Showing papers on "Invariant extended Kalman filter published in 1984"
TL;DR: In this article, a weighted global iteration procedure with an objective function is proposed for stable estimation, being incorporated into the extended Kalman filter algorithm, which is applied to system identification problems of seismic structural systems.
Abstract: The extended Kalman filter is applied to system identification problems of seismic structural systems. In order to obtain the stable and convergent solutions, a weighted global iteration procedure with an objective function is proposed for stable estimation, being incorporated into the extended Kalman filter algorithm. For the effectiveness of this present proposal, the identification problems are investigated for multiple degree-of-freedom linear systems, bilinear hysteretic systems, and equivalent linearization of bilinear hysteretic systems. As numerically shown examples, the weighted global iteration procedure may be useful to identification problems.
521 citations
TL;DR: In this paper, two techniques for optimal tracking of power system voltage phasors and frequency deviation were presented, one based on a two-state linear Kalman filter model and the other based on three-state extended Kalman filters.
Abstract: This paper presents two techniques for optimal tracking of power system voltage phasors and frequency deviation. The first technique is based on a two-state linear Kalman filter model. The second technique is based on a three-state extended Kalman filter model. In the latter the frequency deviation is considered a third state variable and is recursively computed on-line. It is shown that the Kalman filter models are well suited for noisy measurements. The effect of sampling rate, computer burden and overall accuracy are also investigated. Finally comparison with other techniques is presented.
203 citations
TL;DR: In this article, the problem of automatic steering control of a large tanker in a seaway is formulated within the framework of linear quadratic Gaussian (LQG) control theory.
Abstract: The problem of automatic steering control of a large tanker in a seaway is formulated within the framework of linear quadratic Gaussian (LQG) control theory. Wave disturbances are characterized by shaping filters, and Kalman filters are designed using these disturbance noise models. LQG controllers are designed to minimize a performance criterion commonly thought to be representative of propulsion losses due to steering. Performance of the controllers is determined by simulation results, which apply for deep water and are based on data from scale model tests.
32 citations
TL;DR: In this article, a linear stationary optimal filtering problem is considered in which the plant dynamics and noise covariances are incompletely known, and unknown plant parameters in the plant model, such as gains and time constants, are treated as random variables with specified means and variances.
Abstract: A linear stationary optimal filtering problem is considered in which the plant dynamics and noise covariances are incompletely known. Unknown plant parameters in the plant model, such as gains and time constants, are treated as random variables with specified means and variances. Generalized Wiener and Kalman-Bucy filters are derived on the basis of transfer-function matrix or state-space representations of the plant, respectively. An application of the generalized filter to the linear quadratic optimal control of plants with unknown disturbances is also described and a certainty equivalence principle is shown to apply.
27 citations
TL;DR: This paper describes an algorithm to compute a mapping that, when applied to the original system, yields a complete Kalman decomposition, and shows that, of all transformations that yield a Kalman decompposition, the one constructed here has the lowest condition number.
Abstract: In this paper we describe a method for computing the complete Kalman decomposition of a linear dynamical system, and we show that this method is optimal in a certain sense. Specifically, we describe an algorithm to compute a mapping that, when applied to the original system, yields a complete Kalman decomposition. We show that, of all transformations that yield a Kalman decomposition, the one we construct here has the lowest condition number.
26 citations
23 citations
TL;DR: In this article, a fourth-order extended Kalman filter was developed to estimate target maneuvers, and a guidance law using these estimates was implemented, which is based on the guidance law.
Abstract: A fourth-order extended Kalman filter is developed to estimate target maneuvers, and a guidance law using these estimates is implemented.
18 citations
DOI•
01 Jan 1984TL;DR: In this paper, a singularly perturbed, linear, discrete, optimal, stochastic control problem is considered and a singular perturbation method is developed to obtain approximate solutions in terms of an outer series and a correction series.
