Showing papers on "Kalman filter published in 1988"

Repetitive control system: a new type servo system for periodic exogenous signals

Abstract: A control scheme called repetitive control is proposed, in which the controlled variables follow periodic reference commands. A high-accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period L into the closed-loop system. Sufficient conditions for the stability of repetitive control systems and modified repetitive control systems are derived by applying the small-gain theorem and the stability theorem for time-lag systems. Synthesis algorithms are presented by both the state-space approach and the factorization approach. In the former approach, the technique of the Kalman filter and perfect regulation is utilized, while coprime factorization over the matrix ring of proper stable rational functions and the solution of the Hankel norm approximation are used in the latter one. >

Decentralized structures for parallel Kalman filtering

Abstract: Various multisensor network scenarios with signal processing tasks that are amenable to multiprocessor implementation are described The natural origins of such multitasking are emphasized, and novel parallel structures for state estimation using the Kalman filter are proposed that extend existing results in several directions In particular, hierarchical network structures are developed that have the property that the optimal global estimate based on all the available information can be reconstructed from estimates computed by local processor nodes solely on the basis of their own local information and transmitted to a central processor The algorithms potentially yield an approximately linear speedup rate, are reasonably failure-resistant, and are optimized with respect to communication bandwidth and memory requirements at the various processors >

Comparison of two-sensor tracking methods based on state vector fusion and measurement fusion

Abstract: There are two approaches to the two-sensor track-fusion problem. Y Bar-Shalom and L. Campo (ibid., vol.AES-22, 803-5, Nov. 1986) presented the state vector fusion method, which combines state vectors from the two sensors to form a new estimate while taking into account the correlated process noise. The measurement fusion method or data compression of D. Willner et al. (1976) combines the measurements from the two sensors first and then uses this fused measurement to estimate the state vector. The two methods are compared and an example shows the amount of improvement in the uncertainty of the resulting estimate of the state vector with the measurement fusion method. >

Three-axis attitude determination via Kalman filtering of magnetometer data

Abstract: A three-axis Magnetometer/Kalman Filter attitude determination system for a spacecraft in low-altitude Earth orbit is developed, analyzed, and simulation tested. The motivation for developing this system is to achieve light weight and low cost for an attitude determination system. The extended Kalman filter estimates the attitude, attitude rates, and constant disturbance torques. Accuracy near that of the International Geomagnetic Reference Field model is achieved. Covariance computation and simulation testing demonstrate the filter's accuracy. One test case, a gravity-gradient stabilized spacecraft with a pitch momentum wheel and a magnetically-anchored damper, is a real satellite on which this attitude determination system will be used. The application to a nadir pointing satellite and the estimation of disturbance torques represent the significant extensions contributed by this paper. Beyond its usefulness purely for attitude determination, this system could be used as part of a low-cost three-axis attitude stabilization system.

Federated filter for fault-tolerant integrated navigation systems

Abstract: An efficient, federated Kalman filtering method is presented, based on rigorous information-sharing principles. The method applies to decentralized navigation systems in which one or more sensor-dedicated local filters feed a larger master filter. The local filters operate in parallel, processing unique data from their local sensors, and common data from a shared inertial navigation system. The master filter combines local filter outputs at a selectable reduced rate, and yields estimates that are globally optimal or subset-optimal. The method provides major improvements in throughput (speed) and fault tolerance, and is well suited to real-time implementation. Practical federated filter examples are presented, and discussed in terms of structure, accuracy, fault tolerance, throughput, data compression, and other real-time issues. >

Fast Learning in Multi-Resolution Hierarchies

Abstract: A class of fast, supervised learning algorithms is presented. They use local representations, hashing, and multiple scales of resolution to approximate functions which are piece-wise continuous. Inspired by Albus's CMAC model, the algorithms learn orders of magnitude more rapidly than typical implementations of back propagation, while often achieving comparable qualities of generalization. Furthermore, unlike most traditional function approximation methods, the algorithms are well suited for use in real time adaptive signal processing. Unlike simpler adaptive systems, such as linear predictive coding, the adaptive linear combiner, and the Kalman filter, the new algorithms are capable of efficiently capturing the structure of complicated non-linear systems. As an illustration, the algorithm is applied to the prediction of a chaotic timeseries.

