Showing papers on "Kalman filter published in 1985"
TL;DR: In this article, a modified gain extended Kalman observer (MGEKO) was developed for a special class of systems and a sufficient condition for the estimation errors of the MGEKF to be exponentially bounded in the mean square was obtained.
Abstract: A new globally convergent nonlinear observer, called the modified gain extended Kalman observer (MGEKO), is developed for a special class of systems. This observer structure forms the basis of a new stochastic filter mechanization called the modified gain extended Kalman filter (MGEKF). A sufficient condition for the estimation errors of the MGEKF to be exponentially bounded in the mean square is obtained. Finally, the MGEKO and the MGEKF are applied to the three-dimensional bearings-only measurement problem where the extended Kalman filter often shows erratic behavior.
287 citations
TL;DR: In this article, a smoothness priors time varying AR coefficient model approach for the modeling of nonstationary in the covariance time series is presented, where the unknown white noise variances are hyperparameters of the AR coefficient distribution.
Abstract: A smoothness priors time varying AR coefficient model approach for the modeling of nonstationary in the covariance time series is shown. Smoothness priors in the form of a difference equation constraint excited by an independent white noise are imposed on each AR coefficient. The unknown white noise variances are hyperparameters of the AR coefficient distribution. The critical computation is of the likelihood of the hyperparameters of the Bayesian model. This computation is facilitated by a state-space representation Kalman filter implementation. The best difference equation order-best AR model order-best hyperparameter model locally in time is selected using the minimum AIC method. Also, an instantaneous spectral density is defined in terms of the instantaneous AR model coefficients and a smoothed estimate of the instantaneous time series variance. An earthquake record is analyzed. The changing spectral analysis of the original data and of simulations from a time varying AR coefficient model of that data are shown.
266 citations
TL;DR: In this article, the likelihood is defined for a state space model with incompletely specified initial conditions by transforming the data to eliminate the dependence on the unspecified conditions, and this approach is extended to obtain estimates of the state vectors and predictors and interpolators for missing observations.
Abstract: The likelihood is defined for a state space model with incompletely specified initial conditions by transforming the data to eliminate the dependence on the unspecified conditions. This approach is extended to obtain estimates of the state vectors and predictors and interpolators for missing observations. It is then shown that this method is equivalent to placing a diffuse prior distribution on the unspecified part of the initial state vector, and modified versions of the Kalman filter and smoothing algorithms are derived to give exact numerical procedures for diffuse initial conditions. The results are extended to continuous time models, including smoothing splines and continuous time autoregressive processes.
243 citations
TL;DR: A new family of algorithms, principally for Abel inversion, that are recursive and hence computationally efficient are presented, based on a linear, space-variant, state-variable model of the Abel transform.
Abstract: The Abel transform and its inverse appear in a wide variety of problems in which it is necessary to reconstruct axisymetric functions from line-integral projections. We present a new family of algorithms, principally for Abel inversion, that are recursive and hence computationally efficient. The methods are based on a linear, space-variant, state-variable model of the Abel transform. The model is the basis for deterministic algorithms, applicable when data are noise free, and least-squares-estimation (Kalman filter) algorithms, which accommodate the noisy data case. Both one-pass (filtering) and two-pass (smoothing) estimators are considered. In computer simulations, the new algorithms compare favorably with previous methods for Abel inversion.
154 citations
TL;DR: A modified Riccati equation is derived that quantifies the dependence of the state error covariance on these parameters and is shown how to use a receiver operating characteristic (ROC) curve in conjunction with the above relationship to determine the detection threshold in the signal processing system that provides measurements to the tracker so as to minimize tracking errors.
Abstract: In the Kalman-Bucy filter and other trackers, the dependence of tracking performance upon the quality of the measurement data is well understood in terms of the measurement noise covariance matrix, which specifies the uncertainty in the values of the measurement inputs. The measurement noise and process noise covariances determine, via the Riccati equation, the state estimation error covariance. When the origin of the measurements is also uncertain, one has the widely studied problem of data association (or data correlation), and tracking performance depends critically on signal processing parameters, primarily the probabilities of detection and false alarm. In this paper we derive a modified Riccati equation that quantifies (approximately) the dependence of the state error covariance on these parameters. We also show how to use a receiver operating characteristic (ROC) curve in conjunction with the above relationship to determine the detection threshold in the signal processing system that provides measurements to the tracker so as to minimize tracking errors. The approach presented in this paper provides a feedback mechanism from the information processing (tracking) subsystem to the signal processing subsystem so as to optimize the overall performance in clutter.
