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Showing papers on "Alpha beta filter published in 1994"


Journal ArticleDOI
TL;DR: In this paper, the most relevant methods to increase the robustness in both the stage of residual generation and residual evaluation are surveyed, including the generalized observer scheme, the robust parity space check, the unknown input and H ∞ observer scheme and the decorrelation filter.
Abstract: A prerequisite for the feasibility of the technique of observer-based fault detection and isolation (FDI) in dynamic systems is a satisfactory robustness with respect to modelling uncertainties. This paper surveys the most relevant methods to increase the robustness in both the stage of residual generation and residual evaluation. Among these methods are the generalized observer scheme, the robust parity space check, the unknown input and H ∞ observer scheme, the decorrelation filter, and the concept of adaptive threshold selection. It is pointed out that the unknown input observer concept, which provides perfect decoupling from the modelling errors or its optimal approximation with the aid of H ∞ techniques, constitutes a general framework of robust residual generation that generalizes and unifies numerous other approaches, among them the parity space and detection filter approach. It is further shown that this FDI method can even be applied to a certain class of nonlinear systems.

348 citations


Journal ArticleDOI
TL;DR: A new adaptive state estimation algorithm, namely adaptive fading Kalmanfilter (AFKF), is proposed to solve the divergence problem of Kalman filter and has been successfully applied to the headbox of a paper-making machine for state estimation.

210 citations


Journal ArticleDOI
TL;DR: This paper describes federated filter applications to integrated, fault-tolerant navigation systems, with emphasis on real-time implementation issues and numerical simulation results.
Abstract: This paper describes federated filter applications to integrated, fault-tolerant navigation systems, with emphasis on real-time implementation issues and numerical simulation results. The federated filter is a near-optimal estimator for decentralized, multi-sensor data fusion. Its decentralized estimation archi- tecture is based on theoretically sound information-sharing principles. A federated filter consists of one or more sensor- dedicated local filters, generally operating in parallel, plus a master combining filter. The master filter periodically com- bines (fuses) the local filter solutions to form the best total solution. Fusion generally occurs at a reduced rate, relative to the local measurement rates. The method can provide sig- nificant improvements in data throughput, fault tolerance, and system modularity. Numerical simulation results are pre- sented for an example multi-sensor navigation system. These results demonstrate federated filter performance characteristics in terms of estimation accuracy, fault-tolerance, and computation speed. This work was supported by the Defense Small Business Innovation

147 citations


Journal ArticleDOI
TL;DR: A detailed system-theoretic analysis is presented of the stability and steady-state behavior of the fine-to-coarse Kalman filter and its Riccati equation and of the new scale-recursive RicCati equation associated with it.
Abstract: An algorithm analogous to the Rauch-Tung-Striebel algorithm/spl minus/consisting of a fine-to-coarse Kalman filter-like sweep followed by a coarse-to-fine smoothing step/spl minus/was developed previously by the authors (ibid. vol.39, no.3, p.464-78 (1994)). In this paper they present a detailed system-theoretic analysis of this filter and of the new scale-recursive Riccati equation associated with it. While this analysis is similar in spirit to that for standard Kalman filters, the structure of the dyadic tree leads to several significant differences. In particular, the structure of the Kalman filter error dynamics leads to the formulation of an ML version of the filtering equation and to a corresponding smoothing algorithm based on triangularizing the Hamiltonian for the smoothing problem. In addition, the notion of stability for dynamics requires some care as do the concepts of reachability and observability. Using these system-theoretic constructs, the stability and steady-state behavior of the fine-to-coarse Kalman filter and its Riccati equation are analysed. >

134 citations


ReportDOI
02 May 1994
TL;DR: In this article, a navigation Kalman filter is developed according to the state space formulation of Kalman's original papers, which is particularly appropriate for the problem of vehicle position estimation.
Abstract: : The Kalman Filter has many applications in mobile robotics ranging from perception, to position estimation, to control. This report formulates a navigation Kalman Filter. That is, one which estimates the position of autonomous vehicles. The filter is developed according-to the state space formulation of Kalman's original papers. The state space formulation is particularly appropriate for the problem of vehicle position estimation. This filter formulation is fairly general. This generality is possible because the problem has been addressed

