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Wei Gao - One of the best experts on this subject based on the ideXlab platform.
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a maximum correntropy Divided Difference filter for cooperative localization
IEEE Access, 2018Co-Authors: Chengjiao Sun, Yonggang Zhang, Guoqing Wang, Wei GaoAbstract:This paper derives a new maximum correntropy Divided Difference filter (DDF) to address the heavy-tailed measurement noise induced by non-Gaussian measurements in cooperative localization of autonomous underwater vehicles. By integrating the advantages of both the DDF and the maximum correntropy criterion, the proposed filter exhibits localization accuracy and robustness to address the heavy-tailed impulsive noise. The proposed maximum correntropy DDF has been tested through a lake trial. Experimental results indicate the superior performance of the proposed algorithm.
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robust huber based iterated Divided Difference filtering with application to cooperative localization of autonomous underwater vehicles
Sensors, 2014Co-Authors: Wei Gao, Yalong LiuAbstract:A new algorithm called Huber-based iterated Divided Difference filtering (HIDDF) is derived and applied to cooperative localization of autonomous underwater vehicles (AUVs) supported by a single surface leader. The position states are estimated using acoustic range measurements relative to the leader, in which some disadvantages such as weak observability, large initial error and contaminated measurements with outliers are inherent. By integrating both merits of iterated Divided Difference filtering (IDDF) and Huber's M-estimation methodology, the new filtering method could not only achieve more accurate estimation and faster convergence contrast to standard Divided Difference filtering (DDF) in conditions of weak observability and large initial error, but also exhibit robustness with respect to outlier measurements, for which the standard IDDF would exhibit severe degradation in estimation accuracy. The correctness as well as validity of the algorithm is demonstrated through experiment results.
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application for autonomous underwater vehicle initial alignment with Divided Difference filter
International Conference on Information and Automation, 2010Co-Authors: Guiling Zhao, Wei Gao, Xin Zhang, Yueyang BenAbstract:Regarding the problem of the Autonomous Underwater Vehicle (AUV) departing from the mother ship and starting up, this paper proposed a Divided Difference filter (DDF) basing on the Stirling interpolation formula. When AUV separated from the mother ship and restarted, the coarse alignment was not ideal. Its level misalignment error precision was high, but its heading misalignment error precision was low. The large heading misalignment error model was applied to the fine alignment on moving base. The large heading misalignment error model was nonlinear. The first order Divided Difference (DD1) filter and the second order Divided Difference (DD2) filter were adopted to the nonlinear filtering. Simulation results show that the DD1 alignment precision is equivalent with Extended Kalman Filter (EKF), but the alignment time shorts by 33%. The DD2 alignment precision is equivalent with Unscented Kalman Filter (UKF), but the alignment time shorts by 28%. The alignment precision raises by 60% compared to the EKF.
Christopher D Karlgaard - One of the best experts on this subject based on the ideXlab platform.
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robust state estimation using desensitized Divided Difference filter
Isa Transactions, 2013Co-Authors: Christopher D Karlgaard, Haijun ShenAbstract:This paper develops a robust Divided Difference filtering approach based on the concept of Desensitized Kalman Filtering. The filters are formulated using a minimum variance cost function, augmented with a penalty function consisting of a weighted norm of the state sensitivities. Solutions are provided for first and second-order Divided Difference Filters. The resulting filters are non-minimum variance but exhibit reduced sensitivity to deviations in the assumed plant model parameters. The proposed algorithms are demonstrated using Monte Carlo simulation techniques for an induction motor state estimation problem with parameter uncertainties.
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desensitized Divided Difference filtering for induction motor state estimation
Southeastern Symposium on System Theory, 2012Co-Authors: Christopher D Karlgaard, Haijun ShenAbstract:This paper develops a robust Divided Difference filtering approach based on the concept of Desensitized Kalman Filtering, for use in induction motor state estimation. In this approach, reduced-order filters can be developed that are insensitive to parameter uncertainties. The filters are formulated using a minimum variance cost function, augmented with a penalty function consisting of a weighted norm of the state sensitivities. Solutions are provided for first and second-order Divided Difference filters. The proposed algorithms are demonstrated using Monte-Carlo simulation techniques.
