Showing papers on "Alpha beta filter published in 2012"
Book•
07 Feb 2012
TL;DR: Probability and Random Variables: A Review, and more on Modeling: Integration of Noninertial Measurements Into INS.
Abstract: PART 1: RANDOM SIGNALS BACKGROUND Chapter 1 Probability and Random Variables: A Review Chapter 2 Mathematical Description of Random Signals Chapter 3 Linear Systems Response, State-space Modeling and Monte Carlo Simulation PART 2: KALMAN FILTERING AND APPLICATIONS Chapter 4 Discrete Kalman Filter Basics Chapter 5 Intermediate Topics on Kalman Filtering Chapter 6 Smoothing and Further Intermediate Topics Chapter 7 Linearization, Nonlinear Filtering and Sampling Bayesian Filters Chapter 8 the "Go-Free" Concept, Complementary Filter and Aided Inertial Examples Chapter 9 Kalman Filter Applications to the GPS and Other Navigation Systems APPENDIX A. Laplace and Fourier Transforms APPENDIX B. The Continuous Kalman Filter
697 citations
TL;DR: In this paper, a simple and intuitive derivation of the Kalman filter is presented, with the aim of teaching this useful tool to students from disciplines that do not require a strong mathematical background.
Abstract: This article provides a simple and intuitive derivation of the Kalman filter, with the aim of teaching this useful tool to students from disciplines that do not require a strong mathematical background. The most complicated level of mathematics required to understand this derivation is the ability to multiply two Gaussian functions together and reduce the result to a compact form.
288 citations
TL;DR: The simulation results show that the proposed novel type-2 fuzzy membership function with the extended Kalman filter has noise rejection property, which is faster and more efficient than the particle swarm optimization method.
Abstract: In this paper, the use of extended Kalman filter for the optimization of the parameters of type-2 fuzzy logic systems is proposed. The type-2 fuzzy logic system considered in this study benefits from a novel type-2 fuzzy membership function which has certain values on both ends of the support and the kernel, and uncertain values on other parts of the support. To have a comparison of the extended Kalman filter with other existing methods in the literature, particle swarm optimization and gradient descent-based methods are used. The proposed type-2 fuzzy neuro structure is tested on different noisy input-output data sets, and it is shown that extended Kalman filter has a better performance as compared to the gradient descent-based methods. Although the performance of the proposed method is comparable with the particle swarm optimization method, it is faster and more efficient than the particle swarm optimization method. Moreover, the simulation results show that the proposed novel type-2 fuzzy membership function with the extended Kalman filter has noise rejection property. Kalman filter is also used to train the parameters of type-2 fuzzy logic system in a feedback error learning scheme. Then, it is used to control a real-time laboratory setup ABS and satisfactory results are obtained.
132 citations
TL;DR: A novel method for adaptive setting of the parameter in the unscented Kalman filter for state estimation of nonlinear stochastic dynamic systems with a special focus on the scaling parameter of the filter is proposed.
Abstract: This technical note deals with the unscented Kalman filter for state estimation of nonlinear stochastic dynamic systems with a special focus on the scaling parameter of the filter. Its standard choice is analyzed and its impact on the estimation quality is discussed. On the basis of the analysis, a novel method for adaptive setting of the parameter in the unscented Kalman filter is proposed. The results are illustrated in a numerical example.
126 citations
TL;DR: A residual generator based on the Kalman filter is proposed, which can be used to detect if a failure occurs and two Kalman filters are designed to diagnose the fault type.
Abstract: In this paper, we consider the fault diagnosis and fault-tolerant problem for a linear drive system subject to system noise. First, we propose a residual generator based on the Kalman filter, which can be used to detect if a failure occurs. Second, two Kalman filters are designed to diagnose the fault type. Third, when a fault is diagnosed, the fault-tolerant control is used to accommodate this failure. Finally, the proposed method is tested in a real linear drive system.
115 citations
TL;DR: The particle Kalman filter (PKF) as mentioned in this paper is an approximation of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function.
Abstract: This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter, but is different from it in that the standard weight-type correction in the particle filter is complemented by the Kalman-type correction with the associated covariance matrices in the Gaussian mixture. The authors show that this filter is an algorithm in between the Kalman filter and the particle filter, and therefore is referred to as the particle Kalman filter (PKF).In the PKF, the solution of a nonlinear filtering problem is expressed as the weighted average of an “ensemble of Kalman filters” operating in parallel. Running an ensemble of Kalman filters is, however, computationally prohibitive for realistic atmospheric and oceanic data assimilation problems. For this reason, the authors consider the construction of the PKF through an “ensemble” of ensemble Kalm...