115 citations


Journal ArticleDOI
TL;DR: This result provides a dual representation of the well-known linear controller parameterization and gives a new insight into the observer design which may be used for the observer construction and robust observer design.
Abstract: With the aid of the factorization approach linear observers and their estimation error dynamics are parameterized. This result provides a dual representation of the well-known linear controller parameterization and gives a new insight into the observer design which may be used for the observer construction and robust observer design. >

78 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed to incorporate a neural network into the normal Kalman filter configuration such that the neural network provides the adaptive capability the filter needs, thus reducing the estimation error.
Abstract: Kalman filtering is a fundamental building block of most multiple-target tracking (MTT) algorithms. The other building block usually involves some type of data association schemes. Here it is proposed to incorporate a neural network into the normal Kalman filter configuration such that the neural network provides the adaptive capability the filter needs. As such the estimation error of the Kalman filter would be reduced, hence improving the MTT solution. Simulation results have shown that this claim is valid. >

55 citations


Proceedings ArticleDOI
27 Jun 1994
TL;DR: This construct of multiple streams of training examples allows a batch-like update to be performed without violating an underlying principle of Kalman training, and may be used to train robust controllers, i.e. controllers that perform well for a range of plants.
Abstract: Kalman-filter-based training has been shown to be advantageous in many training applications. By its nature, extended Kalman filter (EKF) training is realized with instance-by-instance updates, rather than by performing updates at the end of a batch of training instances or patterns. Motivated originally by the desire to be able to base an update an a collection of instances, rather than just one, we recognized that the simple construct of multiple streams of training examples allows a batch-like update to be performed without violating an underlying principle of Kalman training, vis. that the approximate error covariance matrix remain consistent with the updates that have actually been performed. In this paper, we present this construct and show how it may be used to train robust controllers, i.e. controllers that perform well for a range of plants. >

51 citations


Journal ArticleDOI
TL;DR: Strategies based on nonlinear distributed parameter state observers are presented to reconstruct the missing information in advanced process control of adsorption columns to minimize the computation effort in real-time applications.

42 citations


Journal ArticleDOI
TL;DR: In this paper, the identification problem of a system operating in a closed loop with an existing feedback controller is considered, where the closed-loop system is excited by a known excitation signal, and the resulting time histories of the closedloop system response and the feedback signal are measured.
Abstract: This paper considers the identification problem of a system operating in a closed loop with an existing feedback controller. The closed-loop system is excited by a known excitation signal, and the resulting time histories of the closed-loop system response and the feedback signal are measured. From the time history data, the algorithm computes the Markov parameters of a closed-loop observer, from which the Markov parameters of the individual open-loop plant, observer, and controller are recovered. A state-space model of the open-loop plant and the gain matrices for the controller and the observer are then realized. The results of the paper are demonstrated by an example using wind tunnel aircraft flutter test data.

42 citations


Journal ArticleDOI
TL;DR: In this article, Park and Rizzoni (1993) obtained closed-form expressions for detection filters; the structure of all detection filters for a given fault direction was defined, and the necessary conditions for the existence of the optimal detection filter were obtained, and a numerical solution technique was shown to be feasible by virtue of the uniqueness of the detection filter gains.
Abstract: Park and Rizzoni (1993) obtained closed-form expressions for detection filters; i.e. the structure of all detection filters for a given fault direction was defined. An important consequence of these results is that they permit the formation of the optimal detection filter problem, for optimization with respect to process and measurement noises. The necessary conditions for the existence of the optimal detection filter are obtained, and a numerical solution technique is shown to be feasible by virtue of the uniqueness of the detection filter gains. From an optimization point of view the problem can be regarded as optimal estimation with some structural constraints on the observer gain. This problem is solved for both the continuous-time and the discrete-time cases.

