Showing papers on "Alpha beta filter published in 2010"
TL;DR: In this paper, the authors provide an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications, including the unscented Kalman Filter, the particle filter, and the extended Kalman Filtering.
Abstract: The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications include the extended Kalman filter, the unscented Kalman filter, and the particle filter. Although the Kalman filter and its modifications are powerful tools for state estimation, we might have information about a system that the Kalman filter does not incorporate. For example, we may know that the states satisfy equality or inequality constraints. In this case we can modify the Kalman filter to exploit this additional information and get better filtering performance than the Kalman filter provides. This paper provides an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications. If both the system and state constraints are linear, then all of these different approaches result in the same state estimate, which is the optimal constrained linear state estimate. If either the system or constraints are nonlinear, then constrained filtering is, in general, not optimal, and different approaches give different results.
836 citations
TL;DR: In this paper, a dual-sliding-mode observer consisting of a fast-paced time-varying observer and a slow-paced observer was proposed to estimate the SOH in terms of the capacity fade and resistance deterioration.
Abstract: A new state-of-health (SOH) estimation method for lithium batteries that uses a dual-sliding-mode observer is presented. The capacity fade and resistance deterioration were estimated by the dual-sliding-mode observer. The dual-sliding-mode observer consists of a fast-paced time-varying observer and a slow-paced time-varying observer. The fast-paced time-varying observer estimates parameters, such as the state of charge and terminal voltage, and polarization effects. The slow-paced time-varying observer estimates the SOH in terms of the capacity fade and resistance deterioration. The convergence of the proposed observer was proved by the Lyapunov equation. The structure of the proposed system is simple and easy to implement and shows robust control properties against modeling errors and temperature variations. The test results show that the proposed observer system has superior tracking performance than previous ampere-counting method.
407 citations
TL;DR: A solution to the noise sensitivity of high-gain observers by introducing innovation as the quantity that drives the gain adaptation and proving a general convergence result.
227 citations
TL;DR: It is shown that the truncated Kalman filter may provide a more accurate way of incorporating inequality constraints than other constrained filters (e.g. the projection approach to constrained filtering).
Abstract: Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This article develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter truncates the probability density function (PDF) of the Kalman filter estimate at the known constraints and then computes the constrained filter estimate as the mean of the truncated PDF. The incorporation of state variable constraints increases the computational effort of the filter but also improves its estimation accuracy. The improvement is demonstrated via simulation results obtained from a turbofan engine model. It is also shown that the truncated Kalman filter may provide a more accurate way of incorporating inequality constraints than other constrained filters (e.g. the projection approach to constrained filtering).
152 citations
01 Mar 2010
TL;DR: A novel robust extended Kalman filter for discrete-time nonlinear systems with stochastic uncertainties is proposed and it is illustrated through numerical simulations that the REKF is more effective than the standard extendedKalman filter and the extended robust H¿ filter.
Abstract: In this correspondence paper, a novel robust extended Kalman filter (REKF) for discrete-time nonlinear systems with stochastic uncertainties is proposed. The filter is derived to guarantee an optimized upper bound on the state estimation error covariance despite the model uncertainties as well as the linearization errors. Further analysis shows that the proposed filter has robustness against process noises, measurement noises, and model uncertainties. In addition, the new method is applied in an X-ray pulsar positioning system. It is illustrated through numerical simulations that the REKF is more effective than the standard extended Kalman filter and the extended robust H? filter.
145 citations
TL;DR: The technique used to prove the asymptotical convergence to zero of the observation error, based on the Lyapunov–Razumikhin approach, does not require any assumption about the dependence of the delay on the time.
131 citations
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01 Jan 2010
TL;DR: The Kalman filter as mentioned in this paper is an efficient recursive filter that estimates the internal state of a linear dynamic system from a series of noisy measurements, and is used in a wide range of engineering and econometric applications from radar and computer vision to estimation of structural macroeconomic models.
Abstract: Although the Kalman filter was orginally developed for space satelilte navigation systems, it proved to be very useful for a host of applications, such as radio communication signals, uninterrupted power supplies, and economics. The Kalman filter is an efficient recursive filter that estimates the internal state of a linear dynamic system from a series of noisy measurements. It is used in a wide range of engineering and econometric applications from radar and computer vision to estimation of structural macroeconomic models [10], and is an important topic in control theory and control systems engineering.
128 citations
TL;DR: Through flight tests, it is shown that the PIKF has an obvious accuracy advantage over the IEKF and unscented Kalman filter (UKF) in velocity.