Abstract: A singularly perturbed, linear, discrete, optimal, stochastic control problem is considered. The resulting equations for the Kalman filter for the dynamic and steady-state conditions are formulated. A singular-perturbation method is developed to obtain approximate solutions in terms of an outer series and a correction series. Examples are given to illustrate the proposed method.
14 citations
TL;DR: This structure derives from the conjunction of an extended Kalman filter and of a hierarchical scheme, according to which the overall dynamic state estimation problem is decomposed into smaller, easier to handle subproblems, which leads to important computational savings.
10 citations
TL;DR: A recursive nonlinear filter and tracking methodology is developed for a class of partially observable processes with an approximating model which is linear in the unobservable states and initially has the unob observables conditionally Gaussian with respect to the observations.
Abstract: A recursive nonlinear filter and tracking methodology is developed for a class of partially observable processes with an approximating model which is linear in the unobservable states and initially has the unobservables conditionally Gaussian with respect to the observations. The usual model smoothness is not required, and applications to simulated tracking problems show the filter to be considerably more accurate than the modified second-order filter which in a general sense includes the extended Kalman filter.
25 Jun 1984
01 Dec 1984
TL;DR: In this paper, a maximum likelihood estimation method is developed for applications to the target tracking problem based on bearing observations from a single observer, which involves propagation of states in rectangular co-ordinates in which the linear dynamics permit a closed form solution.
Abstract: A maximum likelihood estimation method is developed for applications to the target tracking problem based on bearing observations from a single observer. The method involves propagation of states in rectangular co-ordinates in which the linear dynamics permit a closed form solution. At the measurement times, the states are converted to a special polar coordinate system in which the measurement is modelled as linear in the transformed state, and updated using the Kalman methodology. The coordinate transformation is chosen so that the direct transformation of the maximum likelihood estimate is approximately preserved. The numerical experiments for a target-intercept problem are presented which show that the performance of this coordinate transformation based filter is superior to that of the cartesian system based extended Kalman filter. Approximate analytical results are also presented to corroborate the numerical results.
TL;DR: Consideration is given here to a simpler Kalman filter state estimation problem, which gives a description of a frequency-multiplexed acoustooptic processor capable of performing all the individual operations required in Kalman filtering.
Abstract: Reference is made to a study by Casasent et al. (1983), which gave a description of a frequency-multiplexed acoustooptic processor and showed how it was capable of performing all the individual operations required in Kalman filtering. The data flow and organization of all required operations however, were not detailed in that study. Consideration is given here to a simpler Kalman filter state estimation problem. Equally spaced time-sampled intervals (k times T sub s, with k the iterative time index) are assumed. It is further assumed that the system noise vector w and the measurement noise vector v are uncorrelated and Gaussian distributed and that the noise statistics (Q and R) and the system model (Phi, Gamma, H) are known. The error covariance matrix P and the extrapolated error covariance matrix M can thus be precomputed and the Kalman gain matrix K sub k can be precomputed and stored for each input time sample.
06 Jun 1984
TL;DR: In this paper, the modified gain extended Kalman filter (MGEKF) is used as an observer and shown to be globally exponentially convergent in the stochastic environment.
Abstract: For a special class of systems, a general formulation and stochastic stability analysis of a new nonlinear filter, called the modified gain extended Kalman filter (MGEKF), is presented. Used as an observer, it is globally exponentially convergent. In the stochastic environment a nominal nonrealizable filter algorithm is developed for which global stochastic stability is proven. With respect to this nominal filter algorithm, conditions are obtained such that the effective deviations of the realizable filter are not destabilizing. In an appropriate coordinate frame, the parameter identification problem of a linear system is shown to be a member of this special class. For the example problems, the MGEKF shows superior convergence characteristics without evidence of instability.
TL;DR: The derivation of a complex-domain recursive linear prediction algorithm with a reduced number of computations is presented, seen to be very similar to real domain fast Kalman, when complex conjugation is considered in formulating the error measure.