Journal ArticleDOI
TL;DR: In this article, the steady-state or asymptotic behavior of the Kalman filter is analyzed in terms of the phase portrait of a universal nonlinear dynamical system.
Abstract: The main purpose of this paper is to address a fundamental open problem in linear filtering and estimation, namely, what is the steady-state or asymptotic behavior of the Kalman filter, or the Kalman gain, when the observed stationary stochastic process is not generated by a finite-dimensional stochastic system, or when it is generated by a stochastic system having higher-dimensional unmodeled dynamics. For example, some time ago Kalman pointed out that the usual positivity conditions assumed in the classical situation are not in fact necessary for the Kalman filter to converge. Using a "fast filtering" algorithm, which incorporates the statistics of the observation process as initial conditions for a dynamical system, this question is analyzed in terms of the phase portrait of a "universal" nonlinear dynamical system. This point of view has additional advantages as well, since it enables one to use the theory of dynamical systems to study the sensitivity of the Kalman filter to (small) changes in initial conditions; e.g., to changes in the statistics of the underlying process. This is especially important since these statistics are often either approximated or estimated. In this paper, for a scalar observation process, necessary and sufficient conditions for the Kalman filter to converge are derived using methods from stochastic systems and from nonlinear dynamics---especially the use of stable, unstable, and center manifolds. It is also shown that, in nonconvergent cases, there exist periodic points of every period $p$, $p\ge 3$ that are arbitrarily close to initial conditions having unbounded orbits, rigorously demonstrating that the Kalman filter can also be "sensitive to initial conditions."

Journal ArticleDOI
Pyung Hun Chang1, Jeong W. Lee1
TL;DR: In this paper, the estimation problem of states and their derivatives for the time delay control (TDC), a robust control technique for nonlinear systems, is addressed, and an observer design method is presented.

Proceedings ArticleDOI
G.S. Christiansen1
28 Nov 1994
TL;DR: This paper demonstrates the equivalence between the timing loop used in the partial response maximum likelihood (PRML) disk-drive channel and a modified Kalman filter, which is shown to reach a steady-state gain that corresponds to the timingloop when in its steady- state tracking mode.
Abstract: This paper demonstrates the equivalence between the timing loop used in the partial response maximum likelihood (PRML) disk-drive channel and a modified Kalman filter. The Kalman filter is shown to reach a steady-state gain that corresponds to the timing loop when in its steady-state tracking mode. The dependence of the steady-state gain on the noise and physical properties of the loop is investigated. The timing loop is then optimized using the properties of the Kalman filter.

Proceedings ArticleDOI
21 Mar 1994
TL;DR: In this article, the use of a Kalman filter for a fully active road vehicle suspension system is discussed, where the usual detectability and stabilizability conditions must be satisfied and all the noise signals must be white.
Abstract: Concerns the use of a Kalman filter for a fully active road vehicle suspension system. The usual detectability and stabilizability conditions must be satisfied and all the noise signals must be white. The detectability condition is obeyed by using the filtered white noise road input. The use of this input, as opposed to the frequency limited integrated white noise input, is justified by r.m.s. simulation results. The stabilizability condition is obeyed by having a spring in parallel with the actuator, which is also of practical significance for suspending the static load, hence decreasing actuator power consumption. The description of the noise processes as bandlimited white noise models a worst case scenario as all of the noise signal is present in the operational bandwidth of the closed loop system. The closed loop system using the Kalman filter was simulated and compared to that using full state feedback. Results using the Kalman filter were encouraging, showing a small degradation in performance compared to the nominal system. Interesting results were obtained for road roughnesses different from those for which it was designed. There was a very small degradation in performance, which indicates that there seems to be no need to adapt the Kalman filter gain for different road conditions. Therefore, the potential improvements of using this system, as opposed to the usual LQG method using full state feedback, are enormous. However, it was found that the use of the Kalman filter led to a marked degradation in the stability margins of the system.< >

