for solving problems in analytical chemistry

Abstract: The application of the Kalman filter to the solution of a variety of problems in analytical chemistry is reviewed. Five examples are selected from the literature to illustrate the use of Kalman filtering techniques for obtaining least-squares estimates fo several parameters of analytical importance. These examples include multicomponent curve resolution and concentration estimation, correction for variable background responses, calibration with drift compensation, and estimation of kinetic parameters for first-order reactions and for heterogeneous charge-transfer reactions. An adaptive Kalman filtering technique is required for the solution of the background correction problem, and the extended Kalman filter algorithm is required for the solution of the nonlinear kinetic problems. For each case, the results that were obtained are summarized, and some advantages of Kalman filtering over traditional least-squares approaches are discussed.

Parameter-Insensitive Technique for Aircraft Sensor Fault Analysis

Abstract: A new method of analyzing faults in the m measurements of an nth-order system is presented. The proposed approach uses the estimation error space of each observer in a bank of observers to detect and isolate sensor faults. The designs are applied to a nonlinear model of an unmanned aircraft that has been described in previous publications. The reconfigurability of the aircraft sensor system is demonstrated, and the results show rapid recovery from a faulty sensor. The use of the observation error eliminates the need for state-space computations, thus producing an effective real-time fault monitor for fly-by-wire aircraft. N an earlier paper,1 a comparison of two techniques of instrument fault diagnosis (IFD) was made. This work is an extension of Patton and Willcox's idea of using analytical redundancy to design a match between m components of the observation error space instead of using state estimates di- rectly as discussed by Clark,3'4 Clark and Setzer,5 Frank and Keller,6 and Watanabe and Himmelblau.7 IFD in dynamic systems has received a significant amount of attention recently.2"11 Most methods described in the liter- ature discuss the analytical redundancy approach in prefer- ence to the use of redundant hardware. Analytical redundancy provides redundant (estimate) information from different measurements of a process, usually with observer or Kalman filter schemes. The commonly discussed state estimate solu- tion to IFD is based on the principle of generating estimates of part or all of the system state vector from subsets of the measurements, which when compared with similar estimates from other observers can be used to monitor the health of an instrument. The problem with the state estimate solution to IFD arises as the observer requires a good linear model of the process, and it must also be assumed that the disturbances on the system are well modeled or else have an insignificant effect on plant parameter variations. These limitations cause the state estimate approach to be inadequate for many real en- gineering applications. Sensitivity to input-induced parameter variations causes uncertain errors between redundant state estimate vectors, and in an IFD scheme these errors could cause false signaling of an instrument fault. It becomes clear that the bandwidth of uncertain signals should be estimated prior to the IFD system design. The use of frequency domain sensitivity information in this way enables a robust approach to the observer design to be made. The conjecture used is that the "innovations" or prediction error signals contain all the information concerning the parameter variations of the pro- cess being identified and controlled. Attention is thus turned toward the use of an innovations-based approach to system fault diagnosis that has wide potential applications. By using a weighting of the measurement estimation error as a parity

Adaptive Weather-Sensitive Short Term Load Forecast

Abstract: This paper introduces an adaptive, weather sensitive, short term load forecast algorithm that has been developed for two South Carolina Power Systems: CEPCI (Central Electric Power Cooperatives, Inc., Central for short) and Combined System. The model is based on a State Space formulation specially tailored for this application. A detailed correlation study is performed to identify the most relevant weather variables. Different models are used for Summer and Winter, since different weather variables are found to be relevant in both seasons. Adaptivity is attained through careful usage of Kalman filtering and Bayesian techniques. An appropriate methodology is developed to identify and correct anomalous load data and to model nonconforming loads. A new technique is introduced for "filling in" weather forecasts. The model has been sucessfully implemented using state-of-the-art data-base and man-machine techniques. Implementation results are reported. This model benefits from the experience gained using a variety of tools and represents important enhancements over existing methods.