110 citations
TL;DR: A reduced-order position observer with stator-resistance adaptation is proposed for motion-sensorless permanent-magnet synchronous motor drives, and an observer gain design that makes the observer robust is proposed.
Abstract: A reduced-order position observer with stator-resistance adaptation is proposed for motion-sensorless permanent-magnet synchronous motor drives. A general analytical solution for the stabilizing observer gain and stability conditions for the stator-resistance adaptation are derived. Under these conditions, the local stability of the position and stator-resistance estimation is guaranteed at every operating point except the zero frequency, if other motor parameters are known. Furthermore, the effect of inaccurate model parameters on the local stability of the position estimation is studied, and an observer gain design that makes the observer robust is proposed. The proposed observer is experimentally tested using a 2.2-kW motor drive; stable operation at very low speeds under different loading conditions is demonstrated.
103 citations
TL;DR: In this paper, several Global Positioning System/inertial navigation system (GPS/INS) algorithms are presented using both extended Kalman filter (EKF) and unscented Kalman Filter (UKF), and evaluated with respect to performance and complexity.
Abstract: In this paper, several Global Positioning System/inertial navigation system (GPS/INS) algorithms are presented using both extended Kalman filter (EKF) and unscented Kalman filter (UKF), and evaluated with respect to performance and complexity. The contributions of this study are that attitude estimates are compared with independent measurements provided by a mechanical vertical gyroscope using 23 diverse sets of flight data, and that a fundamental difference between EKF and UKF with respect to linearization is evaluated.
98 citations
03 Mar 2012
TL;DR: In this paper, the Daum filter, an exact nonlinear filter, the unscented Kalman filter, and the particle filter were reviewed for the solution to the first problem. But the results of the analysis were limited.
Abstract: Model-based prognostics approaches use domain knowledge about a system and its failure modes through the use of physics-based models Model-based prognosis is generally divided into two sequential problems: a joint state-parameter estimation problem, in which, using the model, the health of a system or component is determined based on the observations; and a prediction problem, in which, using the model, the state-parameter distribution is simulated forward in time to compute end of life and remaining useful life The first problem is typically solved through the use of a state observer, or filter The choice of filter depends on the assumptions that may be made about the system, and on the desired algorithm performance In this paper, we review three separate filters for the solution to the first problem: the Daum filter, an exact nonlinear filter; the unscented Kalman filter, which approximates nonlinearities through the use of a deterministic sampling method known as the unscented transform; and the particle filter, which approximates the state distribution using a finite set of discrete, weighted samples, called particles Using a centrifugal pump as a case study, we conduct a number of simulation-based experiments investigating the performance of the different algorithms as applied to prognostics
89 citations
TL;DR: In this article, the authors examined the relation of the SEIK filter to ensemble square root filters in detail, and they showed that SEIK is indeed an ensemble square-root Kalman filter.
Abstract: In recent years, several ensemble-based Kalman filter algorithms have been developed that have been classified as ensemble square root Kalman filters. Parallel to this development, the singular ‘‘evolutive’’ interpolated Kalman (SEIK) filter has been introduced and applied in several studies. Some publications note that the SEIK filter is an ensemble Kalman filter or even an ensemble square root Kalman filter. This study examines the relation of the SEIK filter to ensemble square root filters in detail. It shows that the SEIK filter is indeed an ensemble square root Kalman filter. Furthermore, a variant of the SEIK filter, the error subspace transform Kalman filter (ESTKF), is presented that results in identical ensemble transformations to those of the ensemble transform Kalman filter (ETKF), while having a slightly lower computational cost. Numerical experiments are conducted to compare the performance of three filters (SEIK, ETKF, and ESTKF) using deterministic and random ensemble transformations. The results show better performance for the ETKF and ESTKF methods over the SEIK filter as long as this filter is not applied with a symmetric square root. The findings unify the separate developments that have been performed for the SEIK filter and the other ensemble square root Kalman filters.
89 citations
TL;DR: It is shown that the Derivative-free nonlinear Kalman Filter is faster than the rest of the nonlinear filters while also succeeding accurate, in terms of variance, state estimates.
TL;DR: A novel derivation of the Kalman filter using Newton's method for root finding is described, quite general as it can also be used to derive a number of variations of theKalman filter, including recursive estimators for both prediction and smoothing, estimators with fading memory, and the extended Kalman Filter for nonlinear systems.