Abstract: A derivation of a complex-domain recursive linear prediction algorithm with a reduced number of computations is presented. It is denoted the complex fast Kalman algorithm by virtue of its similarity to the real domain algorithm of that name. It is seen to be very similar to real domain fast Kalman, when complex conjugation is considered in formulating the error measure.
01 Dec 1984
TL;DR: The optimal design of a Kalman filter is considered in respect of its finite wordlength (FWL) characteristics taking into account the round-off noise due to state quantization.
Abstract: The optimal design of a Kalman filter is considered in respect of its finite wordlength (FWL) characteristics taking into account the round-off 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. The optimum filter structure includes state residue feedback compensation which can result in the saving of many bits of additional state wordlength.
01 Nov 1984
TL;DR: A two-stage online parameter and state estimator for multivariable stochastic systems and a special canonical form of the state-space equations that simplifies the parameter estimation problem is used.
Abstract: The problem of combined parameter and state estimation was originally posed as a nonlinear filtering problem using the extended Kalman filter. This led to problems of divergence and excessive computation, especially for multivariable systems. A two-stage online parameter and state estimator for multivariable stochastic systems is proposed that avoids these difficulties. A special canonical form of the state-space equations that simplifies the parameter estimation problem is used. In the first stage the parameters of the system matrices and of the steady-state Kalman filter matrix are estimated by a normalized stochastic approximation algorithm assuming known states. These parameter estimates are then utilized for state estimation in the second stage using the linear Kalman filter. The two stages are then coupled in a bootstrap manner.
01 Mar 1984
TL;DR: The application of the extended Kalman filter to the estimation of frequencies of sinusoids in the additive colored noise is proposed and Comparisons with both the generalized least-squares and the maximum likelihood method show its advantages.
Abstract: In this paper the application of the extended Kalman filter to the estimation of frequencies of sinusoids in the additive colored noise is proposed. Starting from convenient state-space models of the signal two versions of the algorithm are defined. Comparisons with both the generalized least-squares and the maximum likelihood method show its advantages provided adequate initial conditions are ensu - red.
01 Mar 1984
TL;DR: This paper is concerned with Abel inversion from noisy experimental data, and presents a recursive approach based on a state space model of the forward transform and a Kalman filter.
Abstract: The Abel transform and its inverse appear in a wide variety of problems, where it is necessary to reconstruct an axisymmetric function from its line-integral projections. This paper is concerned with Abel inversion from noisy experimental data, and presents a recursive approach based on a state space model of the forward transform and a Kalman filter.
01 Dec 1984
TL;DR: In this article, the estimation of the position and velocity of a sonar target moving in a two-dimensional frame is studied, where the estimator is a Kalman filter which processes noisy bearings of the target gathered by the tracker.
Abstract: : The estimation of the position and velocity of a sonar target moving in a two-dimensional frame is studied in this paper. The estimator is a Kalman filter which processes noisy bearings of the target gathered by the tracker. The case of maneuvering targets is examined a solution using a variable value of the system's noise covariance matrix is studied. Simulation programs in FORTRAN are provided for a simple example and for maneuvering and nonmaneuvering bearings-only targets. Originator-supplied keywords: Kalman filter, Passive tracking, Bearings-only tracking, and Extended kalman filter.
01 Dec 1984
TL;DR: In this paper, the minimum parameter autoregressive moving-average (ARMA) model of a system is identified, when used as a one-step ahead predictor, produces a minimum error variance estimate.
Abstract: In this paper we present a new method to identify the minimum parameter autoregressive moving-average (ARMA) model of a system. The model identified, when used as a one-step ahead predictor, produces a minimum error variance estimate. The parameters are found from output statistics by solving a set of linear equations. The ARMA model found is equivalent to the Kalman filter innovations model but we avoid solving a Riccati-type equation. The equivalence is demonstrated through a numerical example.
