Showing papers on "Alpha beta filter published in 1997"
10 Dec 1997
TL;DR: In this paper, an approach to the nonlinear observer design problem is proposed based on the early ideas that influenced the development of the linear Luenberger observer theory, and the proposed approach develops a nonlinear analogue.
Abstract: The work proposes an approach to the nonlinear observer design problem. Based on the early ideas that influenced the development of the linear Luenberger observer theory, the proposed approach develops a nonlinear analogue. The formulation of the observer design problem is realized via a system of first-order linear singular PDEs, and a rather general set of necessary and sufficient conditions for solvability is derived by using Lyapunov's auxiliary theorem. The solution to the above system of PDEs is locally analytic and this enables the development of a series solution method, that is easily programmable with the aid of a symbolic software package. Within the proposed design framework, both full-order and reduced-order observers are studied.
226 citations
10 Dec 1997
TL;DR: It is proved that the observer output error becomes smaller than a user specified bound for large times and that the adaptation converges.
Abstract: In this paper we present a high-gain observer for a general class of nonlinear SISO systems for which the high-gain parameter is determined on-line in an adaptive fashion. The adaptation scheme is simple and universal in the sense that it is independent of the system the observer is designed for. We prove that the observer output error becomes smaller than a user specified bound for large times and that the adaptation converges. The assumptions required for the adaptive high-gain observer are the same as for the nonadaptive high-gain observer, namely that the system is uniformly observable for any u(t).
116 citations
26 Jun 1997
TL;DR: The Covariance Intersection (CI) framework as mentioned in this paper is a generalization of the Kalman filter that permits filtering and estimation to be performed in the presence of unmodeled correlations.
Abstract: The Covariance Intersection (CI) framework represents a generalization of the Kalman filter that permitsfiltering and estimation to be performed in the presence of unmodeled correlations. As described in previous papers, unmodeled correlations arise in virtually all real-world problems; but in many applications the correlations are so significant that they cannot be "swept under the rug" simply by injecting extra stabilizing noise withina traditional Kalman filter. In this paper we briefly describe some of the properties of the CI algorithm anddemonstrate their relevance to the notoriously difficult problem of simultaneous map building and localization for autonomous vehicles.Keywords: Autonomous vehicles, data fusion, filtering, Covariance Intersection, Kalman filter, map building, matrixinequalities, nonlinear filtering. 1 INTRODUCTION The Kalman filter has been one of the most important and widely used engineering tools since its development in the early 1960s. The Kalman filter represents information about estimated or measured quantities in termsof a mean and covariance. Its importance is that it provides a mathematically rigorous method for combiningmultiple estimates that are assumed to be independent in the probabilistic sense. In other words, if the errors(or noise) associated with two estimates are due to unrelated processes, then the Kalman filter can combine thetwo estimates so that the resulting "filtered" estimate has error less than or equal to that of either of the twoprior estimates. A more general formulation of the Kalman filter can combine estimates with a known degreeof correlation, which is defined by the cross covariance between the two estimates, but it cannot be applied ifsuch information is not known. In practice most estimates are not independent and cross covariances cannot bedetermined.
84 citations
TL;DR: The discrete Kalman filter which enables the treatment of incomplete data and outliers is described and some special cases are considered including a convergence result for recursive parameter estimation in AR(1) process with innovation outliers and missing observations.
Abstract: The discrete Kalman filter which enables the treatment of incomplete data and outliers is described. The incomplete, or missing observations are included in such a way as to transform the Kalman filter to the case when observations have changing dimensions. In order to treat outliers, the Kalman filter is made robust using the M-estimation principle. Some special cases are considered including a convergence result for recursive parameter estimation in AR(1) process with innovation outliers and missing observations.
71 citations
TL;DR: Using the Riccati-equation-based approach, observer-based feedback control laws are designed, which guarantee the quadratic stability of the closed-loop control system and reduce the effect of the disturbance input on the controlled output to a prescribed level.
66 citations
TL;DR: An extended Kalman filter (EKF), implementing the full nonlinear kinematics of the aircraft equations of motion, was used for the estimation of aerodynamic coefficients in aircraft dynamic models from flight-test data.
Abstract: The estimation of aerodynamic coefficients in aircraft dynamic models from flight-test data is addressed in this paper. An extended Kalman filter (EKF), implementing the full nonlinear kinematics of the aircraft equations of motion, was used for this purpose. Flight-test data from NASA's X-31 Drop Model and High Angle-of-attack Research Vehicle (HARV) were analyzed. The EKF parameter estimates for the X-31 compared well with wind-tunnel data and flight-data results using other identification techniques. For the HARV, the assumption of pseudonoise in the parameter dynamic model substantially improved the state and parameter estimates. A residual correlation method was used to estimate the process noise intensity matrix for this aircraft's flight data.
