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Showing papers on "Invariant extended Kalman filter published in 1987"


Book
01 Jan 1987
TL;DR: Kalman Filtering with Real-Time Applications presents a thorough discussion of the mathematical theory and computational schemes of Kalman filtering, including a direct method consisting of a series of elementary steps, and an indirect method based on innovation projection.
Abstract: "Kalman Filtering with Real-Time Applications" presents a thorough discussion of the mathematical theory and computational schemes of Kalman filtering. The filtering algorithms are derived via different approaches, including a direct method consisting of a series of elementary steps, and an indirect method based on innovation projection. Other topics include Kalman filtering for systems with correlated noise or colored noise, limiting Kalman filtering for time-invariant systems, extended Kalman filtering for nonlinear systems, interval Kalman filtering for uncertain systems, and wavelet Kalman filtering for multiresolution analysis of random signals. The last two topics are new additions to this third edition. Most filtering algorithms are illustrated by using simplified radar tracking examples. The style of the book is informal, and the mathematics is elementary but rigorous. The text is self-contained, suitable for self-study, and accessible to all readers with a minimum knowledge.

1,086 citations


Proceedings ArticleDOI
06 Apr 1987
TL;DR: A delayed-Kalman filtering method is proposed which improves the speech enhancement performance of Kalman filter further and is found to be significantly better than the Wiener filtering method.
Abstract: In this paper, the problem of speech enhancement when only corrupted speech signal is available for processing is considered. For this, the Kalman filtering method is studied and compared with the Wiener filtering method. Its performance is found to be significantly better than the Wiener filtering method. A delayed-Kalman filtering method is also proposed which improves the speech enhancement performance of Kalman filter further.

321 citations


Journal ArticleDOI
TL;DR: In this article, the authors proposed a chi-square test for real-time detection of soft failures in navigation systems using Kalman filters based on the overlap between the confidence regions associated with two estimates, one obtained from a Kalman filter using online measurements, and the other based solely on a priori information.
Abstract: A test for real-time detection of soft failures in navigation systems using Kalman filters has been proposed by Kerr. The test is based on the overlap between the confidence regions associated with two estimates, one obtained from a Kalman filter using on-line measurements, and the other based solely on a priori information. An alternate computational technique is presented which is based on constructing a chi-square test statistic from the difference between the two estimates and comparing it to a precomputed threshold. The chi-square test avoids the iterative computations required by the two-ellipsoid method for dimensions of two and higher.

159 citations


Journal ArticleDOI
TL;DR: In this paper, the performance of the extended Kalman filter and the iterated extended k-means filter are compared with the method of least squares for passive position location estimation, and Monte Carlo results are given showing how the a prioricovariance matrix influences the accuracy of the Extended Kalman Filter.
Abstract: Several papers have been published recently using the method ofleast squares for passive position location estimation. While the Kalman filter is mentioned as an alternative approach in most ofthese papers, none of the papers actually compare the performanceof the Kalman filter with the method of least squares. In this paper,the performances of the extended Kalman filter and the iteratedextended Kalman filter are compared with the method of leastsquares. Monte Carlo results are given showing how the a prioricovariance matrix influences the accuracy of the extended Kalmanfilter.

107 citations


Journal ArticleDOI
TL;DR: In this article, a reduced-order Kalman filter is proposed for estimating the state of a Luenberger observer with respect to the noises in the system, where the filler is much like a Luinberger observer for the state to be estimated.
Abstract: This paper presents a method for designing an ‘optimum’ unbiased reduced-order filter. For the proposed approach to work, the order of the filter must be greater than a certain minimum determined by the number of independent observations of the system available. The filler is much like a Luenberger observer for the state to be estimated, but with parameters optimized with respect to the noises in the system. A reduced-order innovation process is proposed that has properties similar to those of the full-order innovation process when the reduced filter is optimized. The approach offers the possibility of significant reduction in real-time computational requirements compared with the full-order filter, though at the cost of some loss of performance. The algorithm for the reduced-order filter is simple to implement— quite similar to that of the Kalman filter. An example is presented to compare the performance of the proposed method with the full-order Kalman filter.

95 citations


Journal ArticleDOI
TL;DR: An algorithm for updating the linear and quadratic weights of a second-order Volterra filter (SVF) is proposed and the fast Kalman filter implementation is shown to converge to the unknown system parameters considerably faster than the LMS implementation.
Abstract: An algorithm for updating the linear and quadratic weights of a second-order Volterra filter (SVF) is proposed. This algorithm uses a fast Kalman filter algorithm to calculate the Kalman gain vector used in updating the linear and quadratic weights of the SVF. The convergence of the algorithm for the quadratic weights is established. A simulation is then performed in which a fast Kalman filter implementation of an SVF is compared to an LMS implementation in a system identification problem. The fast Kalman filter implementation is shown to converge to the unknown system parameters considerably faster than the LMS implementation.