Proceedings ArticleDOI
05 Sep 1994
TL;DR: In this paper, a comparison of performances and characteristics of a nonlinear observer and observation algorithms based on the Kalman filter for induction motor rotor flux estimation, inserted in a field oriented control scheme, is presented.
Abstract: The paper presents a comparison of performances and characteristics of a nonlinear observer and observation algorithms based on the Kalman filter for induction motor rotor flux estimation, inserted in a field oriented control scheme. The construction of the considered algorithms is described in detail, and the different design issues are explained. For fair comparison the same measurements are assumed available to both deterministic and stochastic estimators, and the same controller parameters are used in simulation. The performances of the estimators are compared either in terms of observation errors during transient and steady state operations either in terms of computational complexity in on-line implementation. >

Proceedings ArticleDOI
29 Jun 1994
TL;DR: A general decentralised Kalman filter that requires no fusion center yet allows the different estimators to employ distributed models; minimizes communication with respect to message size and topology; requires no explicit knowledge of the transformations between the estimators; and reduces to previous results when appropriately constrained.
Abstract: This paper considers a general decentralised Kalman filter, unique because it: requires no fusion center yet allows the different estimators to employ distributed models; minimizes communication with respect to message size and topology; requires no explicit knowledge of the transformations between the estimators; and reduces to previous results when appropriately constrained.

Journal ArticleDOI
01 Nov 1994
TL;DR: In this paper, the authors presented a state observer algorithm based on the recursive model of the current and voltage generation process in a three-phase power system in which the orthogonal phasors are used as the model state variables.
Abstract: The paper presents the synthesis of a state observer which can be applied to estimation of the current and voltage symmetrical components in a three-phase electrical network. The state observer algorithm is based on the recursive model of the current and voltage generation process in a three-phase power system in which the orthogonal phasors are used as the model state variables. The synthesis of the state observer is shown under the assumption that the higher harmonics as well as the decaying DC offset may be present in the symmetrical component phasors. The state observer presented can be used as the fast current and voltage symmetrical component estimator in digital power protection systems. The calculation example included shows the basic properties of the observer in such an application. >

Journal ArticleDOI
TL;DR: A survey of dynamic system health monitoring schemes that are based on the theory of linear and nonlinear observer design is presented in this article, where a robust fault detection scheme based on recent developments in the detection filter scheme is also presented.

Proceedings ArticleDOI
Fred Daum1
06 Jul 1994
TL;DR: A new exact recursive filter is derived for nonlinear estimation problems that includes the Kalman filter as a special case and has a computational complexity that is comparable to theKalman filter.
Abstract: A new exact recursive filter is derived for nonlinear estimation problems. The new nonlinear theory includes the Kalman filter as a special case. This filter is practical to implement in real- time applications, and it has a computational complexity that is comparable to the Kalman filter. The measurements are made in discrete time, but the random process to be estimated evolves in continuous time.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Journal ArticleDOI
TL;DR: In this paper, the authors define robustness as the ability of the Global Positioning System/Inertial Navigation System (GPS-INS) Kalman filter to cope with adverse environments and input conditions, to successfully identify such conditions and to take evasive action.
Abstract: Filter robustness is defined herein as the ability of the Global Positioning System/Inertial Navigation System (GPS-INS) Kalman filter to cope with adverse environments and input conditions, to successfully identify such conditions and to take evasive action. The formulation of two such techniques for a cascaded GPS-INS Kalman filter integration is discussed This is an integration in which the navigation solution from a GPS receiver is used as a measurement in the filter to estimate inertial errors and instrument biases. The first technique presented discusses the handling of GPS position biases. These are due to errors in the GPS satellite segment, and are known to be unobservable. They change levels when a satellite constellation change occurs, at which point they introduce undesirable filter response transients. A method of suppressing these transients is presented. The second technique presented deals with the proper identification of the filter measurement noise. Successful formulation of the noise statistics is a factor vital to the healthy estimation of the filter gains and operation. Furthermore, confidence in the formulation of these statistics can lead to the proper screening and rejection of bad data in the filter. A method of formulating the filter noise statistics dynamically based on inputs from the GPS and the INS is discussed. >