Optimal Estimator Model for Human Spatial Orientation

Abstract: A model is presented to predict human dynamic spatial orientation in response to multisensory stimuli. Motion stimuli are first processed by dynamic models of the visual, vestibular, tactile, and proprioceptive sensors. Central nervous system function is modeled as a steady state Kalman filter that optimally blends information from the various sensors to form an estimate of spatial orientation. Where necessary, nonlinear elements preprocess inputs to the linear central estimator in order to reflect more accurately some nonlinear human response characteristics. Computer implementation of the model has shown agreement with several important qualitative characteristics of human spatial orientation.

A Kalman filter for integrating dead reckoning, map matching and GPS positioning

Abstract: A Kalman filter has been developed to integrate the three positioning systems (differential odometer dead reckoning, map matching, and Global Positioning System or GPS) used in the Automatic Vehicle Location System (AVL 2000) being designed and developed in the Department of Surveying Engineering at the University of Calgary The system is being targeted for on road applications and incorporates a digital map The filter has been designed to take into account uncertainties via covariance matrices In wide-open spaces GPS positioning will dominate, while in zones where the GPS signal is obstructed, dead reckoning will be used as interpolation between GPS position fixes Simulation studies and covariance analyses have been performed on a test route located in a sector of the city of Calgary >

The likelihood for a state space model

Abstract: SUMMARY This paper derives an expression for the likelihood for a state space model. The expression can be evaluated with the Kalman filter initialized at a starting state estimate of zero and associated estimation error covariance matrix of zero. Adjustment for initial conditions can be made after filtering. Accordingly, initial conditions can be modelled without filtering implications. In particular initial conditions can be modelled as 'diffuse'. The connection between the 'diffuse' and concentrated likelihood is also displayed.

Minimum model error estimation for poorly modeled dynamic systems

Abstract: A novel strategy (which we call "minimum model error'* estimation) for postexperiment optimal state estimation of discretely measured dynamic systems is developed and illustrated for a simple example. The method is especially appropriate for postexperiment estimation of dynamic systems whose presumed state governing equations are known to contain, or are suspected of containing, errors. The hew method accounts for errors in the system dynamic model equations in a rigorous manner. Specifically, the dynamic model error terms in the proposed method do not require the usual Kalman filter-smoother process noise assumptions of zero-mean, symmetrically distributed random disturbances, nor do they require representation by assumed parameterized time series (such as Fourier series); Instead, the dynamic model error terms require no prior assumptions other than piecewise continuity. Estimates of the state histories, as well as the dynamic model errors, are Obtained as part of the solution of a two-point boundary value problem. The state estimates are continuous and optimal in a global sense, yet the algorithm processes the measurements sequentially. The example demonstrates the method and shows it to be quite accurate for state estimation of a poorly modeled dynamic system.

Covariances for smoothed estimates in state space models

Abstract: SUMMARY Ansley & Kohn (1982) presented a novel proof of the fixed interval smoothing algorithm for state space models. In this note the ideas of their proof are used to provide a new formula for the covariance between smoothed estimates at any two points in time. This equation is substantially simpler than existing special cases.

Suboptimal filter design with pseudomeasurements for target tracking

Abstract: A suboptimal Kalman filter design method is presented for the problem of tracking a maneuvering target. The design method is essentially based on linear target dynamics and linear-like structured measurements called pseudomeasurements. The pseudomeasurements are obtained by manipulating the original nonlinear measurements algebraically. The resulting filter has computational advantages over other filters with similar performance. Also, a variant of the Berg model is proposed as a target acceleration model under the assumption of a coordinated turn maneuver. The proposed model is consistent with the underlying assumption. Monte Carlo computer simulation results are included to demonstrate the effectiveness of the proposed suboptimal filter associated with the target acceleration model. >

