Showing papers on "Kalman filter published in 1990"

Forecasting, Structural Time Series Models and the Kalman Filter

Abstract: List of figures Acknowledgement Preface Notation and conventions List of abbreviations 1. Introduction 2. Univariate time series models 3. State space models and the Kalman filter 4. Estimation, prediction and smoothing for univariate structural time series models 5. Testing and model selection 6. Extensions of the univariate model 7. Explanatory variables 8. Multivariate models 9. Continuous time Appendices Selected answers to exercises References Author index Subject index.

Forecasting, Structural Time Series Models and the Kalman Filter

Abstract: In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Tactical and strategic missile guidance

Abstract: Numerical Techniques Fundamentals of Tactical Missile Guidance Method of Adjoints and the Homing Loop Noise Analysis Convariance Analysis and the Homing Loop Proportional Navigation and Miss Distance Digital Fading Memory Noise Filters in the Homing Loop Advanced Guidance Laws Kalman Filters and the Homing Loop Other Forms of Tactical Guidance Tactical Zones Strategic Considerations Boosters Lambert Guidance Strategic Intercepts Miscellaneous Topics Ballistic Target Properties Extended Kalman Filtering and Ballistic Coefficient Estimation Ballistic Target Challenges Multiple Targets Weaving Targets Representing Missile Airframe with Transfer Functions Introduction to Flight Control Design Three-Loop Autopilot. Appendices: Tactical and Strategic Missile Guidance Software Converting Programmes to C Converting Programmes to MATLAB Units.

Time Series Analysis : Univariate and Multivariate Methods

Abstract: 1. Overview. 2. Fundamental Concepts. 3. Stationary Time Series Models. 4. Non-Stationary Time Series Models. 5. Forecasting. 6. Model Identification. 7. Parameter Estimation, Diagnostic Checking, and Model Selection. 8. Seasonal Time Series Models. 9. Intervention Analysis and Outlier Detection. 10. Fourier Analysis. 11. Spectral Theory of Stationary Processes. 12. Estimation of the Spectrum. 13. Transfer Function Models. 14. Vector Time Series Models. 15. State Space Models and the Kalman Filter. 16. Aggregation and Systematic Sampling in Time Series. 17. References. 18. Appendix.

Federated square root filter for decentralized parallel processors

Abstract: An efficient, federated Kalman filter is developed for use in distributed multisensor systems. The design accommodates sensor-dedicated local filters, some of which use data from a common reference subsystem. The local filters run in parallel, and provide sensor data compression via prefiltering. The master filter runs at a selectable reduced rate, fusing local filter outputs via efficient square root algorithms. Common local process noise correlations are handled by use of a conservative matrix upper bound. The federated filter yields estimates that are globally optimal or conservatively suboptimal, depending upon the master filter processing rate. This design achieves a major improvement in throughput (speed), is well suited to real-time system implementation, and enhances fault detection, isolation, and recovery capability. >

Recursive 3-D motion estimation from a monocular image sequence

Abstract: Consideration is given to the design and application of a recursive algorithm to a sequence of images of a moving object to estimate both its structure and kinematics. The object is assumed to be rigid, and its motion is assumed to be smooth in the sense that it can be modeled by retaining an arbitrary number of terms in the appropriate Taylor series expansions. Translational motion involves a standard rectilinear model, while rotational motion is described with quaternions. Neglected terms of the Taylor series are modeled as process noise. A state-space model is constructed, incorporating both kinematic and structural states, and recursive techniques are used to estimate the state vector as a function of time. A set of object match points is assumed to be available. The problem is formulated as a parameter estimation and tracking problem which can use an arbitrarily large number of images in a sequence. The recursive estimation is done using an iterated extended Kalman filter (IEKF), initialized with the output of a batch algorithm run on the first few frames. Approximate Cramer-Rao lower bounds on the error covariance of the batch estimate are used as the initial state estimate error covariance of the IEKF. The performance of the recursive estimator is illustrated using both real and synthetic image sequences. >

Incremental fuzzy expert PID control

Abstract: An approach to intelligent PID (proportional integral derivative) control of industrial systems which is based on the application of fuzzy logic is presented. This approach assumes that one has available nominal controller parameter settings through some classical tuning technique (Ziegler-Nichols, Kalman, etc.). By using an appropriate fuzzy matrix (similar to Macvicar-Whelan matrix), it is possible to determine small changes on these values during the system operation, and these lead to improved performance of the transient and steady behavior of the closed-loop system. This is achieved at the expense of some small extra computational effort, which can be very easily undertaken by a microprocessor. Several experimental results illustrate the improvements achieved. >