Proceedings ArticleDOI
12 Apr 1994
TL;DR: The authors present an algorithm for power system state estimation based on the square root filtering technique and the estimator proposed is decoupled in nature due to modifications made in the measurement equations resulting in a new observation model.
Abstract: The proper analysis and successful operation of a power system implies a reliable estimate of its state. As a result state estimation (SE) is nowadays considered as the heart of modern control centers. Several dynamic state estimation algorithms based on the extended Kalman filtering theory (EKF) have been proposed in the literature but, as has been reported, numerical problems may arise in its implementation in practice. To circumvent the problems inherent to the Kalman filter algorithm the authors present in this paper an algorithm for power system state estimation based on the square root filtering technique. The estimator proposed is decoupled in nature due to modifications made in the measurement equations resulting in a new observation model. >

Proceedings ArticleDOI
06 Oct 1994
TL;DR: The Nonlinear Information Filter derived from the Extended Kalman Filter is decentralized and distributed, to give the Distributed and Decentralized Non linear Information.
Abstract: In this paper the Nonlinear Information Filter is derived from the Extended Kalman Filter. A nonlinear system is considered. Linearizing the state and observation equations, a linear estimator which keeps track of total state estimates is conceived; the Extended Kalman Filter. The linearized parameters and filter equations are expressed in information space. This gives a filter that predicts and estimates information about nonlinear state parameters given nonlinear observations and nonlinear system dynamics. The Nonlinear Information Filter derivation is contrasted to that of the Linear Information filter. Pitfalls of a naive extension of the later to the former are thus identified. Furthermore, the Nonlinear Information filter is decentralized and distributed, to give the Distributed and Decentralized Nonlinear Information. Application is real decentralized data fusion and distributed control is proposed. Specifically, realtime distributed/decentralized control of a navigating, modular wheeled robot is considered.

Book ChapterDOI
TL;DR: The Kalman filter is a linear filtering algorithm developed to solve estimation and control problems in engineering such as monitoring the position and velocity of a satellite orbiting the earth from signals received at ground tracking stations.
Abstract: Publisher Summary This chapter discusses the application of the Kalman filter to computational problems in statistics The Kalman filter is a linear filtering algorithm developed to solve estimation and control problems in engineering such as monitoring the position and velocity of a satellite orbiting the earth from signals received at ground tracking stations The chapter illustrates its use to evaluate a Gaussian likelihood where the observational error process is Gaussian serially correlated noise The problem of modeling human biological rhythm data is discussed in this chapter Core temperature data is an often studied biological rhythm used to estimate the properties of the human biological clock The sequential manner in which the Kalman filter can be used to evaluate Gaussian likelihoods has led to an efficient technique for handling missing data in a time series estimation problem The Kalman filter can also be used to compute posterior densities for Bayesian statistical models The chapter demonstrates the use of the Kalman filter for evaluating a Gaussian likelihood as part of the expectation and maximization (EM) algorithm

Journal ArticleDOI
01 Jan 1994
TL;DR: A low-order Kalman filter is designed and analyzed for the initial alignment of a ring laser gyro strapdown inertial system that results in a substantially lighter computer burden with a little significant reduction in system accuracy.
Abstract: The use of a full-order Kalman filter for the alignment process of an inertial navigation system (INS) imposes an unacceptable burden on computers. In this paper we intend to design and analyze a low-order Kalman filter for the initial alignment of a ring laser gyro strapdown inertial system that results in a substantially lighter computer burden with a little significant reduction in system accuracy.

