Showing papers on "Invariant extended Kalman filter published in 1973"
TL;DR: In this article, the stationary form of the discrete Kalman filter for state estimation in noisy process systems was demonstrated by simulated and experimental tests on a pilot plant evaporator, which resulted in good control despite process and/or measurement noise levels of 10%.
Abstract: The effectiveness of the stationary form of the discrete Kalman filter for state estimation in noisy process systems was demonstrated by simulated and experimental tests on a pilot plant evaporator. The filter was incorporated into a multivariable, computer control system and resulted in good control despite process and/or measurement noise levels of 10%. The results were significantly better than those obtained when the Kalman filter was omitted or replaced by conventional exponential filters. In this application the standard Kalman filter was reasonably insensitive to incorrect estimates of initial conditions or noise statistics and to errors in model parameters. The filter estimates were sensitive to unmeasured process disturbances. However this sensitivity could be reduced by treating the noise covariance matrices R and Q as design parameters rather than noise statistics and selecting values which result in increased weighting of the process measurements relative to the calculated model states.
30 citations
01 Feb 1973
TL;DR: The performance of the filter is considered, and, for state rather than signal estimation, the performance is found to depend on the details of the model, as distinct from its output statistics.
Abstract: The Kalman filter depends only on the output statistics of the message model; a technique for filter construction using only these statistics is given. The performance of the filter is considered, and, for state rather than signal estimation, the performance is found to depend on the details of the model, as distinct from its output statistics.
23 citations
TL;DR: A simple but effective method of divergence control for Kalman filters is described, which is in principle a considerable simplification of the type of divergence Control which is based on plant noise estimation.
Abstract: A simple but effective method of divergence control for Kalman filters is described. This is in principle a considerable simplification of the type of divergence control which is based on plant noise estimation.
21 citations
TL;DR: In this paper, the Gaussian second-order measurement equations appropriate for the nonlinear elongation of measured range were developed and demonstrated in a spacecraft rendezvous navigation simulation, where the required additions to a linearized Kalman filter are not complex.
Abstract: Advances in nonlinear filter theory have produced the Gaussian second-order filter. This extension of the Kalman filter compensates for measurement nonlinearity by appropriate bias compensation and a priori measurement variance increase. This paper develops the Gaussian second-order measurement equations appropriate for the nonlinear elongation of measured range. The required additions to a linearized Kalman filter are not complex. The performance improvement obtainable is demonstrated in a spacecraft rendezvous navigation simulation. Divergence of the standard linearized filter occurs if the initial error exceeds 1 km. Divergence in the second-order filter does not occur unless the initial error exceeds 10 km.
15 citations
01 Apr 1973
TL;DR: In this article, an application of the Kalmsn filter to equalization of a digital communication Chmnnel is described and the resultant modified Kalman equalizer (KE) is a nonlinear system in which the channel tap gain is estimated via a decision feedback approach and the state variable is estimated by a prediction process.
Abstract: An application of the Kalmsn filter to equalization of a digital communication Chmnnel is described. The resultant modified Kalman equalizer (KE) is a nonlinear system in which the channel tap gain are estimated via a decision feedback approach and the state variable is estimated by a prediction process.
13 citations
TL;DR: In this paper, the performance deterioration of optimal regulators caused by the introduction of Kalman filters as state estimators is investigated and it is shown that, in the ease of single-input single-output (SISO) systems, performance deterioration cannot be made arbitrarily small unless the optimal control law can be implemented by direct output feedback.
Abstract: In this paper, the performance deterioration of optimal regulators caused by the introduction of Kalman filters as state estimators is investigated. It is shown that, in the ease of single-input single-output systems, the performance deterioration cannot be made arbitrarily small unless the optimal control law can be implemented by direct output feedback.
10 citations
TL;DR: An approach based on stochastic approximation is presented and the steady-state gain is obtained by using a recursive algorithm that satisfies the innovations theorem.
Abstract: A Kalman filter requires an exact knowledge of the noise covariance matrices to determine the optimal gain Kop for the filtering equations. In the absence of such prior information, an adaptive technique must be used. An approach based on stochastic approximation is presented. The steady-state gain is obtained by using a recursive algorithm that satisfies the innovations theorem.
9 citations
TL;DR: It is shown that the Estimates of the state and the estimates of the unknown covariances Q and R can be made arbitrarily close to the optimal nonlinear Bayesian estimates by an appropriate choice for the number of parallel paths in the computer.
8 citations
TL;DR: In this article, a class of algorithms which are closely related to the Kalman filter is considered, and with an input signal of appropriate statistics these algorithms are easy to calculate and are characterized by a speed of convergence which is comparable to that of a KF given an imperfect, a priori knowledge of the error covariance matrix.
Abstract: In order to identify a linear system with a discrete non-parametric model a class of algorithms which is closely related to the Kalman filter is considered. With an input signal of appropriate statistics these algorithms are easy to calculate and are characterized by a speed of convergence which is comparable to that of a Kalman filter given an imperfect, a priori knowledge of the error covariance matrix.