Abstract: In this paper, we discuss the Kalman filter for state estimation in noisy linear discrete-time dynamical systems. We give an overview of its history, its mathematical and statistical formulations, and its use in applications. We describe a novel derivation of the Kalman filter using Newton's method for root finding. This approach is quite general as it can also be used to derive a number of variations of the Kalman filter, including recursive estimators for both prediction and smoothing, estimators with fading memory, and the extended Kalman filter for nonlinear systems.
31 Aug 2012
TL;DR: The Kalman filter arose out of R.E. Kalman's interest in applying the concept of state vectors to the Wiener filtering problem, and quickly became an essential component of modern control systems theory and practice.
Abstract: The Kalman filter arose out of R.E. Kalman's interest in applying the concept of state vectors to the Wiener filtering problem. The success of this method was evident in early applications to trajectory estimation and control of spacecraft; it was so successful, in fact, that the Kalman filter quickly became an essential component of modern control systems theory and practice. This initial success led to the propagation of Kalman-filtering ideas to other scientific disciplines, within which the methodology was adapted to suit numerous state–space oriented problems. Kalman filtering (of spatial data) is still an active area of research in the atmospheric and oceanic sciences.
TL;DR: In this article, the robust Kalman filtering problem for discrete-time nonlinear systems with norm-bound parameter uncertainties is studied and a Riccati equation is derived in the presence of both the parameter uncertainties and the linearization errors.
TL;DR: In this article, a pair of positive observers with state-bounding feature is proposed to estimate the state of positive systems at all times, and the observer matrices can be obtained easily through the solutions of a set of linear matrix inequalities (LMIs).
Abstract: SUMMARY
This paper is concerned with the problem of positive observer synthesis for positive systems with both interval parameter uncertainties and time delay. Conventional observers may no longer be applicable for such kind of systems due to the positivity constraint on the observers, and they only provide an estimate of the system state in an asymptotic way. A pair of positive observers with state-bounding feature is proposed to estimate the state of positive systems at all times in this paper. A necessary and sufficient condition for the existence of desired observers is first established, and the observer matrices can be obtained easily through the solutions of a set of linear matrix inequalities (LMIs). Then, to reduce the error signal between the system state and its estimates, an iterative LMI algorithm is developed to compute the optimized state-bounding observer matrices. Finally, a numerical example is presented to show the effectiveness and applicability of the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.
TL;DR: The problem of simultaneously estimating the state and the fault of linear stochastic discrete-time varying systems with unknown inputs is studied and the Optimal three-stage Kalman Filter (OThSKF) is proposed.
Abstract: The paper studies the problem of simultaneously estimating the state and the fault of linear stochastic discrete-time varying systems with unknown inputs. The fault and the unknown inputs affect both the state and the output. However, if the dynamical evolution models of the fault and the unknown inputs are available the filtering problem will be solved by the Optimal three-stage Kalman Filter (OThSKF). The OThSKF is obtained after decoupling the covariance matrices of the Augmented state Kalman Filter (ASKF) using a three-stage U–V transformation. Nevertheless, if the fault and the unknown inputs models are not perfectly known the Robust three-stage Kalman Filter (RThSKF) will be applied to give an unbiased minimum-variance estimation. Finally, a numerical example is given in order to illustrate the proposed filters.
TL;DR: Fourier- Hermite Kalman filters are a new class of Gaussian filters based on expansion of nonlinear functions with the Fourier-Hermite series in same way as the traditional extended Kalman filter is based on the Taylor series.
Abstract: In this note, we shall present a new class of Gaussian filters called Fourier-Hermite Kalman filters. Fourier-Hermite Kalman filters are based on expansion of nonlinear functions with the Fourier-Hermite series in same way as the traditional extended Kalman filter is based on the Taylor series. The first order truncation of the Fourier-Hermite series gives the previously known statistically linearized filter.
TL;DR: In this article, an extended complex Kalman filter (ECKF) based procedure is formulated and assessed, which redefines the state variable representation to directly estimate the modal parameters instead of using the existing polynomial rooting approach.
Abstract: Ringdown detection methods like Kalman filter and Prony analysis have been developed to aid transmission operators to track lightly-damped inter-area oscillations. Kalman filter detection is dependent on a priori system knowledge and is designed to monitor the dominant mode. The objective of this paper is to extend Kalman filter to track multiple modes. Thus, extended complex Kalman filter (ECKF) based procedure is formulated and assessed. While retaining the recursive Kalman filter engine, the proposed method redefines the state variable representation to directly estimate the modal parameters instead of using the existing polynomial rooting approach. It also integrates Hankel singular value decomposition (HSVD) to provide better estimates of the initial conditions.