152 citations
129 citations
TL;DR: In this article, the problem of selecting an initial covariance matrix for the Kalman filter to ensure that the closed-loop filter at every subsequent time instant is exponentially asymptotically stable as a time-invariant filter is considered.
123 citations
TL;DR: In this paper, the basics of the Kalman filter technique in power systems terminology are presented and sample designs for voltage and current phasor estimation during system transients are presented.
Abstract: Digital protection algorithms are becoming more complex as the cost of computational equipment continues to decrease. In particular, optimal response digital filters, such as Kalman filters, can be implemented on presently available devices. Optimal filters are not yet extensively applied because they appear complex and engineers have not become familiar with their use. This paper presents the basics of the Kalman filtering technique in power systems terminology and illustrates its use for estimating rotating phasors. Sample designs are presented for voltage and current phasor estimation during system transients. A method for including decaying dc and harmonic frequency components in the filter design is also described and sample results are presented.
123 citations
01 Nov 1985
TL;DR: In this article, the sequence of events which led the researchers at Ames Research Center to the early discovery of the Kalman filter shortly after its introduction into the literature is recounted. And the scientific breakthroughs and reformulations that were necessary to transform Kalman's work into a useful tool for a specific aerospace application are described.
Abstract: The sequence of events which led the researchers at Ames Research Center to the early discovery of the Kalman filter shortly after its introduction into the literature is recounted. The scientific breakthroughs and reformulations that were necessary to transform Kalman's work into a useful tool for a specific aerospace application are described. The resulting extended Kalman filter, as it is now known, is often still referred to simply as the Kalman filter. As the filter's use gained in popularity in the scientific community, the problems of implementation on small spaceborne and airborne computers led to a square-root formulation of the filter to overcome numerical difficulties associated with computer word length. The work that led to this new formulation is also discussed, including the first airborne computer implementation and flight test. Since then the applications of the extended and square-root formulations of the Kalman filter have grown rapidly throughout the aerospace industry.
122 citations
TL;DR: In this article, an explicit relationship between canonical variables and the linear least squares estimate of the state vector is established, and a more direct approach for order reduction is presented, and also a new design for reduced-order Kalman filters is developed.
Abstract: The problem of discrete-time stochastic model reduction (approximation) is considered. Using the canonical correlation analysis approach of Akaike (1975), a new order-reduction algorithm is developed. Furthermore, it is shown that the inverse of the reduced-order realization is asymptotically stable. Next, an explicit relationship between canonical variables and the linear least-squares estimate of the state vector is established. Using this, a more direct approach for order reduction is presented, and also a new design for reduced-order Kalman filters is developed. Finally, the uniqueness and symmetry properties for the new realization—the balanced stochastic realization—along with a simulation result, are presented.
TL;DR: The method of Kalman filtering has been used to obtain on-line state estimates of a batch styrene polymerization reactor as mentioned in this paper, where the temperatures of the plant and the refractive index of the reaction mixture are given as measurement signals to a Kalman filter realized in a process computer.
TL;DR: In this paper, a dynamic, linear model for the analysis of univariate time series is proposed and the associated Kalman filter is also derived, which is restricted to time invariant dynamic linear models with only one observable dependent variable.
Abstract: SUMMARY A dynamic, linear model for the-analysis of univariate time series is proposed. It encompasses many of the common statistical models as special cases such as multiple regression, exponential smoothing and mixed autoregressive-moving average processes. Its distinguishing feature is that it relies on only one primary source of randomness. It therefore not only provides a simpler framework for the study of dynamic models but also eliminates the need for the contentious system variance matrix which has been credited with hampering the use of recursive forecasting methods in practice. The associated Kalman filter is also derived. This paper considers the issue of the recursive estimation of a dynamic linear statistical model (DLM). Its primary antecedent is the work of Duncan and Horn (1972) which in turn is based extensively on the pioneering ideas of Kalman (1960). The scope of the paper is restricted to time invariant dynamic linear models with only one observable dependent variable. Recently, Ameen and Harrison (1983) have outlined difficulties associated with Kalman filter- ing which have inhibited its use in the context of Bayesian forecasting. The "specification of the associated system variance matrices has proven a major obstacle" and they cite reasons such as its non-uniqueness together with the fact that it is not invariant to scale changes of the independent variables. This paper outlines an approach which eliminates the need for the system variance matrix, relying instead on what is best called a "permanent effects" vector whose ele- ments resemble the role of smoothing constants in exponential smoothing. Throughout the paper lower case letters are used to represent scalars and vectors, capital letters are used for matrices, and Greek letters are reserved for parameters. All vectors are of the column variety and their transpose is indicated in the usual way with a prime. The letter E denotes the expectation operator, I represents an identity matrix and carets are used to indicate estimators.