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nonsingular attitude filtering using modified rodrigues parameters
Journal of The Astronautical Sciences, 2009Co-Authors: Christopher D Karlgaard, Hanspeter SchaubAbstract:A method to estimate the general rigid body attitude using a minimal modified Rodrigues parameters (MRP) coordinate set is presented. The singularity avoidance technique is based on the stereographic projection properties of the MRP set, and makes use of a simple mapping relationship between MRP representations. Previous work has used the MRP duality to avoid singular attitude descriptions but has ignored the associated covariance transformation. This article presents a mapping to transform the state covariance matrix between these two representations as the attitude description is mapped between the two possible MRP sets. Second-order covariance transformations suitable for Divided Difference filtering are also provided. The MRP filter formulation based on extended Kalman filtering and Divided Difference filtering is compared with a standard multiplicative quaternion Kalman filter in an example problem.
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huber based Divided Difference filtering
Journal of Guidance Control and Dynamics, 2007Co-Authors: Christopher D Karlgaard, Hanspeter SchaubAbstract:T HIS Note describes a robust modification of the Divided Difference filtering technique. The robust technique relies on Huber’s generalized maximum likelihood approach to estimation [1]. Specifically,Huber’smethod is a combinedminimum ‘1and ‘2norm estimation technique, which exhibits robustnesswith respect to deviations from the commonly assumed Gaussian error probability density functions, for which the least–squares or minimum ‘2-norm technique exhibits a severe degradation in estimation accuracy [2]. TheHuber-based estimates are robust in the sense that theyminimize the maximum asymptotic estimation variance when applied to contaminated Gaussian densities. The Huber technique was originally developed as a generalization of maximum likelihood estimation, applied first to estimating the center of a probability distribution in [1] and generalized tomultiple linear regression in [2– 4]. The Kalman filter is a recursive minimum ‘2-norm technique and therefore exhibits sensitivity to deviations in the true underlying error probability distributions [5]. For this reason, theHuber technique has been further extended to dynamic estimation problems. Boncelet and Dickinson [6] first proposed to solve the robust filtering problem by means of the Huber technique at each measurement, by expressing the discrete-time Kalman filter as a sequence of linear regression problems. The authors do not provide any simulation results to validate the proposed technique. Kovacevic et al. [7] follow thework of [6] and develop a robust Kalman filter using the Huber technique applied to a linear regression problem at each measurement update. References [8–10] express the dynamic filtering problem as a sequential linear regression to be solved by the Huber technique and apply the filter to underwater vehicle tracking, power system state estimation, and spacecraft rendezvous navigation, respectively. The increase in computation due to the use of the Huber technique was found in [10] to be small. It should be noted that [6–10] apply the Huber methodology to linearized filters. The Divided Difference filter is one of several new estimation techniques that are collectively known as sigma-point Kalman filters (SPKF). The first-order (DD1) and second-order (DD2) Divided Difference filters [11,12] are generalizations of the filter introduced by Schei [13] and are two examples of SPKF-class estimators; other examples can be found in [14–16]. Like the basic Kalman filter, the SPKFs seek to determine a state estimate that minimizes the ‘2 norm of the residuals. The SPKF technique differs from the standard Kalmanfilter in the sense that the SPKFs do not linearize the dynamic system for the propagation, but instead propagate a cluster of points centered around the current estimate to form improved approximations of the conditional mean and covariance. Specifically, the Divided Difference filters make use of multidimensional interpolation formulas to approximate the nonlinear transformations. As a result of this approach, the filter does not require knowledge or existence of the partial derivatives of the system dynamics and measurement equations. SPKFs have the additional advantage over the basic Kalman filter in that they can easily be extended to determine second-order solutions to the minimum ‘2-norm filtering problem, which increases the estimation accuracywhen the system andmeasurement equations are nonlinear. It is important to note that the SPKFs use a minimum ‘2-norm measurement update and are therefore subject to the same sensitivity to non-Gaussian measurement errors as the Kalman filter. Therefore, the purpose of this Note is tomodify the DD1 andDD2measurement update equations by making use of the Huber technique to provide robustness against deviations from Gaussianity without a large increase in computation. This Note first provides a short review of the DD1 and DD2 filters and then shows how the measurement update can be expressed in terms of a standard regression problem, which can be solved using the robust Huber technique. The filtering techniques are then applied to a benchmark problem that involves estimating the trajectory of an entry body from discrete-time range data measured by a radar tracking station. The simulation is conducted using Monte Carlo techniques for both Gaussian and non-Gaussian cases. The computational cost associated with each filter is provided.
