Showing papers on "Invariant extended Kalman filter published in 1975"

Approximate non-Gaussian filtering with linear state and observation relations

Abstract: Two approaches to the non-Gaussian filtering problem are presented. The proposed filters retain the computationally attractive recursive structure of the Kalman filter and they approximate well the exact minimum variance filter in cases where either 1) the state noise is Gaussian or its variance small in comparison to the observation noise variance, or 2) the observation noise is Gaussian and the system is one step observable. In both cases, the state estimate is formed as a linear prediction corrected by a nonlinear function of past and present observations. Some simulation results are presented.

A Comparison of Complementary and Kalman Filtering

Abstract: A technique used in the flight control industry for estimation when combining measurements is the complementary filter. This filter is usually designed without any reference to Wiener or Kalman filters, although it is related to them. This paper, which is mainly tutorial, reviews complementary filtering and shows its relationship to Kalman and Wiener filtering.

Measurement updating using the U-D factorization

Abstract: In this paper we describe a fresh approach to the discrete linear filtering problem. Our method involves an upper triangular factorization of the filter error covariance matrix, i.e. P = UDUT. Efficient and stable measurement updating recursions are developed for the unit upper triangular factor, U, and the diagonal factor, D. This paper treats only the parameter estimation problem; effects of mapping, inclusion of process noise and other aspects of filtering are treated in separate publications. The algorithm is surprisingly simple and, except for the fact that square roots are not involved, can be likened to square root filtering. Indeed, like the square root filter our algorithm guarantees nonnegativity of the computed covariance matrix. As in the case of the Kalman filter, our algorithm is well suited for use in real time. Attributes of our factorization update include: efficient one point at a time processing that requires little more computation than does the optimal but numerically unstable conventional Kalman measurement update algorithm; stability that compares with the square root filter and the variable dimension flexibility that is enjoyed by the square root information filter. These properties are the subject of this paper.

Dynamical Model Compensation for Near-Earth Satellite Orbit Determination

Abstract: Operational requirements in modern space applications often demand orbit determination accuracies which are limited by fundamental mathematical and computational restrictions. It is shown in realistic computer simulation studies how these difficulties can be alleviated for typical near-Earth satellites by employing dynamical model compensation (DMC) and accurate observations in the extended Kalman filter. Unmodeled and unknown accelerations affecting the motion of the satellite are effectively compensated by treating them as a firstorder, Gauss-Markov stochastic process. Although conventional state noise compensation (SNC) can provide satisfactory results for many applications, the DMC method offers a significant increase in estimation accuracy. Numerical behavior of the DMC structure is summarized as a function of a priori statistical parameters to aid in filter design analyses for operational applications.

Fixed memory least squares filtering (Corresp.)

Abstract: Buxbaum has reported on three algorithms for computing least squares estimates that are based on fixed amounts of data. In this correspondence, the filter is arranged as a point-deleting Kalman filter concatenated with the standard point-inclusion Kalman filter. The resulting algorithm is couched in a square root framework for greater numerical stability, and special attention is given to computer implementation.

Performance Evaluation of Suboptimal Filters

Abstract: The use of a Kalman filter in an applications problem requires a detailed model of both the system dynamics and the measurement dynamics. The model for many problems may be extremely large in dimensionality. However, in many instances one has a limited computer capability and, thus, must purposely introduce modeling errors into the filter in order to gain a computational advantage. However, as is well known, this may lead to the phenomenon of filter divergence. This paper considers the development of equations which allow one to evaluate a filter of reduced state. The equations are based upon using covariance analysis techniques in order to determine the true root-mean-square estimation error. These equations are computationally more advantageous than others appearing in the literature.

Real‐time time‐optimal control of a stirred‐tank reactor using Kalman Filtering for state estimation

Abstract: This paper presents the development and real-time implementation of a time-optimal control algorithm for a continuous stirred-tank reactor. A multivariable time-optimal control law is derived and an Extended Kalman Filter formuated for on-line estimation and filtering. The work demonstrates the powerful capability of real-time computation and decision-making in optimal control and optimal estimation of process states.