TL;DR: In this article, a dynamic observer-based robust controller that facilitates the acquisition of information used for fault detection (FD) purpose in feedback control systems has been proposed, where the combination of observer states is used to generate a residual signal to detect faults and a convex fault detector condition with some parameter matrices fixed is developed for guaranteeing the H− performance used to measure the fault sensitivity.
Abstract: This study is concerned with the design of dynamic observer-based robust controller that also facilitates the acquisition of information used for fault detection (FD) purpose in feedback control systems. Through introducing a weighting matrix, the combination of observer states is utilised to generate a residual signal to detect faults. The first technical contribution is to construct a new linearising change-of-variables that is able to convert the dynamic observer-based controller design problem into linear matrix inequality-based optimisation problem. The second one is to show that the proposed dynamic observer-based controller can achieve a better H∞ performance compared with the existing static (Luenberger) observer-based controller design approaches. Finally, via the simple residual structure, a convex fault detector design condition with some parameter matrices fixed is developed for guaranteeing the H− performance used to measure the fault sensitivity. An F-18 aircraft model is given to show the satisfactory FD performance and control performance.
TL;DR: In this paper, a reduced-order nonlinear observer is developed to estimate the distance from a moving camera to a feature point on a static object, where full velocity and linear acceleration feedback of the calibrated camera is provided.
TL;DR: An algorithm based on centroid weighted Kalman filter (CWKF) for object tracking is proposed and tracking experiments show that the algorithm can detect effectively moving objects and at the same time it can quickly and accurately track moving objects with good robustness.
TL;DR: The paper develops a sequential Monte Carlo implementation of the Bernoulli filter and the reward based on an information theoretic criterion to solve the autonomous bearings-only tracking problem with observer control.
Abstract: The context is autonomous bearings-only tracking of a single appearing/disappearing target in the presence of detection uncertainty (false and missed detections) with observer control. The optimal tracking method for this problem in the sequential Bayesian estimation framework is the Bernoulli filter. Observer control is based on previously acquired measurements and is formulated as a partially observable Markov decision process (POMDP) where future actions are ranked according to their associated reward. The paper develops a sequential Monte Carlo implementation of the Bernoulli filter and the reward based on an information theoretic criterion.
01 Dec 2012
TL;DR: In this article, a modified Sage-Husa adaptive Kalman filter (SHAKF) was used to denoise the fiber optic gyroscope signal using a first order auto regressive (AR) model and used the coefficients of the model to initialize the transition matrix of SHAKF.
Abstract: Fiber Optic Gyroscope (FOG) is a key component in Inertial Navigation System. The performance of FOG degrades due to different types of random errors in the measured signal. Although Kalman filter and its variants like Sage-Husa Kalman filters are being used to denoise the Gyroscope signal the performance of Kalman filter is limited by the initial values of measurement and process noise covariance matrix, and transition matrix. To address this problem, this paper uses modified Sage-Husa adaptive Kalman filter to denoise the FOG signal. In this work, the random error of fiber optic gyroscope is modeled using a first order auto regressive (AR) model and used the coefficients of the model to initialize the transition matrix of Sage-Husa Adaptive Kalman filter. Allan variance analysis is used to quantify the random errors of the measured and denoised signal. The performance of proposed algorithm is compared with conventional Kalman filter and the simulation results show that the modified Sage-Husa adaptive Kalman filter (SHAKF) algorithm outperforms the conventional Kalman filter technique while denoising FOG signal.
TL;DR: A new adaptive fuzzy sliding mode (AFSM) observer is proposed which can be used for a class of MIMO nonlinear systems and the performance of the observer shows its effectiveness in the real world.
Abstract: In this paper, a new adaptive fuzzy sliding mode (AFSM) observer is proposed which can be used for a class of MIMO nonlinear systems. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. In this method, a fuzzy system is designed to estimate the nonlinear behavior of the observer. The output of fuzzy rules are tuned adaptively, based on the observer error. The output connection matrix is used to combine the observer errors of individual subsystems. A robust term, which is designed based on the sliding mode theory, is added to the observer to compensate the fuzzy estimation error. The estimation error bound is adjusted by an adaptive law. The main advantage of the proposed observer is that, unlike many of the previous works, the measured outputs is not limited to the first entries of a canonical-form state vector. The proposed observer estimates the closed-loop state tracking error asymptotically, provided that the output gain matrix includes Hurwitz coefficients. The chattering is eliminated by using boundary layers around the sliding surfaces and the observer convergence is proved using a Lyapunov-based approach. The proposed method is applied on a real multilink robot manipulator. The performance of the observer shows its effectiveness in the real world.