Continuous time series models for unequally spaced data applied to modeling atomic clocks

Abstract: State space representations and Kalman filters used to calculate likelihoods have increased the ease and flexibility of fitting time series models to data. When data are unequally spaced with no underlying basic sampling interval, continuous time series models are more natural than discrete time series models. State space representations still provide the flexibility needed to include a large class of models. This paper gives a survey of state space methods for continuous time processes, discusses extensions to multivariate data at unequally spaced time points with missing data within the observation vector, and gives an example of estimating time and model parameters from an ensemble of atomic clocks.

Adaptive Kalman Filtering in fault classification

Abstract: An Adaptive Kalman Filtering scheme for statistically predicting the occurence and type of a fault on a three phase power transmission line. Additionally, estimations of the steady-state postfault phasor quantities, distance protection and fault location information is provided. Current and voltage data for each phase is processed in two separate Adaptive Kalman Filtering models simultaneously. One model assumes that the phase is unfaulted, while the other model assumes the features of a faulted phase. The condition of the phase, faulted or unfaulted, is then decided from the computed a posteriori probabilities. Upon the secure identification of the condition of the phase, faulted or unfaulted, the corresponding Adaptive Kalman Filtering model continues to obtain the best estimates of the current or voltage state variables. Thus, the Adaptive Kalman Filtering model having the correct initial assumptions adapts itself to the actual condition of the phase faulted or unfaulted. Upon convergence of the computed a posteriori probabilities indicative of a faulted phase to highly accurate values, the type of fault is classified and the appropriate current and voltage pairs are selected to compute fault location and to provide distance protection. The voltage models are two state variable Adaptive Kalman Filtering schemes. The model for the current with no fault condition is two state variable, while the model that assumes that the phase is faulted is a three state variable model. Estimation convergence reached exact values within half a cycle and consequently, in the same time fault location was determined.

Identification of Running Load and Beam System

Abstract: Identification problems on dynamic parameters of a running load and beam system were investigated, using the EK-WGI method, which is a weighted global iteration procedure incorporated with the extended Kalman filter. By suitably formulating a set of state vector equations and observation equations for the system on which this method was applied, dynamic parameters of both the running load and the beam were identified with high accuracy, where numerically simulated data were used as observation waves so that accuracy and convergency of estimated parameters might be examined.

Estimation using a multirate filter

Abstract: This note presents both optimal and suboptimal filtering algorithms for estimating state variables based on measurements sampled at two different data rates. The optimal algorithm consists of two parallel Kalman filters; one processes the fast rate measurement and is of reduced-order, and the other processes the residuals from the first filter along with the slow rate measurement. This algorithm is used to design a suboptimal algorithm that has decreased computational requirements with only a small performance penalty.

Uncertainty, Robustness and Sensitivity Reduction in the Design of Single Input Control Systems

Abstract: Feedback control of systems modelled as single input, time invariant, linear and continuous time systems is the subject of this thesis. A growing interest in the design of feedback control systems that can cope with model uncertainties has been the motivation for the study. Some commonly used design approches for various kinds of systems are investigated with respect to robustness properties.The Smith controller, often propsed to controlling open loop stable plants with an input delay, state feedback control based on linear quadratic optimization techniques and output feedback control using a Kalman filter are considered.Also some new design strategies are given. A graphical design philosphy suitable for open loop stable plants with no modelled input delay, feedback stabilization of systems with a known number of unstable poles and modification of the Kalman filter based controller are proposed. The objective in common for these control strategies is to obtain control systems with good robustness properties.

Ocean Data Assimilation and the Moan Filter: Spatial Regularity

Abstract: Ocean circulation models are infinite-dimensional dynamical systems. If the Kalman filter is used to assimilate data into such systems, then their infinite-dimensionality must be recognized. In other words, numerical approximations to the Kalman gains must converge to smooth functions of position, as spatial resolution is improved. It is shown here, by asymptotic analysis and numerical experiment, that the Kalman gains converge if and only if the wavenumber spectrum of the system noise is suitably colored. For a quasi-geostrophic ocean model without eddy viscosity, the wavenumber spectrum of the vorticity system noise must be o(n−1) as n->∞, in order to ensure a continuously differentiable vorticity gain. It the model includes eddy viscosity then a milder requirement holds, but the streamfunction and vorticity gains have unphysical boundary layer structure near measurement points. The analysis and experiments described here employ linear ocean models, and include the cases of data available conti...