52 citations
TL;DR: In this paper, a Kalman filter for the assimilation of long-lived atmospheric chemical constituents was developed for two-dimensional transport models on isentropic surfaces over the globe.
Abstract: A Kalman filter for the assimilation of long-lived atmospheric chemical constituents was developed for two-dimensional transport models on isentropic surfaces over the globe. Since the Kalman filter calculates the error covariances of the estimated constituent field, there are five dimensions to this problem, x1, x2, and time, where x1 and x2 are the positions of two points on an isentropic surface. Only computers with large memory capacity and high floating point speed can handle problems of this magnitude. This article describes an implementation of the Kalman filter for distributed-memory, message-passing parallel computers. To evolve the forecast error covariance matrix, an operator decomposition and a covariance decomposition were studied. The latter was found to be scalable and has the general property, of considerable practical advantage, that the dynamical model does not need to be parallelized. Tests of the Kalman filter code examined variance transport and observability properties. This...
43 citations
04 Jun 1997
TL;DR: In this paper, the design of observers for autonomous nonlinear systems with one output is discussed and necessary and sufficient conditions for existence of a solution to the observer error linearization problem are given.
Abstract: We discuss the design of observers for autonomous nonlinear systems with one output. New necessary and sufficient conditions for existence of a solution to the observer error linearization problem are given. In the case when an exact linearization of the observer error dynamics is impossible, a simple least-squares scheme is proposed that yields an observer whose error dynamics is approximately linear. An algorithm for observer construction is provided. An example of observer design for a mass-spring system with nonlinear spring and dynamic friction forces is given.
34 citations
04 Jun 1997
TL;DR: It is shown that a Luenberger observer modified, so that feedback is impulsive at the quantizer transitions, is one such observer that can be designed with exponentially stable tracking error.
Abstract: State estimation via nonlinear observers is described for a linear system with quantized outputs. Although there may be significant quantization error on average, it is possible to design observers with exponentially stable tracking error. Here we show that a Luenberger observer modified, so that feedback is impulsive at the quantizer transitions, is one such observer.
33 citations
TL;DR: The link between the bound of the modelling errors and the dynamic of the observer is given and the stability of the observers where the non-linearities are bounded is considered.
31 citations
04 Jun 1997
TL;DR: In this paper, a suboptimal algorithm, the relative filter, is introduced that avoids many of the computational and practical problems of the direct Kalman filter approach to this problem.
Abstract: This paper examines the problem of automatically constructing a map of an unknown environment from a vehicle whose location is also unknown. The application of the Kalman filter to this problem is briefly described and the practical limitation of the filter in this context is discussed. A suboptimal algorithm, the relative filter, is introduced that avoids many of the computational and practical problems of the direct Kalman filter approach to this problem. The performance of the full Kalman filter and the relative filter is compared in a real map building scenario.
TL;DR: In this paper, the authors investigate two techniques for filtering signals from noisy nonlinear systems: a modified Kalman filter and a noise reduction algorithm based on shadowing from dynamical systems theory.
Abstract: We investigate two techniques for filtering signals from noisy nonlinear systems. Both the dynamics and the observed signals may be subject to noise. The first technique is a modified Kalman filter which accounts for the noise-amplification properties of chaotic systems and has less tendency to diverge than the usual Kalman filter. The second is the noise-reduction algorithm of Hammel, based on the concept of shadowing from dynamical systems theory.
TL;DR: In such an application, the state-space system can be replaced by an equivalent one that has the same number of measurements as states that will produce the same state estimates for both systems.
Abstract: The Kalman filter is a powerful tool in linear-systems analysis. The authors present a particular application in which there are more measurements than states. In such an application, the state-space system can be replaced by an equivalent one that has the same number of measurements as states. The Kalman filter will produce the same state estimates for both systems. Using the equivalent system leads to a substantial saving in computer operations.
TL;DR: It is shown that the proof of Theorem1 in the above- mentioned paper is incomplete and that the state observer scheme results in steady-state error and a memoryless state observer for linear time-delay systems is provided.
Abstract: This note first shows that the proof of Theorem1 in the above- mentioned paper is incomplete and that the state observer scheme results in steady-state error. Alternatively, a memoryless state observer for linear time-delay systems is provided.
04 Jun 1997
TL;DR: In this article, inequalities from probability theory associated with the probabilities of convex sets have been used to characterize the estimation error of a Kalman filter in such a non-Gaussian (distribution-free) setting.