Abstract: This paper deals with the problem of state estimation for the integration of an inertial navigation system (INS) and Global Positioning System (GPS). For a nonlinear system that has the model error and white Gaussian noise, a predictive filter (PF) is used to estimate the model error, and based on this, a modified iterated extended Kalman filter (IEKF) is proposed and is called predictive iterated Kalman filter (PIKF). The basic idea of the PIKF is to compensate the state estimate by the estimated model error. An INS/GPS integration system is implemented using the PIKF and applied to synthetic aperture radar (SAR) motion compensation. Through flight tests, it is shown that the PIKF has an obvious accuracy advantage over the IEKF and unscented Kalman filter (UKF) in velocity.
121 citations
TL;DR: In this paper, two data assimilation methods based on sequential Monte Carlo sampling are studied and compared: the ensemble Kalman filter and the particle filter, each of which has its own advantages and drawbacks.
Abstract: In this paper, two data assimilation methods based on sequential Monte Carlo sampling are studied and compared: the ensemble Kalman filter and the particle filter. Each of these techniques has its own advantages and drawbacks. In this work, we try to get the best of each method by combining them. The proposed algorithm, called the weighted ensemble Kalman filter, consists to rely on the Ensemble Kalman Filter updates of samples in order to define a proposal distribution for the particle filter that depends on the history of measurement. The corresponding particle filter reveals to be efficient with a small number of samples and does not rely anymore on the Gaussian approximations of the ensemble Kalman filter. The efficiency of the new algorithm is demonstrated both in terms of accuracy and computational load. This latter aspect is of the utmost importance in meteorology or in oceanography since in these domains, data assimilation processes involve a huge number of state variables driven by highly non-linear dynamical models. Numerical experiments have been performed on different dynamical scenarios. The performances of the proposed technique have been compared to the ensemble Kalman filter procedure, which has demonstrated to provide meaningful results in geophysical sciences.
118 citations
TL;DR: It is shown that in this kind of sensor fusion problem the Particle Filter has better performance than the Extended Kalman Filter, at the cost of more demanding computations.
92 citations
26 Jul 2010
TL;DR: A novel hybrid filter is developed, which is called the KFGP, which uses Gaussian process kernels to model the spatial field while exploiting efficient Kalman filter state-based approaches tomodel the temporal component.
Abstract: We examine the close relationship between Gaussian processes and the Kalman filter and show how Gaussian processes can be interpreted using familiar Kalman filter mathematical concepts. We use this insight to develop a novel hybrid filter, which we call the KFGP, for spatial-temporal modelling. The KFGP uses Gaussian process kernels to model the spatial field while exploiting efficient Kalman filter state-based approaches to model the temporal component. We also develop a Gaussian process kernel for the familiar Kalman filter near constant acceleration model.
TL;DR: This result confirms that the Gaussian assumption in the Kalman filter formulation, which is violated by most ensemble Kalman filters through the nonlinearity in the model, is a necessary condition to avoid catastrophic filter divergence.
Abstract: Two types of filtering failure are the well known filter divergence where errors may exceed the size of the corresponding true chaotic attractor and the much more severe catastrophic filter divergence where solutions diverge to machine infinity in finite time. In this paper, we demon- strate that these failures occur in filtering the L-96 model, a nonlinear chaotic dissipative dynamical system with the absorbing ball property and quasi-Gaussian unimodal statistics. In particular, catas- trophic filter divergence occurs in suitable parameter regimes for an ensemble Kalman filter when the noisy turbulent true solution signal is partially observed at sparse regular spatial locations. With the above documentation, the main theme of this paper is to show that we can suppress the catastrophic filter divergence with a judicious model error strategy, that is, through a suitable linear stochastic model. This result confirms that the Gaussian assumption in the Kalman filter formulation, which is violated by most ensemble Kalman filters through the nonlinearity in the model, is a necessary condition to avoid catastrophic filter divergence. In a suitable range of chaotic regimes, adding model errors is not the best strategy when the true model is known. However, we find that there are several parameter regimes where the filtering performance in the presence of model errors with the stochastic model supersedes the performance in the perfect model simulation of the best ensemble Kalman filter considered here. Secondly, we also show that the advantage of the reduced Fourier domain filtering strategy (A. Majda and M. Grote, Proceedings of the National Academy of Sciences, 104, 1124-1129, 2007), (E. Castronovo, J. Harlim and A. Majda, J. Comput. Phys., 227(7), 3678-3714, 2008), (J. Harlim and A. Majda, J. Comput. Phys., 227(10), 5304-5341, 2008) is not simply through its numerical efficiency, but significant filtering accuracy is also gained through ignoring the correlation between the appropriate Fourier coefficients when the sparse observations are available in regular space locations.