84 citations


01 Jan 1987
TL;DR: The Radar Tracker example was chosen to demonstrate Altera’s unique solution of the Kalman Filter that demonstrates the possibility of offloading a CPU by executing a portion of the algorithm in FPGA fabric.
Abstract: of the Kalman Filter that is suited to work with systems whose model contains non-linear behavior. The algorithm linearizes the non-linear model at the current estimated point in an iterative manner as a process evolves. Although EKF can be used in a very wide range of applications, the Radar Tracker example was chosen to demonstrate Altera’s unique solution. Typically EKF requires significant computational efforts due to multiple matrix operations, including matrix inversion. This design demonstrates the possibility of offloading a CPU by executing a portion of the algorithm in FPGA fabric.

82 citations


Journal ArticleDOI
TL;DR: Five examples are selected from the literature to illustrate the use of Kalman filtering techniques for obtaining least‐squares estimates fo several parameters of analytical importance, including multicomponent curve resolution and concentration estimation, correction for variable background responses, calibration with drift compensation, and estimation of kinetic parameters for first‐order reactions.
Abstract: The application of the Kalman filter to the solution of a variety of problems in analytical chemistry is reviewed. Five examples are selected from the literature to illustrate the use of Kalman filtering techniques for obtaining least-squares estimates fo several parameters of analytical importance. These examples include multicomponent curve resolution and concentration estimation, correction for variable background responses, calibration with drift compensation, and estimation of kinetic parameters for first-order reactions and for heterogeneous charge-transfer reactions. An adaptive Kalman filtering technique is required for the solution of the background correction problem, and the extended Kalman filter algorithm is required for the solution of the nonlinear kinetic problems. For each case, the results that were obtained are summarized, and some advantages of Kalman filtering over traditional least-squares approaches are discussed.

80 citations


Journal ArticleDOI
TL;DR: In this article, a modified-gain extended Kalman filter (MGEKF) is applied to the problem of on-line state estimation and identification of the stability derivatives of a F-111 type of vehicle.
Abstract: A new on-line state and parameter identification algorithm called the modified-gain extended Kalman filter (MGEKF) is applied to the problem of on-line state estimation and identification of the stability derivatives of a F-111 type of vehicle. The conceptual basis for the MGEKF is the existence of a class of nonlinear functions that allow a universal linearization with respect to the measurement function. This class includes the problem of identification of linear systems. The previous single-output formulation is extended to a multioutput formulation where the only available measurements are acceleration and pitch rate, but not elevator deflection. The filter formulation includes a simplified Dryden wind gust model. The inclusion of the wind gust model results mainly in a slowed response in the estimation of the stability derivatives associated with the acceleration state; estimates of the stability derivatives associated with the pitch rate still respond very quickly. The accuracy of the acceleration stability derivatives depends upon the amplitude and frequency components of the persistently exciting dither signal.

34 citations


Journal ArticleDOI
TL;DR: In this article, the second-order filter was developed for the estimation of attitude quaternion using three-axis gyro and star tracker measurement data, and the uniqueness of this algorithm is the online generation of the time-varying process and measurement noise covariance matrices, derived as a function or the process nonlinearity, respectively.
Abstract: The stringent attitude determination accuracy and faster slew maneuver requirements demanded by present-day spacecraft control systems motivate the development of recursive nonlinear filters for attitude estimation. This paper presents the second-order filter development for the estimation of attitude quaternion using three-axis gyro and star tracker measurement data. Performance comparisons have been made by computer simulation of system models and filter mechanization. It is shown that the second-order filter consistently performs better than the extended Kalman filter when the performance index of the root sum square estimation error of the quaternion vector is compared. The second-order filter identifies the gyro drift rates faster than the extended Kalman filter. The uniqueness of this algorithm is the online generation of the time-varying process and measurement noise covariance matrices, derived as a function or the process and measurement nonlinearity, respectively.

29 citations


Patent
01 Apr 1987
TL;DR: In this paper, a modified Faddeeva algorithm is embodied into electrical signals which are applied as inputs to a systolic array processor, which performs triangulation and nullification on the input signals, and delivers an output signal which is a real-time solution to the input signal.
Abstract: A method and apparatus for processing signals representative of a complex matrix/vector equation. More particularly, signals representing an orderly sequence of the combined matrix and vector equation, known as a Kalman filter algorithm, are processed in real time in accordance with the principles of this invention. The Kalman filter algorithm is rearranged into a Faddeeva algorithm, which is a matrix-only algorithm that is modified to represent both the matrix and vector portions of the Kalman filter algorithm. The modified Faddeeva algorithm is embodied into electrical signals which are applied as inputs to a systolic array processor. The processor performs triangulation and nullification on the input signals, and delivers an output signal which is a real-time solution to the input signals.