5 citations
01 Dec 1973
TL;DR: An iterative procedure for the adaptation of the assumed a priori observation-noise covariances of time-variable systems is investigated and the calculated error covariance is shown to tend to the actual in the limit.
Abstract: The application of Kalman-Bucy filters entails precise knowledge on the a priori noise covariances as well as the system parameters. In many practical cases, however, such precise knowledge is not available, and approximate values are usually used or assumed. It has been pointed out that incorrect covariances often cause severe inconsistency between the calculated error covariance and the actual one. Approaches of adaptive filtering have been studied by various researchers for mainly time-invariant systems. An iterative procedure for the adaptation of the assumed a priori observation-noise covariances of time-variable systems is investigated in this paper. The procedure proposed here computes at each iteration a necessary correction from the covariances of the innovation process, and adapt the noise covariances thereby. The calculated error covariance is shown to tend to the actual in the limit. Simulated examples show that initial choices of the a priori covariance do not seem to be crucial to the convergence. An approach to adaptive filtering is also proposed.
4 citations
01 Dec 1973
TL;DR: In this paper, a specific post-flight data analysis (PFDA) technique is described, which is termed adaptive, iterated, extended Kalman filtering (AIEKF), and illustrates the application of the PFDA tool to the estimation of aerodynamic coefficients (C_{x}, C_{N}, and C_{m} ) for a single-axis model of a thrust-vector-controlled missile.
Abstract: This paper describes a specific postflight data analysis (PFDA) technique, which is termed adaptive, iterated, extended Kalman filtering (AIEKF), and illustrates the application of the PFDA tool to the estimation of aerodynamic coefficients ( C_{x}, C_{N}, and C_{m} ) for a single-axis model of a thrust-vector-controlled missile. It is demonstrated that PFDA embraces many areas of interest to control specialists, such as simulation of nonlinear systems, estimation, optimization, and validation.
TL;DR: In this article, a general recursive method for learning the optimal stationary Kalman filter Kopt was proposed, where the plant and measurement noise covariance kernels, denoted by Q and R, respectively, are unknown.
Abstract: It is the purpose of the letter to provide a short description of a general recursive method for learning the optimal stationary Kalman filter Kopt, when the plant and measurement noise covariance kernels, denoted by Q and R, respectively, are unknown. Experimental verification that confirms the theoretical expectations is presented.
TL;DR: Among several second-order approximations to the filter of a non-linear system, it is found that the extended Kalman filter is generally the most versatile as discussed by the authors, which can be further improved by using stochastic linear approximation as suggested by Sunahara.
Abstract: Among several second-order approximations to the filter of a non-linear system, it is found that the extended Kalman filter is generally the most versatile. The second-order likelihood filter, also known ns the Detchmendy—Sridhar filter is inferior to the ahove and at the same time involves more computation. In the special ease when analytical expressions For the gaussian expectation integrals of the non-linearities can be found, the extended Kalman filter can be further improved by using stochastic linear approximations as suggested by Sunahara. The third-order likelihood filter derived in this paper is more accurate than the above, but calls for considerable storage space and computing time.
01 Dec 1973
TL;DR: A survey of algorithms for linear estimation of dynamical systems with time-invariant parameters can be found in this article, where the authors present several special cases of the algorithms that are closely related to certain early work in astrophysics by So Chandrasekhar and in estimation by Levinson.
Abstract: The paper is an outline of a talk that will survey some algorithms that have recently been developed for linear estimation in dynamical systems with time-invariant parameters. The algorithms have potential numerical advantages and in particular require less effort than the Kalman filter. Special cases of the algorithms are closely related to certain early (1947) work in astrophysics by So Chandrasekhar and in estimation by N. Levinson. The algorithms can be used to solve several other problems beside estimation. Furthermore, they are closely related to algorithms for minimal realization and for system inversion.
TL;DR: In this article, the Kalman filter theory was used to derive a set of difference equations by which the lateral position of a ship relative to the desired (straight) course can be estimated from measured yaw-angle values containing noise.
Abstract: The Kalman filter theory has been used to derive a set of difference equations by which the lateral position of a ship relative to the desired (straight) course can be estimated from measured yaw-angle values containing noise. Special attention has been paid to the standard deviation of the estimation error.
TL;DR: The structure of the innovations process is examined as the gain of a Kalman filter is allowed to deviate from its optimum structure in this article, and the state model of the resulting pseudo-innovations process is determined, and it is shown how the level of variance of the process depends on the difference between the desired Kalman gain and the gain actually being employed.
Abstract: The structure of the innovations process is examined as the gain of a Kalman filter is allowed to deviate from its optimum structure. The state model of the resulting pseudoinnovations process is determined, and it is shown how the level (or variance) of the process depends on the difference between the desired Kalman gain and the gain actually being employed. The model illustrates requirements on an arbitrary gain matrix to ensure stable filter performance.
TL;DR: The state-space method has been used to evaluate the statistical error due to the finite-precision arithmetic in a digital filter.
Abstract: The state-space method has been used to evaluate the statistical error due to the finite-precision arithmetic in a digital filter. The actual error of a 2nd-order filter obtained from computer simulation has also been plotted against the expected error