Book•
12 Feb 2010
TL;DR: A Bayesian Probability Theory Approach to Kalman Filters for Nonlinear Systems and a Cube-In-Corner Assembly for Task Planning with Active Sensing are presented.
Abstract: Introduction- Literature Survey: Autonomous Compliant Motion- Literature Survey: Bayesian Probability Theory- Kalman Filters for Nonlinear Systems- The Non-Minimal State Kalman Filter- Contact Modelling- Geometrical Parameter Estimation and CF Recognition- Experiment: A Cube-In-Corner Assembly- Task Planning with Active Sensing- General Conclusions
TL;DR: In this article, the relative performance of two major EnKF methods when the forecast ensemble is non-Gaussian is investigated. But the approach is based on the stability of the filtering methods against small model violations, using the expected squared L2 distance as a measure of the deviation between the updated distributions.
Abstract: Recently various versions of ensemble Kalman filters (EnKFs) have been proposed and studied. This work concerns, in a mathematically rigorous manner, the relative performance of two major versions of EnKF when the forecast ensemble is non-Gaussian. The approach is based on the stability of the filtering methods against small model violations, using the expected squared L2 distance as a measure of the deviation between the updated distributions. Analytical and experimental results suggest that both stochastic and deterministic EnKFs are sensitive to the violation of the Gaussian assumption, while the stochastic filter is relatively more stable than the deterministic filter under certain circumstances, especially when there are wild outliers. These results not only agree with previous empirical studies, but also suggest a natural choice of a free parameter in the square root Kalman filter algorithm.
TL;DR: The full order robust unknown input observers for continuous systems are presented, which can handle both noise and uncertainties simultaneously and are demonstrated by applying it to the robust state estimation of single link robot arm.
Abstract: The full order robust unknown input observers for continuous systems are presented The observers are designed for both linear and nonlinear systems considering both noise and uncertainties First, an unknown input observer is designed for linear systems The observer is derived based on linear matrix inequality (LMI) approach Then the observer design problem is extended for a class of nonlinear systems whose nonlinear function satisfies the Lipschitz condition The main advantage of these observers over the existing works on UIO design is that these can handle both noise and uncertainties simultaneously The performance of the observers is demonstrated by applying it to the robust state estimation of single link robot arm
02 Aug 2010
TL;DR: In this paper, a generalized multiplicative extended Kalman filter (GMEKF) was proposed to estimate the position and velocity vectors and the orientation of a flying rigid body.
Abstract: In this paper, we propose a “Generalized Multiplicative Extended Kalman Filter” (GMEKF) to estimate the position and velocity vectors and the orientation of a flying rigid body, using measurements from lowcost Earth-fixed position and velocity, inertial and magnetic sensors. Thanks to well-chosen state and output errors, the gains and covariance equations converge to constant values on a much bigger set of trajectories than equilibrium points as it is the case for the standard Multiplicative Extended Kalman Filter (MEKF). We recover thus the fundamental properties of the Kalman filter in the linear case, especially the convergence and optimality properties, for a large set of trajectories, and it should result in a better convergence of the estimation. We illustrate the good performance and the nice properties of the GMEKF on simulation and on experimental comparisons with a commercial system.
TL;DR: A new filter is proposed that allows for the consistent treatment of a class of control problem involving nonlinear estimation from measurements with state-dependent noise and is computed by an iterative root-searching method that maximizes a maximum likelihood function.
Abstract: We consider the problem of estimating the state of a system when measurement noise is a function of the system's state. We propose generalizations of the extended Kalman filter and the iterated extended Kalman filter that can be utilized when the state estimate distribution is approximately Gaussian. The state estimate is computed by an iterative root-searching method that maximizes a maximum likelihood function. The new filter allows for the consistent treatment of a class of control problem involving nonlinear estimation from measurements with state-dependent noise. The effectiveness of the estimation algorithm is illustrated for a control problem with a mobile bearing-only sensor.
TL;DR: For a novel type of automatic transmissions adopting clutch-to-clutch shift control technology with electro-hydraulic actuators, a clutch pressure observer method based on input- to-state stability (ISS) is proposed.