Linear systems and optimal control

Abstract: A knowledge of linear systems provides a firm foundation for the study of optimal control theory and many areas of system theory and signal processing. State-space techniques developed since the early sixties have been proved to be very effective. The main objective of this book is to present a brief and somewhat complete investigation on the theory of linear systems, with emphasis on these techniques, in both continuous-time and discrete-time settings, and to demonstrate an application to the study of elementary (linear and nonlinear) optimal control theory. An essential feature of the state-space approach is that both time-varying and time-invariant systems are treated systematically. When time-varying systems are considered, another important subject that depends very much on the state-space formulation is perhaps real-time filtering, prediction, and smoothing via the Kalman filter. This subject is treated in our monograph entitled "Kalman Filtering with Real-Time Applications" published in this Springer Series in Information Sciences (Volume 17). For time-invariant systems, the recent frequency domain approaches using the techniques of Adamjan, Arov, and Krein (also known as AAK), balanced realization, and oo H theory via Nevanlinna-Pick interpolation seem very promising, and this will be studied in our forthcoming monograph entitled "Mathematical Ap proach to Signal Processing and System Theory." The present elementary treatise on linear system theory should provide enough engineering and mathe of these two subjects."

Measuring Image Flow By Tracking Edge-lines

Abstract: This paper describes a technique for measuring the movement of edge-lines in a sequence of images by maintalning an image plane "flow model". Edge-lines are expressed as a set of parameter vectors representing the center-point, orientation and length of a segment. Each parameter vector is composed of an estimate, a temporal derivative, and their covariance matrix. Line segment parameters in the flow model are updated using a Kalman filter. The eorrespondance of observed edge-lines segments to segments predicted from the flow model is determined by a linear complexity algorithm using distance normalized by covariance. The existence of segments in the flow model is controlled using a confidence factor. This technique is in everyday use as part of a larger system for building 3-D scene descriptions using a camera mounted on a robot arm. A near video-rate hardware implementation is currently under development

Connection between continuous and discrete Riccati equations with applications to kalman filtering

Abstract: The aim of the paper is to explore the relationship between the continuous-time Riccati equation and the corresponding discrete-time equation with fast sampling. The interconnection is established by formulating the discrete case using delta operators. The application of these results to the Kalman filtering problem highlights the importance of analogue prefiltering in the sampling process. A secondary benefit arising from the use of the delta operator is that improved numerical behaviour is obtained for solution algorithms, compared with that obtainable with the usual shift operator.

Kalman Filter Analysis in Dendroclimatology

Abstract: SUMMARY The use of the Kalman filter in the analysis of tree-ring data is summarized. By use of this filter technique, the traditional multiple regression models can be modified to cover linear models with time-dependent coefficients. In that way changes in tree response to weather variations could be detected, possibly indicating anthropogenic influences. The filtering and smoothing operations of the filter are illustrated using simulated tree-ring series. A method for the selection of predictor variables is proposed, which takes into account the special features of time-dependent regression models. Furthermore, the consequences of highly correlated predictors are discussed. An application is given to a ring-width series of a European silver fir from Bad Herrenalb (F.R.G.). The method appears suitable for dealing with both gradual changes and sudden shocks in tree response.

Estimation for non-linear time series models using estimating equations

Abstract: Godambe's (1985) theorem on optimal estimating equations for stochastic processes is applied to non-linear time series estimation problems. Examples are considered from the usual classes of non-linear time series models. A recursive estimation procedure based on optimal estimating equations is provided. It is also shown that pre-filtered estimates can be used to obtain the optimal estimate from a non-linear state-space model.

Application of adaptive Kalman filtering in fault classification, distance protection, and fault location using microprocessors

Abstract: An adaptive Kalman filtering scheme is presented for estimation of the 60 Hz phasor quantities, fault type identification, distance protection, and fault location. The current and voltage data of each phase are simultaneously processed in two Kalman filter models. One model assumes that the phase is unfaulted, while the other model assumes the features of a faulted phase. The condition of the phase is then decided from the computed a posteriori probabilities. Upon the secure identification of the condition of the phase, the corresponding Kalman filtering model continues to obtain the best estimates of the current or voltage state variables. Upon convergence to highly accurate values, the appropriate current and voltage pairs are selected to decide the zone of the fault and the fault location. The scheme was tested on digitally simulated data. The fault classification was doubly secure using both voltage and current data. The convergence of estimates reached exact values within half a cycle. >

A new method to stabilize fast RLS algorithms based on a first-order of the propagation of numerical errors

Abstract: An effective method to stabilize fast RLS algorithms is proposed. It is based on the analysis of the propagation of the numerical errors according to a first-order linear model. Two variables are shown to be responsible for the numerical instability. The proposed method modifies the numerical properties of these variables, while preserving the theoretical form of the algorithms. This method is applied to the FTF (fast transversal filter) and fast Kalman algorithms. Experimental results in floating- and fixed-point arithmetic show the efficiency of the method. >

A Kalman filter theory of the cerebellum

Abstract: A variety of evidence suggests that the cerebellum is directly involved in certain sensory tasks. The specific hypothesis developed in this article is that the cerebellum is a neural analog of a Kalman-Bucy filter, whose function is to estimate state variables of the motor system and of external dynamical systems.