TL;DR: In this paper, the authors present an efficient computational algorithm for estimating the noise covariance matrices of large linear discrete stochasticdynamic systems, which is based on the ideas of Belanger, and is algebraically equivalent to his algorithm.
Abstract: We present an efficient computational algorithm for estimating the noise covariance matrices of large linear discrete stochasticdynamic systems. Such systems arise typically by discretizing distributed-parameter systems, and their size renders computational efficiency a major consideration. Our adaptive filtering algorithm is based on the ideas of Belanger, and is algebraically equivalent to his algorithm. The earlier algorithm, however, has computational complexity proportional to p6, where p is the number of observations of the system state, while the new algorithm has complexity proportional to only p3. Furthermore, our formulation of noise covariance estimation as a secondary filter, analogous to state estimation as a primary filter, suggests several generalizations of the earlier algorithm. The performance of the proposed algorithm is demonstrated for a distributed system arising in numerical weather prediction.
TL;DR: In this paper, a closed form solution to the stationary discrete-time linear filtering problem is obtained explicitly in terms of the system state-space matrices in the limiting singular case where the measurement noise tends to zero.
Abstract: A closed form solution to the stationary discrete-time linear filtering problem is obtained explicitly in terms of the system state-space matrices in the limiting singular case where the measurement noise tends to zero Simple expressions, in closed form, are obtained for the Kalman gain matrix both for uniform and nonuniform rank systems and the explicit eigenstructure of the Kalman filter closed loop matrix is derived The minimum error covariance matrices of the a priori and a posteriori filtered estimates are obtained using this special eigenstructure, and a remarkably different behavior of the solution in the minimum- and nonminimum-phase cases is found
01 Feb 1985
TL;DR: In this article, the problem of estimating parameters of dynamic systems is addressed in order to present the theoretical basis of system identification and parameter estimation in a manner that is complete and rigorous, yet understandable with minimal prerequisites.
Abstract: The problem of estimating parameters of dynamic systems is addressed in order to present the theoretical basis of system identification and parameter estimation in a manner that is complete and rigorous, yet understandable with minimal prerequisites. Maximum likelihood and related estimators are highlighted. The approach used requires familiarity with calculus, linear algebra, and probability, but does not require knowledge of stochastic processes or functional analysis. The treatment emphasizes unification of the various areas in estimation in dynamic systems is treated as a direct outgrowth of the static system theory. Topics covered include basic concepts and definitions; numerical optimization methods; probability; statistical estimators; estimation in static systems; stochastic processes; state estimation in dynamic systems; output error, filter error, and equation error methods of parameter estimation in dynamic systems, and the accuracy of the estimates.
TL;DR: In this paper, an extension of the Kalman filter, an approach already used with linear forecasting models, is applied to the estimation of the growth curve coefficients, allowing the coefficients the flexibility to change over time if the market environment changes.
Abstract: Growth curves such as the logistic and Gompertz are widely used for forecasting market development. The approach proposed is specifically designed for forecasting, rather than fitting available data—the usual approach with non-linear least squares regression. Two innovations form the foundation for this approach. The growth curves are reformulated from a time basis to an observation basis. This ensures that the available observations and the forecasts form a monotonic series; this is not necessarily true for least squares extrapolations of growth curves. An extension of the Kalman filter, an approach already used with linear forecasting models, is applied to the estimation of the growth curve coefficients. This allows the coefficients the flexibility to change over time if the market environment changes. The extended Kalman filter also proves the information for the generation of confidence intervals about the forecasts. Alternative forecasting approaches, least squares and an adaptive Bass model, suggested by Bretschneider and Mahajan, are used to produce comparative forecasts for a number of different data sets. The approach using the extended Kalman filter is shown to be more robust and almost always more accurate than the alternatives.
TL;DR: The results demonstrate one compromise between the selection of the sampling rate and the selection the state wordlength in the design of FWL Kalman filters for continuous-time systems operating under a fast sampling rate.