DOI
01 Jun 1987
TL;DR: In this article, two nonrigorous applications of the Kalman filter to the adaptive infinite-impulse-response (IIR) equaliser problem are presented, one direct approach, involves a simultaneous parameter and state estimation algorithm, and the second, an indirect approach, a Kalman-based IIR system identification algorithm is used to estimate the parameters which define the closed-form optimum IIR equaliser.
Abstract: The application of Kalman estimation techniques to adaptive filtering problems is briefly reviewed. In particular, three common scenarios are examined in detail. The themes that link these areas are that they involve rigorous or almost rigorous application of the Kalman filter, and they can be modelled by a finite-impulse-response (FIR) filter structure. Two new nonrigorous applications of the Kalman filter to the adaptive infinite-impulse-response (IIR) equaliser problem are presented. The first, a direct approach, involves a simultaneous parameter and state estimation algorithm. In the second, an indirect approach, a Kalman-based IIR system identification algorithm is used to estimate the parameters which define the closed-form optimum IIR equaliser. Finally, the convergence of the two algorithms is compared by computer simulation.

01 Jan 1987
TL;DR: This paper has been submitted for publication to the Journal of Mathematics of Control, Signals, and Systems and will be published later this year.
Abstract: Cover title. "This paper has been submitted for publication to the Journal of Mathematics of Control, Signals, and Systems."

Proceedings ArticleDOI
01 Dec 1987
TL;DR: In this article, the authors studied the behavior of the discrete-time Kalman filter under incorrect noise covariances and quantified the filter performance by the actual one-step predictor error covariance.
Abstract: In this paper, we study the behavior of the discrete-time Kalman filter under incorrect noise covariances. In particular, we are interested in the characteristic of the actual performance of the Kalman filter. The filter performance is quantified by the actual one-step predictor error covariance. Convergence and divergence analyses of the actual one-step predictor error covariance are given. The results developed in the paper provide useful insights in the behavior of the Kalman filter when the noise covariances used in designing the filter are inexact.


Journal ArticleDOI
TL;DR: In this paper, the problem of implementing the Kalman filter recursions in square root information filter form was considered and a general linear, dynamical model which directly incorporates the fact that many of the unknowns are not time varying was proposed.
Abstract: We consider the problem of implementing the Kalman filter recursions in square root information filter form. We suggest a general linear, dynamical model which directly incorporates the fact that many of the unknowns are not time varying. The resulting implementation is widely applicable, numerically sound, and extends easily to smoothing problems.

Proceedings ArticleDOI
01 Dec 1987
TL;DR: This paper examines various discrete-time parallel Kalman filtering implementations, with special attention given to square-root versions in both covariance and information filter forms.
Abstract: In this paper we examine various discrete-time parallel Kalman filtering implementations, with special attention given to square-root versions in both covariance and information filter forms. A special feature of the suggested architecture is the ability to accomodate parallel local filters that have a smaller state dimension than the global filter. The estimates and covariances from these reduced-order filters are collated at a central filter at each step to generate the full-order, globally optimal estimates and their associated error covariances.

Proceedings ArticleDOI
Fred Daum1
10 Jun 1987
TL;DR: In this paper, a new exact nonlinear filtering theory is applied to a practical radar tracking problem, where the standard extended Kalman filter for this application suffers from a fundamental flaw due to linearization.
Abstract: A new exact nonlinear filtering theory is applied to a practical radar tracking problem. The standard extended Kalman filter for this application suffers from a fundamental flaw due to linearization. The new nonlinear filter does not require this linear approximation.

Journal ArticleDOI
TL;DR: In this paper, the robustness properties of extended-Kalman-type observers for linear plants when actuators and sensors have nonlinearities or linear dynamics were investigated, and sufficient conditions for the stability of the estimation error were obtained for time-varying extended Kalman filters (EKF) for time varying plants, and for constant gain, exponentially weighted EKF for time invariant plants.
Abstract: Robustness properties of extended-Kalman-type observers are investigated for linear plants when actuators and sensors have non-linearities or linear dynamics. Sufficient conditions for the stability of the estimation error are obtained for time-varying extended Kalman filters (EKF) for time-varying plants, and for constant-gain, exponentially weighted EKF for time-invariant plants. When the non-linearities are known only within bands of uncertainty, it is proved that the observer is non-divergent.