Yalong Liu - One of the best experts on this subject based on the ideXlab platform.
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robust huber based iterated Divided Difference filtering with application to cooperative localization of autonomous underwater vehicles
Sensors, 2014Co-Authors: Wei Gao, Yalong LiuAbstract:A new algorithm called Huber-based iterated Divided Difference filtering (HIDDF) is derived and applied to cooperative localization of autonomous underwater vehicles (AUVs) supported by a single surface leader. The position states are estimated using acoustic range measurements relative to the leader, in which some disadvantages such as weak observability, large initial error and contaminated measurements with outliers are inherent. By integrating both merits of iterated Divided Difference filtering (IDDF) and Huber's M-estimation methodology, the new filtering method could not only achieve more accurate estimation and faster convergence contrast to standard Divided Difference filtering (DDF) in conditions of weak observability and large initial error, but also exhibit robustness with respect to outlier measurements, for which the standard IDDF would exhibit severe degradation in estimation accuracy. The correctness as well as validity of the algorithm is demonstrated through experiment results.
Meihong Liu - One of the best experts on this subject based on the ideXlab platform.
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nonlinear regression huber based Divided Difference filtering
Proceedings of the Institution of Mechanical Engineers Part G: Journal of Aerospace Engineering, 2017Co-Authors: Meihong LiuAbstract:This article derives a nonlinear regression Huber-based Divided Difference filtering algorithm using a nonlinear regression approach for dynamic state estimation problems with non-Gaussian noises a...
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state augmentation based iterated Divided Difference filtering
Proceedings of the Institution of Mechanical Engineers Part G: Journal of Aerospace Engineering, 2015Co-Authors: Meihong Liu, Xingqun ZhanAbstract:Due to the drawbacks in the two typical iterated Divided Difference filters with additive measurement noise, a state augmentation-based iterated Divided Difference filter (SIDDF) is proposed in thi...
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improved robust huber based Divided Difference filtering
Proceedings of the Institution of Mechanical Engineers Part G: Journal of Aerospace Engineering, 2014Co-Authors: Meihong Liu, Dengping DuanAbstract:This article derives an improved robust Huber-based Divided Difference filter by using the Huber’s technique, in which the nonlinear measurement function is directly used in the nonlinear regressio...
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huber based Divided Difference filter with application to relative navigation
Proceedings of the Institution of Mechanical Engineers Part G: Journal of Aerospace Engineering, 2014Co-Authors: Meihong Liu, Deren Gong, Dengping DuanAbstract:In this article, a simplified Divided Difference filter based on the model structure with linear output equations and the assumption of additive Gaussian noise is introduced. By making use of the H...
M. Foupouagnigni - One of the best experts on this subject based on the ideXlab platform.
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On the Polynomial Solution of Divided-Difference Equations of the Hypergeometric Type on Nonuniform Lattices
Axioms, 2019Co-Authors: M. Foupouagnigni, S. MboutngamAbstract:In this paper, we provide a formal proof of the existence of a polynomial solution of fixed degree for a second-order Divided-Difference equation of the hypergeometric type on non-uniform lattices, generalizing therefore previous work proving existence of the polynomial solution for second-order differential, Difference or q-Difference equation of hypergeometric type. This is achieved by studying the properties of the mean operator and the Divided-Difference operator as well as by defining explicitly, the right and the “left” inverse for the second operator. The method constructed to provide this formal proof is likely to play an important role in the characterization of orthogonal polynomials on non-uniform lattices and might also be used to provide hypergeometric representation (when it does exist) of the second solution—non polynomial solution—of a second-order Divided-Difference equation of hypergeometric type.