Kalman filter analysis for real time applications of clocks and oscillators

Abstract: An optimum algorithm has been developed for estimating the time, frequency, and frequency aging of clocks and oscillators. The algorithm is sufficiently general to be used with all types of quartz oscillators and atomic clocks, yet the approach is appropriate for use with an embedded controller in automated systems intended for field applications. The algorithm is based on Kalman filtering techniques and can process either time or frequency calibration data from various sources of different qualities. Data are accepted whenever available and are not required at fixed multiples of fixed sampling time. This algorithm can be used to analyze data already available in many systems in order to improve system timing with no additional hardware. Alternatively, it may be possible to maintain system timing performance while reducing the cost of the clocks. These goals are an important part of the modular intelligent frequency, time and time interval subsystem currently under development. >

Adaptive Filters and Equalisers

Abstract: 1 Introduction.- 1.1 Adaptive Signal Processing.- 1.2 The Adaptive Filter.- 1.3 Modes of Operation.- 1.4 Application of Adaptive Filters.- 1.5 Summary.- 2 Adaptive Fir Filter Algorithms.- 2.1 Introduction.- 2.2 Optimum Linear Estimation.- 2.2.1 The Optimum FIR Filter.- 2.2.2 FIR System Identification.- 2.3 Sampled Matrix Inversion.- 2.4 Least Squares Estimation.- 2.4.1 Recursive Least Squares.- 2.4.2 Data Windows.- 2.4.3 Fast Algorithms.- 2.4.4 Properties of the Least Squares Estimate.- 2.5 Stochastic Gradient Methods.- 2.5.1 The Least Mean Squares Algorithm.- 2.5.2 The Block Least Mean Squares Algorithm.- 2.6 Self-Orthogonalising Algorithms.- 2.6.1 The Sliding DFT Adaptive Filter.- 2.7 Summary and Complexity Comparison.- 3 Performance Comparisons.- 3.1 Introduction.- 3.2 System Identification.- 3.3 Channel Equalisation.- 3.4 Summary and Conclusions.- 4 A Self-Orthogonalising Block Adaptive Filter.- 4.1 Introduction.- 4.2 Theoretical Development.- 4.2.1 Comparison of Theory with Simulation.- 4.3 A Practical Algorithm.- 4.4 Computational Complexity.- 4.5 Simulation Results.- 4.6 Conclusions.- 5 The Infinite Impulse Response Linear Equaliser.- 5.1 Introduction.- 5.2 The Linear Equaliser.- 5.2.1 Structure of an IIR Equaliser.- 5.3 FIR and IIR Equaliser Performance.- 5.4 System Identification.- 5.4.1 Adaptive IIR Solutions.- 5.5 Conclusions.- 6 An Adaptive IIR Equaliser.- 6.1 Introduction.- 6.2 The Kalman Filter.- 6.3 The Kalman Filter as an IIR Equaliser.- 6.4 An Adaptive Kalman Equaliser.- 6.4.1 System Identification.- 6.4.2 Model Uncertainty.- 6.4.3 Verification of Compensation Technique.- 6.4.4 Comparison with an RLS FIR Equaliser.- 6.4.5 Computational Complexity.- 6.5 RLS System Identification.- 6.6 Conclusions.- 7 Conclusions.- 7.1 Summary.- 7.2 Limitations and Further Work.- Appendix A The Fast Kalman Algorithm.- Appendix B The RLS Lattice Algorithm.- Appendix C Circular and Linear Convolution.- References.