Abstract: For a novel type of automatic transmissions adopting clutch-to-clutch shift control technology with electro-hydraulic actuators, a clutch pressure observer method based on input-to-state stability (ISS) is proposed. Model uncertainties including steady state error and unmodelled dynamics are considered as additional disturbance inputs and the observer is designed in order that the error dynamics is input-to-state stable. Lookup tables, which are widely used to represent complex nonlinear characteristics of engine systems, appear in their original form in the designed reduced-order observer. The designed pressure observer is tested on an AMESim powertrain simulation model. Comparing with the sliding mode method, the designed pressure observer has the better performance.
TL;DR: In this article, the authors discuss several different Kalman filter methods to estimate signal parameters in a GNSS receiver's signal tracking loop with a special emphasis given on how to construct the measurement residuals and the relevant design matrix.
Abstract: In this paper we discuss several different Kalman filter methods to estimate signal parameters in a GNSS receiver's signal tracking loop with a special emphasis given on how to construct the measurement residuals and the relevant design matrix There are three variations of error state Kalman filters for a loop filter, and a direct state Kalman filter for the entire signal tracking loop Based on detailed signal models for a signal tracking loop, four different Kalman filters for signal tracking are compared with the traditional one Block diagram implementation of the direct state Kalman filter for the entire signal tracking loop is proposed by using the analogy relationship with the traditional method in a scalar tracking mode and a vector tracking mode Numerical simulation results show that the Kalman filter methods provide 2 to 3 dB carrier-to-noise ratio gain in carrier phase and Doppler tracking compared to the traditional method
02 Aug 2010
TL;DR: In this article, the authors analyze the applicability of three types of consider Kalman fllters on a simple asteroid rendezvous scenario and show that a Minimum Variance Consider Kalman Filter can provide not only improved state estimates to a traditional Kalman filter, but also produces consistent results from a statistical perspective.
Abstract: Parameter errors in dynamic and measurement models of dynamic systems can result in poor state estimates when using a traditional Kalman fllter structure. In dealing with these parameter errors it is possible to: 1) Ignore them completely; 2) Add the parameters as additional states to be estimated; or 3) \Consider" the error in the state covariance matrix by introducing additional parameter covariance matrices. This paper analyzes the efiect of using all three of these types of fllters on a simple asteroid rendezvous scenario to determine the applicability of each. Two types of consider Kalman fllters are explored, namely an Augmented Measurement Consider Kalman Filter and a Minimum Variance Consider Kalman Filter. This paper flnds that a Minimum Variance Consider Kalman Filter can provide not only improved state estimates to a traditional Kalman fllter, but also produces consistent results from a statistical perspective.
14 Mar 2010
TL;DR: The resulting algorithms are robust to node and link failure, scalable, and fully distributed, in the sense that no fusion center is required, and nodes communicate with their neighbors only.
Abstract: We study the problem of distributed state-space estimation, where a set of nodes are required to estimate the state of a nonlinear state-space system based on their observations. We extend our previous work on distributed Kalman filtering to the nonlinear case, and propose algorithms for Extended and Unscented Kalman filtering. The resulting algorithms are robust to node and link failure, scalable, and fully distributed, in the sense that no fusion center is required, and nodes communicate with their neighbors only. We apply the algorithms to the problem of estimating the position of every node in an ad-hoc network, also known as wireless localization. Simulation results illustrate the performance of the proposed algorithms.
TL;DR: In this article, the minimum number of repeated experiments for accurate recovery of the system Markovparameters is determined from the developments of the Kalman filter in the stochastic environment and an asymptotically stable realized observer.
Abstract: the Kalman filter in the stochastic environment and an asymptotically stable realized observer are discussed briefly to develop insights for the analyst. The minimum number of repeated experiments for accurate recovery of the system Markovparameters isdetermined from these developments. The time-varying observer gains realized in the process are subsequently shown to be in consistent coordinate systems for observer state propagation. It is also demonstrated that the observer gain sequence realized in the case of the minimum number of experiments corresponds naturally to a time-varying deadbeat observer. Numerical examples demonstrate the utility of the concepts developed in the paper.
TL;DR: Two extended versions of the previously proposed robust two-stage Kalman filter, augmented-unknown-input R TSKF (ARTSKF) and decoupled-unknown -input RTSKf (DRTSF) are presented to solve the general unknown input filtering problem and it is shown that under less restricted conditions, the proposed ARTSkF and DRTSKFs are equivalent to the corresponding MUMVFs.