01 Jan 1984
TL;DR: In this article, the formulation of appropriate state-space models for Kalman filtering applications is studied, and it is shown that many common processes encountered in applied work (such as band-limited white noise) simply do not lend themselves very well to Kalman filter modeling.
Abstract: The formulation of appropriate state-space models for Kalman filtering applications is studied. The so-called model is completely specified by four matrix parameters and the initial conditions of the recursive equations. Once these are determined, the die is cast, and the way in which the measurements are weighted is determined foreverafter. Thus, finding a model that fits the physical situation at hand is all important. Also, it is often the most difficult aspect of designing a Kalman filter. Formulation of discrete state models from the spectral density and ARMA random process descriptions is discussed. Finally, it is pointed out that many common processes encountered in applied work (such as band-limited white noise) simply do not lend themselves very well to Kalman filter modeling.
TL;DR: In this article, a recursive nonlinear filter and tracking methodology is developed for a class of partially observable processes, which is based on an approximation of a nonlinear system by a system which is linear in the unobservable states.
Abstract: A recursive nonlinear filter and tracking methodology is developed here for a class of partially observable processes. The method is based on an approximation of a nonlinear system by a system which is linear in the unobservable states and has the unobservables conditionally Gaussian with respect to the observations initially. Model smoothness, such as required with most approximating filters is not required here, and applications to simulated tracking problems show the filter to be considerably more accurate than the modified second-order filter which in general sense includes the extended Kalman filter.
TL;DR: In this article, an alternative state estimation scheme to extract gaussian message from nongaussian observation was proposed, which consists of a modification of Kalman filter to include a prefilter instead Kalman gain scheme.
TL;DR: In this paper, the authors extended the two-stage bootstrap identification method to large-scale interconnected systems by imbedding the estimation of interaction variables into the state estimation algorithm.
Abstract: The proposed method extends the two-stage bootstrap identification method to large-scale interconnected systems. It removes the requirement for information exchange between the subsystems by imbedding the estimation of interaction variables into the state estimation algorithm. Three schemes have been proposed for divergence minimization. An algorithm based on extended Kalman filter has also been proposed for comparison. Numerical results are presented through simulation of a two-machine power system.
TL;DR: The closed-loop poles of the continuous-time Kalman filter reside in a region in the left half of the complex plane that is confined by two concentric circles whose radii depend on the system matrices and the signal-to-noise ratio as mentioned in this paper.
Abstract: It is shown that the closed-loop poles of the continuous-time Kalman filter reside in a region in the left half of the complex plane that is confined by two concentric circles whose radii depend on the system matrices and the signal-to-noise ratio. This region includes the system open-loop poles and excludes the imaginary axis. In the case where the system dynamic matrix has a simple eigenstructure, this region possesses an additional boundary, that is parallel to the imaginary axis at a distance that varies with the signal-to-noise ratio.
TL;DR: Analysis of quantization errors in Kalman filters and synthesis of minimum quantization error Kalman filter structures are studied and synthesized by using minimization method of quantized errors in state-space digital filters.
Abstract: When Kalman filters are implemented with microprocessors or signal processors, quantization errors (rounfoff errors and coefficient quantization errors) due to finite wordlength implementation affect the state estimate. This paper studies analysis of quantization errors in Kalman filters and synthesis of minimum quantization error Kalman filter structures. Infinite wordlength Kalman filters are described by the state and output equations, and filter structures are introduced to Kalman filters by the state transformation, since quantization effects of digital systems highly depend on structures. Finite wordlength Kalman filters are also described by the equations. Roundoff errors and coefficient quantization errors are analyzed for any structures of Kalman filters. The results of error analysis are in agreement with the results of simulation. Minimum quantization error Kalman filters are synthesized by using minimization method of quantization errors in state-space digital filters. Synthesis method of minimum quantization error Kalman filters is very effective to reduce quantization errors.