TL;DR: A robust circle criterion observer is designed and applied to neural mass models and it is shown how to apply the observer to estimate the mean membrane potential of neuronal populations of a popular single cortical column model from the literature.
TL;DR: In this paper, a model of the car containing fifteen degrees of freedom has been developed, and the observer algorithm that combines the equations of motion and the integrator has been reformulated so that duplication of the problem size is avoided, in order to improve efficiency.
Abstract: This work is part of a project aimed to develop automotive real-time observers based on detailed nonlinear multibody models and the extended Kalman filter (EKF). In previous works, a four-bar mechanism was studied to get insight into the problem. Regarding the formulation of the equations of motion, it was concluded that the state-space reduction method known as matrix-R is the most suitable one for this application. Regarding the sensors, it was shown that better stability, accuracy and efficiency are obtained as the sensored magnitude is a lower derivative and when it is a generalized coordinate of the problem. In the present work, the automotive problem has been addressed, through the selection of a Volkswagen Passat as a case-study. A model of the car containing fifteen degrees of freedom has been developed. The observer algorithm that combines the equations of motion and the integrator has been reformulated so that duplication of the problem size is avoided, in order to improve efficiency. A maneuver of acceleration from rest and double lane change has been defined, and tests have been run for the “prototype,” the “model” and the “observer,” all the three computational, with the model having 100 kg more than the prototype. Results have shown that good convergence is obtained for position level sensors, but the computational cost is high, still far from real-time performance.
TL;DR: A flexible and computationally efficient method for solving the spacecraft attitude using only an inexpensive and reliable magnetometer would be a useful option for satellitemissions, particularly those with modest budgets.
Abstract: Determining spacecraft attitude in real time using only magnetometer data presents a challenging filtering problem. A flexible and computationally efficient method for solving the spacecraft attitude using only an inexpensive and reliablemagnetometerwould be a useful option for satellitemissions, particularly thosewithmodest budgets. The primary challenge is that magnetometers only instantaneously resolve two axes of the spacecraft attitude. Typically, magnetometers are used in conjunction with other sensors to resolve all three axes. However, by using a filter over an adequately long orbit arc, the magnetometer data can yield full attitude, and in real time. The methodpresented solves the problemusing a two-step extendedKalmanfilter. In thefirst step, themagneticfield data are filtered to obtain the magnetic field derivative vector, which is combined with the magnetic field vector in the second step to fully resolve the attitude. A baseline scenario is developed, and a parametric study is conducted using the parameters of interest.
02 Jul 2012
TL;DR: The Kalman Filter is implemented for Inertial Measurement Unit (IMU) on the ATMega8535 and a pipeline configuration is recommended if the control algorithm needs more space in a sampling time.
Abstract: The Kalman Filter is very useful in prediction and estimation. In this paper, the Kalman Filter is implemented for Inertial Measurement Unit (IMU) on the ATMega8535. The sensors used in this system are accelerometer MMA7260QT and gyroscope GS-12. The system chooses the arbitrary sampling time and then it is evaluated for possible using smaller value. As the Kalman Filter operation needs matrix calculation, the formula is converted into several ordinary equations. The parameter being investigated in this paper is measurement covariance matrix. This parameter influences the way the Kalman Filter responses to noise. Bigger value makes the Kalman Filter less sensitive to noise and the estimation is too smooth, thus it does not give real angle estimation. Using smaller value makes the Kalman Filter more sensitive to noise. This makes the estimated angle still suffers from noise and it is likely that the Kalman Filter is useless. This paper recommends 0.0001 to 0.001 for the measurement covariance noise parameter. This paper also recommended a pipeline configuration if the control algorithm needs more space in a sampling time.
TL;DR: The theory of symmetry-preserving observers is applied to Extended Kalman Filter-based Simultaneous Localization and Mapping (EKF SLAM) and it is proved that a special choice of the noise covariances ensures global exponential convergence.
Abstract: In this paper, we first review the theory of symmetry-preserving observers and we mention some recent results. Then, we apply the theory to Extended Kalman Filter-based Simultaneous Localization and Mapping (EKF SLAM). It allows deriving a new (symmetry-preserving) Extended Kalman Filter for the non-linear SLAM problem that possesses convergence properties. We also prove that a special choice of the noise covariances ensures global exponential convergence.