Abstract: This paper is concerned with the optimal solution of two-stage Kalman filtering for linear discrete-time stochastic time-varying systems with unknown inputs affecting both the system state and the outputs. By means of a newly-presented modified unbiased minimum-variance filter (MUMVF), which appears to be the optimal solution to the addressed problem, the optimality of two-stage Kalman filtering for systems with unknown inputs is defined and explored. Two extended versions of the previously proposed robust two-stage Kalman filter (RTSKF), augmented-unknown-input RTSKF (ARTSKF) and decoupled-unknown-input RTSKF (DRTSKF), are presented to solve the general unknown input filtering problem. It is shown that under less restricted conditions, the proposed ARTSKF and DRTSKF are equivalent to the corresponding MUMVFs. An example is given to illustrate the usefulness of the proposed results.
Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society
21 Nov 2010
TL;DR: This study presents a maneuvering ocean vessel model based on a curvilinear motion model with the measurementsbased on a linear position model for the same purpose and proposes the Extended Kalman Filter as an adaptive filter algorithm for the estimation of position, velocity and acceleration.
Abstract: The accurate estimation and prediction of the trajectories of maneuvering vessels in ocean navigation are important tools to improve maritime safety and security. Therefore, many conventional ocean navigation systems and Vessel Traffic Management & Reporting Services are equipped with Radar facilities for this purpose. However, the accuracy of the predictions of maneuvering trajectories of vessels depends mainly on the goodness of estimation of vessel position, velocity and acceleration. Hence, this study presents a maneuvering ocean vessel model based on a curvilinear motion model with the measurements based on a linear position model for the same purpose. Furthermore, the system states and measurements models associated with a white Gaussian noise are also assumed. The Extended Kalman Filter is proposed as an adaptive filter algorithm for the estimation of position, velocity and acceleration that are used for prediction of maneuvering ocean vessel trajectory. Finally, the proposed models are implemented and successful computational results are obtained with respect to prediction of maneuvering trajectories of vessels in ocean navigation in this study. KeywordsTrajectory estimation; Trajectory prediction; Target tracking; Extended Kalman Filter; Curvilinear motion model.
TL;DR: In this paper, a federated unscented Kalman filter is proposed for attitude estimation in nonlinear spacecraft systems, which provides better performance than the Extended Kalman Filter (EKF).
Abstract: We propose a spacecraft attitude estimation algorithm using a federated unscented Kalman filter. For nonlinear spacecraft systems, the unscented Kalman filter provides better performance than the extended Kalman filter. Also, the decentralized scheme in the federated configuration makes a robust system because a sensor fault can be easily detected and isolated by the fault detection and isolation algorithm through a sensitivity factor. Using the proposed algorithm, the spacecraft can continuously perform a given mission despite navigation sensor faults. Numerical simulation is performed to verify the performance of the proposed attitude estimation algorithm.
TL;DR: In this paper, an adaptive sidelip angle observer considering tire-road friction adaptation is proposed for a single-track vehicle model with nonlinear tire characteristics, which can be easily obtained through road test data without using special test rigs.
Abstract: An adaptive sideslip angle observer considering tire-road friction adaptation is proposed in this paper. The single-track vehicle model with nonlinear tire characteristics is adopted. The tire parameters can be easily obtained through road test data without using special test rigs. Afterwards, this model is reconstructed and a high-gain observer (HGO) based on input-output linearisation is derived. The observer stability is analysed. Experimental results have confirmed that the HGO has a better computational efficiency with the same accuracy when compared with the extended Kalman filter and the Luenberger observer. Finally, a road friction adaptive algorithm based on vehicle lateral dynamics is proposed and validated through driving simulator data. As long as the tires work in the nonlinear region, the maximal friction coefficient could be estimated. This algorithm has excellent portability and is also suitable for other observers.
TL;DR: In this article, a reduced-order observer is developed by choosing a special observer gain matrix, which can be used to not only reconstruct the actuator faults but also estimate the disturbances of the system.
02 Aug 2010
TL;DR: In this paper, a maximum likelihood algorithm for simultaneous estimation of state and parameter values in nonlinear stochastic state-space models is proposed, which uses a combination of expectation maximization, nonlinear filtering and smoothing algorithms.
TL;DR: In this article, the authors presented an approach based on two filters α β and α β γ using Interacting Multiples Models (IMM) design instead of a Kalman filter second and third order for the tracking a single maneuver target.
Abstract: In this paper we present an new approach based on two filters α β and α β γ using Interacting Multiples Models (IMM) design instead of a Kalman filter second and third order for the tracking a single maneuver target. The comparison between the proposed filter and the IMM improves the computing time amount about 60% while having a high accuracy.