Showing papers on "Alpha beta filter published in 1984"

Optimal Estimation Of Voltage Phasors And Frequency Deviation Using Linear And Non-Linear Kalman Filtering: Theory And Limitations

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.

The use of wave filter design in Kalman filter state estimation of the automatic steering problem of a tanker in a seaway

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.

Singular perturbation method for Kalman filter in discrete systems

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.

A coordinate-transformation based filter for improved target tracking

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.

State estimation Kalman filter using optical processing: noise statistics known.

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.

The Modified Gain Extended Kalman Filter and Parameter Identification in Linear Systems

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.

State and parameter estimation of linear stochastic multivariable sampled data systems

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.

Abel inversion by Kalman filtering

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.

Kalman filter design using the Levinson algorithm and output statistics

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.

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.

Sensitivity considerations in the design of instrument failure detection and isolation systems

Abstract: This paper considers the problem of designing the observers in an observer based instrument failure detection scheme for a system in which all the states are directly measured. Use is made of the singular values of a matrix to calculate a sensitivity measure and to adjust the observer gain matrix.

The location of the continuous-time stationary Kalman filter poles

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.

Synthesis of Filter Structures in Finite Wordlength Kalman 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.

Regions of pole location of the discrete stationary Kalman filter

Abstract: Two regions are found inside the complex unit circle that exclude all the poles of the discrete stationary Kalman filter. The sizes of these regions depend on the ratio between the intensities of the signal and the measurement noise, and in the limit where this ratio tends to infinity, one of the regions shrinks to the origin.