An Assessment of Air-to-Air Missile Guidance and Control Technology

Abstract: This paper provides an assessment of current air-to-air missile guidance and control technology. Areas explored include target state estimators, advanced guidance laws, and bank-to-turn autopilots. The assumptions, benefits, and limitations of recent applications of nonlinear filtering, adaptive filtering, modern control, adaptive control, dual control, differential game theory, and modern control design techniques to the air-to-air missile problem are discussed.

On System Identification in one and two Dimensions with Signal Processing Applications

Abstract: This thesis consists of four parts, with system identification as the common theme. The first part studies the asymptotic properties of two-dimensional identification methods. In the second part an approach to identification of time varying systems is presented. Part three applies system identification to the problem of transmission line protection. Finally part four deals with input estimation in speech coding.Part I is devoted to system identification in two dimensions. First we study the asymptotic properties of the estimates as the number of data tends to infinity. The main objective is to investigate what happens if the model order also tends to infinity. The focus is on frequency expressions of the extimation variance. The analysis covers both the least squares method for causal models, and the maximum likelihood method for noncausal models.In Part II we study one approach to identification of time varying sytems. The parameter variations are modelled as process noise in a state space model, and identified using adaptive Kalman filtering. A method for adaptive Kalman filtering is derived and analysed. The simulations indicate that this new approach is superior to previous methods based on adjusting the forgetting factor. The improvement is however gained at the price of a significant increase in computational complexity.Part III describes the use of recursive identification in protective relaying. The Fourier coefficients of voltage and current are estimated using recursive least squares identification. The estimates are then used to detect short circuits. The method is evaluated using data generated by the standard program EMTP.In Part IV a method for inverse glottal filtering is presented. The basis of the method is to use a parameterized model of the input signal, i.e. the glottal pulses. The algorithm simultaneously estimates the parameters of the input signal and the parameters of the system transfer function, the vocal tract model. The presentation is restricted to transfer functions of all-pole type.

Frequency Domain Aspects of Modeling and Control in Adaptive Systems

Abstract: In this thesis various aspects of modeling and control in adaptive systems are presented from a frequency domain viewpoint.The thesis consists of three parts, where the first part contains a general introduction and background information concerning the problems that will be treated. In the second part some recursive identification algorithms are studied with respect to their ability to track time-varying systems and their disturbance sensitivity. Simple and illustrative frequency domain expressions that describe these properties are derived using asymptotic methods. The algorithms that are treated are the constant gain gradient (LMS) algorithm, the recursive least squares algorithm with constant forgetting factor and the Kalman filter respectively. The behavior of these methods when applied to FIR and ARX systems are studied. In the third part of the thesis adaptive control based on low order models is studied. The adaptive control algorithm that is investigated is the recursive least squares algorithm combined with pole placement regulator design. Starting from frequency domain expressions, that describe how a low order model obtained by system identification approximates a higher order system, the consequences for adaptive control are investigated. It is shown how a proper use of filtering in the identification part of the adaptive regulator can improve the robustness properties of the adaptive regulator with respect to unmodelled dynamics.

Estimability and regulability of linear systems

Abstract: A linear state-space system is said to be estimable if in estimating its state from its output the posterior error covariance matrix is strictly smaller than the prior covariance matrix. It is said to be regulatable if the quadratic cost of the state feedback control is strictly smaller than the cost when no feedback is used. Estimability and regulability are shown to be dual properties, equivalent to the nonreducibility of the Kalman filter and of the optimal linear quadratic regulator, respectively. >

Satellite attitude determination and control system with agile beam sensing

Abstract: Agile (electronically steerable) beam sensing with associated on-board processing, previously used exclusively for positioning of antennas for beam formation and tracking in communications systems, is now also used for satellite active attitude determination and control. A spinning satellite (100) is nadir oriented and precessed at orbit rate using magnetic torquing determined through use of an on-board stored magnetic field model (520) and attitude and orbit estimates (212). A Kalman filter (211) predicts parameters (202, 203) associated with a received signal (204) impinging on the satellite's wide angle beam antenna (201). The antenna system measures the error between the parameter predictions and observed values and sends appropriate error signals (207) to the Kalman filter for updating its estimation procedures. The Kalman filter additionally outputs the spacecraft attitude error signals (215) to an attitude control law (213), which determines commands to attitude-altering magnetic torque elements (220) to close the control loop via the spacecraft dynamics (230).