Proceedings ArticleDOI
01 Dec 1987
TL;DR: In this article, it was shown that the RKF achieves zero steady state variance of the estimation error if and only if the plant has no transmission zeros in the right half plane, since these would be among the poles of the KF.
Abstract: Several known results are unified by considering properties of reduced-order Kalman filters. For the case in which the number of noise sources equals the number of observations, it is shown that the reduced-order Kalman filter achieves zero steady state variance of the estimation error if and only if the plant has no transmission zeros in the right half plane, since these would be among the poles of the Kalman filter. The reduced order Kalman filter cannot achieve zero variance of the estimation error if the number of independent noise sources exceed the number of observations. It is also shown that the reduced order Kalman filter achieves the generalized Doyle-Stein condition for robustness when the noise sources are collocated with the control inputs. When there are more observations than noise sources, additional noise sources can be postulated to improve the observer frequency response without diminishing robustness.


Journal ArticleDOI
TL;DR: The analytical expression for the steady-state solution to acontinuous-time Kalman filter with two state variables considered by Ekstrand is found by directly solving the continuous-timealgebraic Ricatti equation.
Abstract: The analytical expression for the steady-state solution to acontinuous-time Kalman filter with two state variables consideredby Ekstrand is found by directly solving the continuous-timealgebraic Ricatti equation.

01 Jul 1987
TL;DR: A new approach to state estimation in deterministic digital control systems based on sampling the output of the plant at a high rate and prefiltering the discrete measurements in a multi-input/multi-output moving average process is presented.
Abstract: The paper presents a new approach to state estimation in deterministic digital control systems. The scheme is based on sampling the output of the plant at a high rate and prefiltering the discrete measurements in a multi-input/multi-output moving average (MA) process. The coefficient matrices in the MA prefilter are selected so the estimated state equals the true state. An example is presented which illustrates the procedure to follow to completely design the estimator.

Book ChapterDOI
01 Jan 1987
TL;DR: In this paper, the authors considered the special case where all known constant matrices are independent of time, and they considered the time-invariant linear stochastic system with the state-space description.
Abstract: In this chapter, we consider the special case where all known constant matrices are independent of time. That is, we are going to study the time-invariant linear stochastic system with the state-space description: $$ \left\{ {\begin{array}{*{20}{c}} {{x_{k + 1}} = A{x_k} + \Gamma {{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\xi } }_k}} \\ {{v_k} = C{x_k} + {{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\eta } }_k}} \end{array}} \right. $$ (6.1)

Journal ArticleDOI
TL;DR: In this article, extended Kalman filtering is applied to estimate the parameters of a linear dynamic stochastic system given in a state space description, where the equation describing the dynamics of the system is implicit and the equation yields a linear transform of the new state vector.


01 Jan 1987
TL;DR: An algorithm for updating the linear and quadratic weights of a second-order Volterra filter (SVF) is proposed that uses a fast Kalman filter algorithm to calculate the Kalman gain vector and the convergence of the algorithm for the quadRatic weights is established.
Abstract: An algorithm for updating the linear and quadratic weights of a second-order Volterra filter (SVF) is proposed. This al- gorithm uses a fast Kalman filter algorithm to calculate the Kalman gain vector used in updating the linear and quadratic weights of the SVF. The convergence of the algorithm for the quadratic weights is established. A simulation is then performed in which a fast Kalman filter implementation of an SVF is compared to an LMS implementa- tion in a system identification problem. The fast Kalman filter imple- mentation is shown to converge to the unknown system parameters considerably faster than the LMS implementation.

Proceedings ArticleDOI
10 Jun 1987
TL;DR: In this article, the extended Kalman filter is constrained to be of reduced order to avoid excessive computational complexity, where the filter can be used to estimate the state without some approximation being made.
Abstract: When a nonlinear dynamical or observational model is used to describe a system, the Kalman filter cannot be used to estimate the state without some approximation being made. If the approximation used is linearization of the equations about the state estimate, the resulting modification of the Kalman filter is often called an extended Kalman filter. In this paper we obtain a similar result, where the filter is constrained to be of reduced order to avoid excessive computational complexity.

Journal ArticleDOI
TL;DR: In this article, it was shown that the Zeros of the Kalman filter are determined by the poles of the disturbance model in a more representative case of a block-diagonal structure with feedback coupling.
Abstract: Several classical industrial filtering applications have used notch filters to reject the unwanted dominant frequencies. For a class of industrial systems, it has been shown that the filter gain between the observations and the signal estimates is unity. While the gain between the observations and the disturbance state estimates is zero, the zeros of the Kalman filter are determined by the poles of the disturbance model. These results are generalised to a more representative case of a block-diagonal structure with feedback coupling.