Abstract: The optimal design of a Kalman filter is considered with respect to its finite wordlength (FWL) characteristics taking into account the roundoff noise due to state quantization. The issues are particularly relevant in the design of FWL Kalman filters for continuous-time systems operating under a fast sampling rate. In this respect, the results demonstrate one compromise between the selection of the sampling rate and the selection of the state wordlength. The optimum filter structure includes state residue feedback compensation which can result in the saving of many bits of additional state wordlength.
TL;DR: In this article, a bound on the perturbation of an asymptotically stable linear system is obtained to maintain stability using Liapunov matrix equation solution, which is shown to be an improved upper bound over the ones recently reported in the literature.
Abstract: The stability robustness aspect of linear systems is analyzed in the time domain. A bound on the perturbation of an asymptotically stable linear system is obtained to maintain stability using Liapunov matrix equation solution. The resulting bound is shown to be an improved upper bound over the ones recently reported in the literature. The proposed methodology is then extended to Linear Quadratic (LQ) and Linear Quadratic Gaussian (LQG) regulators. Examples given include comparison with an aircraft control problem previously analyzed.
TL;DR: This paper examines the problem of adaptively tracking in range and velocity an underwater maneuvering target using passive time delay measurements and finds a partial decoupling of depth estimation from the polar range estimator which considerably reduces the computational level of the adaptive tracking system.
Abstract: This paper examines the problem of adaptively tracking in range and velocity an underwater maneuvering target using passive time delay measurements. The target can make large scale random velocity and depth changes at times which are unknown to the observer. Tracking is accomplished by making use of the basic linearized polar model of target and observer motion previously developed [1]. Now, however, a nonlinear system block has been added to the tracking system [2], [3], which leads to two major benefits. First, the need for extended Kalman filters is eliminated making the passive tracking system more robust than it was previously [3]. The second benefit is a partial decoupling of depth estimation from the polar range estimator, which considerably reduces the computational level of the adaptive tracking system.
26 Apr 1985
TL;DR: The purpose of this paper is to demonstrate the importance of the boundary values in image restoration and to show how to improve the transient response of the steady-state Kalman filters in [2] and [3] with better choices for the boundaryvalues.
Abstract: Recursive spatial domain filtering is often used in image restoration. The techniques range from deterministic inverse filter algorithms [1] to stochastic Kalman filters [2,3]. However, all the techniques have in common the problem of choosing the appropriate boundary values. It is the purpose of this paper to demonstrate the importance of the boundary values in image restoration and to show how we can improve the transient response of the steady-state Kalman filters in [2] and [3] with better choices for the boundary values.
TL;DR: In this article, the use of the Kalman filter to perform the seasonal adjustment and to calculate the variance of the signal extraction error in model-based seasonal adjustment procedures is considered, and the steady-state filter covariance is seen to provide a convenient basis for obtaining the variances not only of the current adjustment but also of subsequent revisions.
Abstract: This article considers the use of the Kalman filter to perform the seasonal adjustment and to calculate the variance of the signal extraction error in model-based seasonal adjustment procedures. The steady-state filter covariance is seen to provide a convenient basis for obtaining the variances not only of the current adjustment but also of subsequent revisions. The method is applied to the unobserved-components model we have recently proposed as a justification of the X-11 method and to a real economic time series.
TL;DR: It is shown that for the channel estimation problem considered here, LS algorithms converge in approximately 2N iterations where N is the order of the filter and the equivalence between an LS algorithm and a fast converging modified SG algorithm which uses a maximum length input data sequence is shown.
Abstract: The convergence properties of adaptive least squares (LS) and stochastic gradient (SG) algorithms are studied in the context of echo cancellation of voiceband data signals. The algorithms considered are the SG transversal, SG lattice, LS transversal (fast Kalman), and LS lattice. It is shown that for the channel estimation problem considered here, LS algorithms converge in approximately 2N iterations where N is the order of the filter. In contrast, both SG algorithms display inferior convergence properties due to their reliance upon statistical averages. Simulations are presented to verify this result, and indicate that the fast Kalman algorithm frequently displays numerical instability which can be circumvented by using the lattice structure. Finally, the equivalence between an LS algorithm and a fast converging modified SG algorithm which uses a maximum length input data sequence is shown.
TL;DR: In this paper, a spatial model of a medium-range passenger vehicle is augmented by a disturbance model (stochastic dual track excitation of the road surface with excitation delay time, if need be with irregularity sensors), a perception filter (weighting of human sensitivity to vibration) and a filter fo...