A non-linear filter with higher-order weighting functions via invariant imbedding

Abstract: The problem considered is the sequential estimation of states and parameters in noisy non-linear dynamical systems. The class of systems considered are those in which the dynamical behaviour is described by an ordinary differential equation. No statistical assumptions are required concerning the nature of the unknown inputs to the system or the measurement errors on the output. The equations of the estimator is derived by a least squares criterion and the invariant imbedding approach. The new feature of the algorithms derived lb that a non-linear filter with higher-order weighting functions (higher-order approximated optimal filter) is obtained by using the approximate method in the function space. Simulation results are presented which yield a comparison of the performance of the higher-order approximated optimal filter versus the other nonlinear filters when applied to a chemical batch reactor system. The results indicate that the proposed non-linear estimation scheme is feasible.

Kalman filter estimation of human pilot-model parameters

Abstract: The parameters of a human pilot-model transfer function are estimated by applying the extended Kalman filter to the corresponding retarded differential-difference equations in the time domain. Use of computer-generated data indicates that most of the parameters, including the implicit time delay, may be reasonably estimated in this way. When applied to two sets of experimental data obtained from a closed-loop tracking task performed by a human, the Kalman filter generated diverging residuals for one of the measurement types, apparently because of model assumption errors. Application of a modified adaptive technique was found to overcome the divergence and to produce reasonable estimates of most of the parameters.

Divergence and the fading memory filter

Abstract: The fading memory filter has been proposed as a substitute for the Kalman filter when model errors exist because it discounts old data, thereby, compensating for the influence of model errors. For model errors in the form of completely unknown inputs, this paper presents computational examples for which the asymptotic error of all fading memory filters will be greater than the Kalman error. This contradicts the assumption that, when the Kalman filter is no longer optimal, there exists a fading memory filter which will achieve lower mean squared error. An explanation for this error behavior and a discussion of its implications are included.

Application of Adaptive Filtering Methods to Maneuvering Trajectory Estimation

Abstract: : The purpose of this report is to examine several modifications of extended Kalman filters which can be used to estimate the position, velocity, and other key parameters associated with maneuvering re-entry vehicles. These filters will be described and discussed in terms of the fundamental problems of modeling accuracy, filter sophistication, and the real-time computational requirements. A nine-state, extended Kalman filter based upon the maneuvering vehicle dynamics is compared with several other candidate filters. These candidate filters include a simple filter based upon polynomial dynamics decoupled with respect to the coordinates and a more complex, fully coupled, seven-state, extended Kalman filter based upon a ballistic re-entry vehicle dynamics. Techniques which adaptively increase the process noise to compensate for modeling errors during the maneuvers are examined.

A counterexample to harmonic linearization

Abstract: A counterexample to harmonic linearization is discussed.

Extending the Intercept Range of Tactical Missiles Against Jamming Targets.

Abstract: : The main emphasis of this report is on the application of nonlinear filtering techniques to state estimation of radiating targets in range-denied systems. The mathematical model for the measurements and the target dynamics is derived, with emphasis on the development of a simplified model for the correlated errors introduced by the inertial reference unit. The nonlinear estimators considered (triangulation, extended Kalman filter, and Gaussian second-order filter) are evaluated using linearized covariance and Monte Carlo methods. Large initial errors often resulted in poor performance for the extended Kalman filter, while the Gaussian second-order filter provides acceptable performance.

Optimal estimates in thermal measurements

Abstract: Presented is an analysis of the use of a Kalman filter to improve the accuracy of thermalmeasurement systems and to increase the information which can be obtained from them.

Passive Range Estimation for Antishipping Missiles

Abstract: : This report deals with several techniques for passive ranging, i.e., the estimation of target range from noisy measurements of bearing or line-of- sight angle alone. The type of engagement treated in this investigation involves a maneuvering surface target and a missile without an altimeter. The missile approaches the target along a trajectory that is characterized by a low- altitude cruise phase followed by a terminal pitch-up maneuver. Several modified Kalman filter-like algorithms are applied to this nonlinear filtering problem; these include the extended Kalman filter (based on small-signal linearization) and several quasi-linear Kalman filters (based on random-input describing function theory). Performance comparisons are obtained by applying the filters to a number of trajectories.