Geodesy by radio interferometry: The application of Kalman Filtering to the analysis of very long baseline interferometry data

Abstract: The application of Kalman filtering techniques to the analysis of VLBI data is discussed. The VLBI observables are geometrically related to the geodetic and astrometric parameters which can be determined from them. However, contributions to the observables from the clocks at, and the atmospheres above, the VLBI sites must be accounted for if reliable estimates of geodetic and astrometric parameters are to be obtained. Here, an implementation of a Kalman filter to account for stochastic behavior on those parameters which vary during the course of a VLBI experiment is discussed. Both the nature of the stochastic processes which should be used in the model for the VLBI data and the implementation of the Kalman filter estimator are considered. It is concluded that the Kalman filter is appropriate for analyzing VLBI data.

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 three-axis knowledge using magnetic field measurements only. The extended Kalman filter estimates the attitude, attitude rates, and constant disturbance torques. Covariance computation and simulation testing are used to evaluate performance. 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 a part of a low-cost, three-axis attitude stabilization system. I. Introduction T HE objective of this work has been to develop a low-cost system for estimation of three-axis, spacecraft-attitude information based solely on three-axis magnetometer measurements from one satellite orbit. Such a system will be useful for missions that operate in an inclined, low-Earth orbit and require only coarse attitude information. It can also serve as the sensor part of a low-cost, three-axis, closed-loop attitude control system or as a backup attitude estimator. A single three-axis magnetometer measurement can give only two-axes worth of attitude information and no attitude rate or disturbance torque information. Therefore, this attitude determination system must use a sequence of magnetometer measurements. It processes these measurements recursively in a Kalman filter. This paper describes the design, development, analysis, and simulation testing of a Kalman filter arid reports its expected peformance. A follow-on, postlaunch paper is planned to report actual performance.

Joint estimation of PN code delay and multipath using the extended Kalman filter

Abstract: The problem of delay estimation in the presence of multipath is considered. It is shown that the extended Kalman filter (EKF) can be used to obtain joint estimates of time-of-arrival and multipath coefficients for deterministic signals when the channel can be modeled as a tapped-delay line. Simulation results are presented for the EKF joint estimator used for synchronization in a direct-sequence spread-spectrum system operating over a frequency-selective fading channel. A simplified model of the EKF joint estimator is considered for analysis purposes. The evolution in time of the tracking error probability density function and the nonlinear tracking error variance are examined through numerical solution of the Chapman-Kolmogorov equation. The nonlinear tracking error variance is compared to both the linear error variance estimate directly provided by the EKF and the Cramer-Rao lower bound. >

H/sub infinity /-minimum error state estimation of linear stationary processes

Abstract: A state estimator is derived which minimizes the H/sub infinity /-norm of the estimation error power spectrum matrix. Two approaches are presented. The first achieves the optimal estimator in the frequency domain by finding the filter transfer function matrix that leads to an equalizing solution. The second approach establishes a duality between the problem of H/sub infinity /-filtering and the problem of unconstrained input H/sub infinity /-optimal regulation. Using this duality, previously published results for the latter regulation problem are applied which lead to an optimal filter that possess the structure of the corresponding Kalman filter. The two approaches usually lead to different results. They are compared by a simple example which also demonstrates a clear advantage of the H/sub infinity /-estimate over the conventional l/sub 2/-estimate. >

Estimation Procedures for Structural Time Series Models

Abstract: A univariate structural time series model based on the traditional decomposition into trend, seasonal and irregular components is defined. A number of methods of computing maximum likelihood estimators are then considered. These include direct maximization of various time domain likelihood function. The asymptotic properties of the estimators are given and a comparison between the various methods in terms of computational efficiency and accuracy is made. The methods are then extended to models with explanatory variables. Ktv WORDS Structural time series model Forecasting Kalman filter Stochastic trend Unobserved components model EM algorithm

An integrated spatio-temporal approach to automatic visual guidance of autonomous vehicles

Abstract: The Kalman filter approach to recursive state estimation making use of dynamic models for the motion of massive objects has been extended to image sequence processing. This confines image processing to the last frame of the sequence only, and derives a direct spatial interpretation including spatial velocity components by smoothing integrations of prediction errors. Results are presented for road-vehicle guidance at high speeds including obstacle detection and monocular relative spatial state estimation. The corresponding data-processing architecture is discussed; the system has been implemented on a MIMD parallel processing system. Speeds up to 100 km/h have been demonstrated. >