Proceedings ArticleDOI
27 Jun 1994
TL;DR: This paper shows how a neural network can augment a Kalman filter by estimating initial conditions and unknown system parameters, and real-time operation can take place using the neural network without the computational requirements of multiple Kalman filters.
Abstract: This paper shows how a neural network can augment a Kalman filter by estimating initial conditions and unknown system parameters. The neural network training is done off-line, using an approach similar to multiple Kalman filters. After off-line training, real-time operation can take place using the neural network without the computational requirements of multiple Kalman filters. An example shows how the general regression neural network (GRNN) augments a Kalman filter for terminal guidance of an interceptor missile. >

Proceedings ArticleDOI
29 Jun 1994
TL;DR: The filter performance is quantified by the actual one-step predictor error covariance, and the divergent behavior of the filter is investigated through this quantity.
Abstract: Presents the divergence analysis of the Kalman filter under incorrect noise covariances for linear periodic discrete-time systems. The filter performance is quantified by the actual one-step predictor error covariance, and the divergent behavior of the filter is investigated through this quantity. The investigation results provide useful insights in the divergent behavior of the Kalman filter under incorrect noise covariances for linear periodic discrete-time systems.

Journal ArticleDOI
TL;DR: This paper investigates the parallel implementation of tracking Kalman filters in both 2- and 3-D frames onto a range of transputer topologies to enable practical realisations and presents real-time implementation results.
Abstract: For target tracking applications, a Kalman filter is generally used to estimate the kinematic components of a manoeuvring target (position, velocity and acceleration) from noisy measurements. The tracking algorithm is selected according to a trade-off between its performance and real-time computational requirements when choosing the level of complexity of the model. According to the application, either a linear or a nonlinear Kalman filter algorithm can be used to track manoeuvring targets. However, although excellent accuracy estimates can be achieved with any chosen algorithm, it requires a huge amount of calculation thus making real-time processing impossible.This paper investigates the parallel implementation of tracking Kalman filters (EKF, GRF, LDKF and MGEKF) in both 2- and 3-D frames onto a range of transputer topologies to enable practical realisations. The partitioning strategies are highlighted, real-time implementation results are presented, and the relative speedup and efficiency are calculat...

Journal ArticleDOI
TL;DR: A key feature of the filter is replaced with a principle that uses a more global approach through the utilization of a set of preselected regimes, and a compromise between the different error models is found through the use of a weighting function that reflects the 'closeness' of the error model to the correct model.
Abstract: Data assimilation via the extended Kalman filter can become problematic when the assimilating model is strongly nonlinear, primarily in connection with sharp, "switchlike" changes between different regimes of the system. The filter seems too inert to follow those switches quickly enough, a fact that can lead to a complete failure when the switches occur often enough. In this paper we replace the key feature of the filter, the use of local linearity for the error model update, with a principle that uses a more global approach through the utilization of a set of preselected regimes. The method uses all regime error models simultaneously. Being mutually incompatible, a compromise between the different error models is found through the use of a weighting function that reflects the 'closeness' of the error model to the correct model. To test the interactive Kalman filter a series of numerical experiments is performed using the double-well system and the well-known Lorenz system, and the results are compared to the extended Kalrnan filter. It turns out that, depending on the set of preselected regimes, the performance is worse than, comparable to, or better than that of the extended Kalman filter.

Proceedings ArticleDOI
14 Dec 1994
TL;DR: In this paper, an algorithm for the state estimation of a class of bilinear systems in the presence of noise is proposed, which is obtained paralleling two Kalman filters: each of them estimates a part of the state, considering the other part as known time-varying parameters.
Abstract: In this paper an algorithm for the state estimation of a class of bilinear systems in the presence of noise is proposed. The systems considered are such that a suitable partition of the state vector into two parts allows a bilinear representation of the system. The proposed algorithm is obtained paralleling two Kalman filters: each of them estimates a part of the state, considering the other part as known time-varying parameters. >