Abstract: The Kalman filter is frequently used for state estimation in state-space models when the standard Gaussian noise assumption does not apply. A problem arises, however, in that inference based on the incorrect Gaussian assumption can lead to misleading or erroneous conclusions about the relationship of the Kalman filter estimate to the true (unknown) state. This paper shows how inequalities from probability theory associated with the probabilities of convex sets have potential for characterizing the estimation error of a Kalman filter in such a non-Gaussian (distribution-free) setting.
TL;DR: It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman Filter requires significantly less computer time and storage to implement as compared to the traditional explicit Kalman filter.
Abstract: For an implicitly defined discrete system, a new algorithm for Kalman filtering is developed and an efficient numerical implementation scheme is proposed. Unlike the traditional explicit approach, the implicit filter can be readily applied to ill-conditioned systems and allows for generalization to descriptor systems. The implementation of the implicit filter depends on the solution of the congruence matrix equation (A1)(Px)(AT1) = Py. We develop a general iterative method for the solution of this equation, and prove necessary and sufficient conditions for convergence. It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman filter requires significantly less computer time and storage to implement as compared to the traditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments.
TL;DR: The neural network is employed to estimate the nonlinear dynamics of the extended Kalman filter to filter three types of noise commonly observed in financial data: process noise, measurement noise, and arrival noise.
Abstract: In this paper we present a neural network extended Kalman filter for modeling noisy financial time series. The neural network is employed to estimate the nonlinear dynamics of the extended Kalman filter. Conditions for the neural network weight matrix are provided to guarantee the stability of the filter. The extended Kalman filter presented is designed to filter three types of noise commonly observed in financial data: process noise, measurement noise, and arrival noise. The erratic arrival of data (arrival noise) results in the neural network predictions being iterated into the future. Constraining the neural network to have a fixed point at the origin produces better iterated predictions and more stable results. The performance of constrained and unconstrained neural networks within the extended Kalman filter is demonstrated on "Quote" tick data from the $/DM exchange rate (1993-1995).
TL;DR: In this paper, the Kalman filter equations and state space partition are used to formulate an optimal tracking filter without such restrictions, and the input to the new filter are two consecutive measurements, and it is initialized by using the first available measurements and the error model correlation matrix.
Abstract: The existing algorithms for the design of digital filters with colored measurement noise involve a restriction on the dimension of the measurement error model. Kalman filter equations and state space partition are used to formulate an optimal tracking filter without such restrictions. The input to the new filter are two consecutive measurements, and it is initialized by using the first available measurements and the error model correlation matrix. Several examples illustrate the filter formulation and initialization.
05 Oct 1997
TL;DR: In this article, the proportional integral Kalman filter (PIKF) was used to improve the disturbance rejection property of the Kalman Filter-based controller, and the integral term of the PIKF allowed effective estimation and rejection of arbitrary disturbances.
Abstract: The proportional Kalman filter (PKF) is formulated with integral action and generalized to the proportional-integral Kalman filter (PIKF). The PIKF can be utilized to improve the disturbance rejection property of the Kalman filter-based controller. Through extensive simulations, as applied to the lightly damped flexible structure of the 1992 ACC Benchmark, we show that the integral term of the PIKF allows effective estimation and rejection of arbitrary disturbances. As a result, a single PIKF-based controller robustly achieves full loop transfer recovery even when perturbed by an unknown shaped disturbance.
02 Jul 1997
TL;DR: In this article, a modified extended Kalman (1960) filter is proposed to formulate a more accurate linearization of the underlying system, hence improving the state estimates, and an additional modification is suggested to further improve the performance.
Abstract: This paper examines a previously published modified extended Kalman (1960) filter. The modification provides better estimates than the extended Kalman filter under certain system conditions. The modification attempts to formulate a more accurate linearization of the underlying system, hence improve the state estimates. This paper investigates conditions where the algorithm outperforms the extended Kalman filter. The paper also suggests an additional modification which further improves the performance.
09 Nov 1997
TL;DR: In this article, extended Kalman filters are applied and optimized for deterministic parameter variations by integrating basis function networks into the common structure of the Kalman filter and it is shown that learning of nonlinear load or parameter characteristics becomes feasible by this measure.
Abstract: For high performance speed and position control of electrical drives, fast online identification is needed for time-varying inertia or load conditions in combination with adaptive controllers. In this paper extended Kalman filters are applied and optimized for deterministic parameter variations by integrating basis function networks into the common structure of the Kalman filter. It is shown that learning of nonlinear load or parameter characteristics becomes feasible by this measure and the performance of the extended Kalman filter can be improved.
10 Dec 1997
TL;DR: The proposed observer is a direct forward Euler discretization of the continuous-time observer given in Gautier et al. (1992) for uniformly observable systems.