Abstract: SUMMARY In vehicles with traditional passive suspension, the spring and damping elements between car body and axles have a fixed characteristic. This means that when the suspension is adjusted, a compromise between comfort and safety has to be arrived at. With active suspension, on the other hand, both these criteria can be enhanced at the same time. Moreover, further improvements in driving behaviour can be made which are not possible with passive suspension. In this case, the time delay between front and rear axle excitation is represented by a fade approximation, which means that linear controller design methods in the state space (Riccati controller, Kalman filter) can be used to implement active vehicle suspension. A spatial model of a medium-range passenger vehicle is augmented by a disturbance model (stochastic dual track excitation of the road surface with excitation delay time, if need be with irregularity sensors), a perception filter (weighting of human sensitivity to vibration) and a filter fo...
TL;DR: In this paper, a new probabilistic technique for fault classification using an adaptive Kalman filter using voltage measurements is described. But this technique assumes the features of a faulted phase while the other has features of an unfaulted phase and the condition of the phase, faulted or non-faulted, is then decided from the computed a posteriori probabilities.
Abstract: This paper describes a new probabilistic technique for fault classification to be used in digital distance protection of power systems. The new technique is based on an adaptive Kalman filter using voltage measurements. The voltage data of each phase is processed in two Kalman filter models simultaneously. One Kalman filter assumes the features of a faulted phase while the other has the features of an unfaulted phase. The condition of the phase, faulted or non-faulted, is then decided from the computed a posteriori probabilities.
01 Jan 1985
TL;DR: In this paper, a two-dimensional Kalman filter is described for data assimilation for making weather forecasts, which is regarded as superior to the optimal interpolation method because the filter determines the forecast error covariance matrix exactly instead of using an approximation.
Abstract: A two-dimensional Kalman filter is described for data assimilation for making weather forecasts. The filter is regarded as superior to the optimal interpolation method because the filter determines the forecast error covariance matrix exactly instead of using an approximation. A generalized time step is defined which includes expressions for one time step of the forecast model, the error covariance matrix, the gain matrix, and the evolution of the covariance matrix. Subsequent time steps are achieved by quantifying the forecast variables or employing a linear extrapolation from a current variable set, assuming the forecast dynamics are linear. Calculations for the evolution of the error covariance matrix are banded, i.e., are performed only with the elements significantly different from zero. Experimental results are provided from an application of the filter to a shallow-water simulation covering a 6000 x 6000 km grid.
TL;DR: The application of state estimation in flow injection analysis is described in this paper, where a set of algorithms for prediction, filtering, smoothing, evaluation, control and optimization are described.
Proceedings Article•
19 Jun 1985TL;DR: In this article, new conditions for regulator loop transfer recovery (LTR) of minimum phase, non-square, left-invertible, full- or reduced-order observer-based multivariable feedback control systems are derived.
Abstract: In this paper, new conditions for regulator loop transfer recovery (LTR) of minimum phase, non-square, left-invertible, full- or reduced-order observer-based multivariable feedback control systems are derived. It is proved that these conditions are satisfied asymptotically by either the full- or the reduced-order Kalman filters that assume fictitious process noise at the input in the design model. These results eliminate the need for artificially squaring a non-square system and extend the theory to reduced-order observer-based LOG designs. The results are illustrated by a numerical example.
TL;DR: In this paper, a recursive procedure for the estimation of the lactation curve of a dairy cow, which allows the inclusion of prior information on the curve and which takes account of the correlation between successive observations, is described.
Abstract: A recursive procedure for the estimation of the lactation curve of a dairy cow, which allows the inclusion of prior information on the curve and which takes account of the correlation between successive observations, is described. The method is based on the Kalman filter. It was found to give accurate estimates of the total milk yield at early stages of lactation.
TL;DR: In this article, a real-time monitoring system of tool breakage, which measures the cutting torque from the spindle motor current, is described, using an auto-regressive (AR)-model which is adapted for the measured signal using the Kalman filtering technique.
Abstract: In this paper, a real-time monitoring system of tool breakage, which measures the cutting torque from the spindle motor current, is described. The system uses an auto-regressive (AR)-model which is adapted for the measured signal using the Kalman filtering technique. The tool breakage is detected by monitoring the residual, that is, the deviation of the observed signal from the estimated value obtained by the AR-model. Additional processing of the residual is introduced to discriminate the signature of tool breakage from the effect caused by the marked change in the cutting condition. To reduce the computation time, the fast calculation algorithm is adopted for estimating the coefficient vector of the AR-model. The monitoring experiment has proven the effectiveness of the system in a milling operation.