Adaptive estimation of power system frequency deviation and its rate of change for calculating sudden power system overloads

Abstract: A novel Kalman filtering-based technique is presented for estimating power system frequency deviation and its average rate of change during emergency operating conditions that may require load shedding. This method obtains the optimal estimate of the power system frequency deviation from noisy voltage samples and the best estimate of the mean system frequency deviation and its rate of change while accounting for low-frequency synchronizing oscillations which occur during large disturbances. The proposed technique is a two-stage algorithm which uses an adaptive extended Kalman filter in series with an adaptive linear Kalman filter. The extended Kalman filter calculates the frequency deviation, magnitude, and phase angle of the voltage phasor, which may change during the time period covered by the estimation window. Both the measurement noise variance and the system noise covariance associated with the voltage samples are calculated online. The instantaneous frequency deviation is used as the input to a linear Kalman filter, which models the frequency deviation as a random walk plus a random ramp process. The estimated average rate of frequency decay is represented by the slope of the random ramp. Results for both single and multiple measurements are reported. >

Modeling and estimation of discrete-time Gaussian reciprocal processes

Abstract: Discrete-time Gaussian reciprocal processes are characterized in terms of a second-order two-point boundary-value nearest-neighbor model driven by a locally correlated noise whose correlation is specified by the model dynamics. This second-order model is the analog for reciprocal processes of the standard first-order state-space models for Markov processes. The model is used to obtain a solution to the smoothing problem for reciprocal processes. The resulting smoother obeys second-order equations whose structure is similar to that of the Kalman filter for Gauss-Markov processes. It is shown that the smoothing error is itself a reciprocal process. >

Quality control in integrated navigation systems

Abstract: A recursive testing procedure for use in integrated navigation systems is introduced. It can be used in conjunction with the Kalman filter algorithm. Diagnostic tools for inferring the detectability of particular model errors are given. The testing procedure consists of three steps: detection, identification, and adaptation. It can accommodate model errors in both the measurement model and the dynamic model of the integrated navigation system. The tests proposed are optimal in the uniformly-most-powerful-invariant sense. The procedure can accommodate slippages in the mean of the predicted residuals caused by outliers in the data, sensor failures, or switches in the dynamic model. The method is therefore also applicable to the important problem of GPS (Global Positioning System) failure detection and integrity checking. >

An estimation-theoretic framework for image-flow computation

Abstract: A novel framework for computing image flow from time-varying imagery is described. This framework offers the following principal advantages. First, it allows estimation of certain types of discontinuous flow fields without any prior knowledge about the location of discontinuities. The flow fields thus recovered are not blurred at motion boundaries. Second, covariance matrices (or alternatively, confidence measures) are associated with the estimate of image flow at each stage of computation. The estimation-theoretic nature of the framework and its ability to provide covariance matrices make it very useful in the context of applications such as incremental estimation of scene-depth using techniques based on Kalman filtering. The framework is used to recover image flow from two image sequences. To illustrate an application, the image-flow estimates and their covariance matrices thus obtained are also used to recover scene depth. >

Toward a fully decentralized architecture for multi-sensor data fusion

Abstract: A fully decentralized architecture is presented for data fusion problems. This architecture takes the form of a network of sensor nodes, each with its own processing facility, which together do not require any central processor or any central communication facility. In this architecture, computation is performed locally and communication occurs between any two nodes. Such an architecture has many desirable properties, including robustness to sensors failure and flexibility to the addition or loss of one or more sensors. This architecture is appropriate for the class of extended Kalman filter (EKF)-based geometric data fusion problems. The starting point for this architecture is an algorithm which allows the complete decentralization of the multisensor EKF equations among a number of sensing nodes. This algorithm is described, and it is shown how it can be applied to a number of different data-fusion problems. An application of this algorithm to the problem of multicamera, real-time tracking of objects and people moving through a room is described. >

Estimating time-varying parameters by the Kalman filter based algorithm: stability and convergence

Abstract: Convergence and stability properties of the Kalman filter-based parameter estimator are established for linear stochastic time-varying regression models. The main features are: both the variances and sample path averages of the parameter tracking error are shown to be bounded; the regression vector includes both stochastic and deterministic signals, and no assumptions of stationarity or independence are requires; and the unknown parameters are only assumed to have bounded variations in an average sense. >