Abstract: A discrete-time observer for a class of nonlinear systems is proposed. The proposed observer is a direct forward Euler discretization of the continuous-time observer given in Gautier et al. (1992) for uniformly observable systems. An extension of the observer design to a larger class of systems is also given.
04 Jun 1997
TL;DR: The (linear) information filter is introduced as an algebraic equivalent to the Kalman filter and the benefits of nonlinear information space are illustrated by considering a system involving both nonlinear state evolution and nonlinear observations.
Abstract: State and information space estimation methods used in both linear and nonlinear systems are compared. The (linear) information filter is introduced as an algebraic equivalent to the Kalman filter. Linear information space is extended to nonlinear information space by outlining the extended information filter. The algebraic equivalence of this filter to the extended Kalman filter and the benefits of nonlinear information space are illustrated by considering a system involving both nonlinear state evolution and nonlinear observations.
10 Dec 1997
TL;DR: An equivalent filter bank structure for multiple model adapative estimation (MMAE) is developed that uses the residual and state estimates from a single Kalman filters and linear transforms to produce equivalent residuals of a complete Kalman filter bank.
Abstract: An equivalent filter bank structure for multiple model adapative estimation (MMAE) is developed that uses the residual and state estimates from a single Kalman filter and linear transforms to produce equivalent residuals of a complete Kalman filter bank. The linear transforms, which are a function of the differences between the system models used by the various Kalman filters, are developed for modeling differences in the system input matrix, the output matrix, and the state transition matrix. The computational cost of this new structure is compared to the cost of the standard Kalman filter bank (SKFB) for each of these modeling differences. This structure is quite similar to the generalized likelihood ratio (GLR) structure, where the linear transforms can be used to compute the matched filters used in the GLR approach. This approach produces the best matched filters in the sense that they truly represent the time history of the residuals caused by a physically motivated failure model.
04 Jun 1997
TL;DR: In this paper, a nonlinear filter, referred to as the state dependent Riccati equation filter, is applied to the model of an induction machine to estimate the velocity and the rotor flux components of induction machine.
Abstract: A nonlinear filter, referred to as the state dependent Riccati equation filter, is applied to the model of an induction machine. The filter is used to estimate the velocity and the rotor flux components of induction machine.
09 Mar 1997
TL;DR: In this paper, a method of gain adjustment for an alpha-beta filter when data points are lost or when the tracking interval changes is presented, where the standard predictor-corrector forms of the filter equations are algebraically rearranged into two uncoupled difference equations; one equation for the smoothed position and one for smoothed velocity.
Abstract: Presents a method of gain adjustment for an alpha-beta filter when data points are lost or when the tracking interval changes. The steady-state position and velocity lags are first derived for a step acceleration input. The standard predictor-corrector forms of the filter equations are algebraically rearranged into two uncoupled difference equations; one equation for the smoothed position and one for smoothed velocity. The equations are then solved for the smoothed estimates using the method of undetermined coefficients. The solution is shown to consist of the input acceleration, transient terms and steady-state lags. The transient terms counteract the effects of the steady-state lags until the time determined by the filter's lag time. The steady-state lags are used for optimal adjustment of filter gains for aperiodic track conditions. For a varying track update interval, the filter gains which preserve a nominal periodic filter lag are derived. Such gain selection preserves the nominal lags associated with the constant tracking interval regardless of how the update interval varies. An example demonstrates the improvement in performance from using this approach.
08 Apr 1997
TL;DR: In this paper, the authors consider the fault isolation problem for linear time varying systems and prove that the isolation problem can be solved by generalized Luenberger's observer if and only if the detectability and the weak separability of fault signatures holds.
Abstract: In this paper we consider the fault isolation problem for the linear time varying systems. Our approach is based on characterization of the observability of LTV systems by Kalman's rank condition, which permits us to design fault detection filters, feeding also the derivatives of the inputs and the outputs. We prove, using a computable method, that the isolation problem can be solved by generalized Luenberger's observer if and only if the detectability and the weak separability of fault signatures holds.
01 Jul 1997
TL;DR: In this paper, the problem of stability analysis of the Extended Kalman Filter (EKF) when used as an observer for the class of non-linear discrete-time systems with linear output map is addressed.
Abstract: This paper deals with the problem of stability analysis of the Extended Kalman Filter (EKF) when used as an observer for the class of non linear discrete-time systems with linear output map. The proposed technique uses the Lyapnnov approach and evaluates the propagation errors due to the first order linearisation. Sufficient conditions to ensure robust stability of the modified gain EKF are established. One of the main features in this paper is how to design an instrumental matrix, namely R k in the paper. in order to enlarge domain of attraction and to improve the convergence significantly. To show performances and accuracy of the proposed algorithm, it will be applied to a physical process largely used in the literature.