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Divided Difference equation inversion connection multiplication and linearization formulae of the continuous hahn and the meixner pollaczek polynomials
Ramanujan Journal, 2018Co-Authors: D D Tcheutia, Wolfram Koepf, Njionou P Sadjang, M. FoupouagnigniAbstract:From the study of various properties of some Difference operators, we prove in the first part of this work that the continuous Hahn and the Meixner–Pollaczek polynomials are solutions of a second-order Divided-Difference equation of hypergeometric- type. Next, using some algorithmic tools, we solve the inversion, connection, multiplication and linearization problems for the continuous Hahn and the Meixner–Pollaczek polynomials.
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Divided Difference equation and three term recurrence relations of some systems of bivariate q orthogonal polynomials
Journal of Difference Equations and Applications, 2017Co-Authors: D D Tcheutia, M. Foupouagnigni, Guemo Y Tefo, I AreaAbstract:AbstractPartial Divided-Difference equations and three-term recurrence relations satisfied by the bivariate Askey–Wilson and the bivariate q-Racah polynomials are computed in this work. By using limiting processes, partial Divided (or q)-Difference equations and three-term recurrence relations are also provided for each of the following families of orthogonal polynomials: the bivariate continuous dual q-Hahn, the bivariate Al-Salam-Chihara, the bivariate continuous q-Hahn, the bivariate q-Hahn, the bivariate dual q-Hahn, the bivariate q-Krawtchouk, the bivariate q-Meixner, and the bivariate q-Charlier polynomials.
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linear partial Divided Difference equation satisfied by multivariate orthogonal polynomials on quadratic lattices
Mathematical Modelling of Natural Phenomena, 2017Co-Authors: D D Tcheutia, M. Foupouagnigni, Guemo Y Tefo, E Godoy, I AreaAbstract:In this paper, a fourth-order partial Divided-Difference equation on quadratic lattices with polynomial coefficients satisfied by bivariate Racah polynomials is presented. From this result, we recover the Difference equation satisfied by the bivariate Racah polynomials given by Geronimo and Iliev. Moreover, we obtain explicitly the matrix coefficients appearing in the three-term recurrence relations satisfied by any bivariate orthogonal polynomial solution of the equation. In particular, we provide explicit expressions for the matrices in the three-term recurrence relations satisfied by the bivariate Racah polynomials introduced by Tratnik. Moreover, we present the family of monic bivariate Racah polynomials defined from the three-term recurrence relations they satisfy, and we solve the connection problem between two different families of bivariate Racah polynomials. These results are then applied to other families of bivariate orthogonal polynomials, namely the bivariate Wilson, continuous dual Hahn and continuous Hahn, the latter two through limiting processes. The fourth-order partial Divided-Difference equations on quadratic lattices are shown to be of hypergeometric type in the sense that the Divided-Difference derivatives of solutions are themselves solution of the same type of Divided-Difference equations.
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linear partial Divided Difference equation satisfied by multivariate orthogonal polynomials on quadratic lattices
arXiv: Classical Analysis and ODEs, 2016Co-Authors: D D Tcheutia, M. Foupouagnigni, Guemo Y Tefo, E Godoy, I AreaAbstract:In this paper, a fourth-order partial Divided-Difference equation on quadratic lattices with polynomial coefficients satisfied by bivariate Racah polynomials is presented. From this equation we obtain explicitly the matrix coefficients appearing in the three-term recurrence relations satisfied by any bivariate orthogonal polynomial solution of the equation. In particular, we provide explicit expressions for the matrices in the three-term recurrence relations satisfied by the bivariate Racah polynomials introduced by Tratnik. Moreover, we present the family of monic bivariate Racah polynomials defined from the three-term recurrence relations they satisfy, and we solve the connection problem between two different families of bivariate Racah polynomials. These results are then applied to other families of bivariate orthogonal polynomials, namely the bivariate Wilson, continuous dual Hahn and continuous Hahn, the latter two through limiting processes. The fourth-order partial Divided-Difference equations on quadratic lattices are shown to be of hypergeometric type in the sense that the Divided-Difference derivatives of solutions are themselves solution of the same type of Divided-Difference equations.