Separate bias Kalman estimator with bias state noise

Abstract: A modified decoupled Kalman estimator suitable for use when the bias vector varies as a random-walk process is defined and demonstrated in a practical application consisting of the calibration of a strapdown inertial navigation system. The estimation system accuracy associated with the modified estimator is shown to be essentially the same as that of the generalized partitioned Kalman estimator. Considering that the sensor error random rates assumed in the example are on the order of 5 to 10 times greater than normally associated with contemporary strapdown systems, it may be inferred that inertial navigation systems possessing more typical sensor error random growth characteristics should be amenable to a decoupled estimator approach in a broad spectrum of aided-navigation system applications. This should also be true in a variety of other applications in which the bias vector experiences only limited random variation. >

Analysis of discrete-time Kalman filtering under incorrect noise covariances

Abstract: Analysis tools are developed that can be effectively used to study the performance degradation of a filter when incorrect models of the state and measurement noise covariances are used. For a linear time-variant system with stationary noise processes, it is shown that under certain stability conditions on the system model, the one-step prediction error covariance matrix will converge to a steady-state solution even when the filter gain is not optimal. On the other hand, if the state transition matrix has an unreachable mode outside a unit circle, then the modeling errors in the noise covariances may cause the filter to diverge. Bounds on the asymptotic filter performance are computed when the range of errors in the noise covariance matrices are known. Using simple examples, insights into the behavior of a Kalman filter under nonideal conditions are provided. >

Serial correlation in unequally spaced longitudinal data

Abstract: SUMMARY Serial correlation in the within subject error structure in longitudinal data with unequally spaced observations is modelled using continuous time autoregressive moving averages. The models considered have both fixed and random effects in addition to serially correlated within subject errors. Two approaches are presented for calculating the exact likelihood for a model when the errors are Gaussian. The first calculates the covariance matrices for each subject for assumed values of the unknown parameters and estimates the fixed parameters by weighted least squares. The second uses a state space model and the Kalman filter to calculate the exact likelihood. Both methods involve the use of complex arithmetic. Nonlinear optimization is used to obtain maximum likelihood estimates of the parameters.

Radar Principles with Applications to Tracking Systems

Abstract: The Radar Sensor Signal Processing Waveform Selection Pulse Compression Measurement Theory Kalman Filtering Adaptive Kalman Filtering Coordinate Systems A Representative STT Radar Data Correlation Logic A Representative TWS System ESA Allocation Logic A Representative ESA Radar System

Simultaneous pattern recognition and track fitting by the Kalman filtering method

Abstract: A progressive pattern recognition algorithm based on the Kalman filtering method has been tested. The algorithm starts from a small track segment or from a fitted track of a neighbouring detector, then extends the candidate tracks by adding measured points one by one. The fitted parameters and weight matrix of the candidate track are updated when adding a point, and give an increasing precision on prediction of the next point. Thus, pattern recognition and track fitting can be accomplished simultaneously. The method has been implemented and tested for track reconstruction for the vertex detector of the ZEUS experiment at DESY. Detailed procedures of the method and its performance are presented. Its flexibility is described as well.

Autonomous spacecraft navigation system

Abstract: A method and corresponding apparatus for providing spacecraft attitude, position and orbit data without the need for externally supplied data. Using onboard observations of the earth, sun and moon, the system determines spacecraft attitude, instantaneous position, and the orbit based on multiple position estimates. Position and orbit data are derived by multiple deterministic solutions, including some that employ star sensors and gyros, and the multiple solutions are accumulated in a Kalman filter, to provide continuous estimates of position and orbit for use when the sun or moon is not visible. The best estimate of position is selected from the multiple deterministic solutions and the Kalman filter solution, and can be used to control the spacecraft in various ways, without having to rely on ground-based equipment or other spacecraft for the determination of position and orbit.

Tracking targets using adaptive Kalman filtering

Abstract: A simple algorithm for estimating the unknown process noise variance of an otherwise known linear plant, using a Kalman filter is suggested. The process noise variance estimator is essentially dead beat, using the difference between the expected prediction error variance, computed in the Kalman filter, and the measured prediction error variance. The estimate is used to adapt the Kalman filter. The use of the adaptive filter is demonstrated in a simulated example in which a wildly maneuvering target is tracked. >