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Xianfei Pan - One of the best experts on this subject based on the ideXlab platform.

  • velocity position Integration Formula part i application to in flight coarse alignment
    IEEE Transactions on Aerospace and Electronic Systems, 2013
    Co-Authors: Xianfei Pan
    Abstract:

    The in-flight alignment is a critical stage for airborne inertial navigation system/Global Positioning System (INS/GPS) applications. The alignment task is usually carried out by the Kalman filtering technique that necessitates a good initial attitude to obtain a satisfying performance. Due to the airborne dynamics, the in-flight alignment is much more difficult than the alignment on the ground. An optimization-based coarse alignment approach that uses GPS position/velocity as input, founded on the newly-derived velocity/position Integration Formulae is proposed. Simulation and flight test results show that, with the GPS lever arm well handled, it is potentially able to yield the initial heading up to 1 deg accuracy in 10 s. It can serve as a nice coarse in-flight alignment without any prior attitude information for the subsequent fine Kalman alignment. The approach can also be applied to other applications that require aligning the INS on the run.

  • velocity position Integration Formula part ii application to strapdown inertial navigation computation
    IEEE Transactions on Aerospace and Electronic Systems, 2013
    Co-Authors: Xianfei Pan
    Abstract:

    Inertial navigation applications are usually referenced to a rotating frame. Consideration of the navigation reference frame rotation in the inertial navigation algorithm design is an important but so far less seriously treated issue, especially for super high-speed flying vehicles or the future ultraprecision navigation system of several meters per hour. A rigorous approach is proposed to tackle the issue of navigation frame rotation in velocity/position computation by use of the newly-devised velocity/position Integration Formulae in the Part I companion paper. The two Integration Formulae set a well-founded cornerstone for the velocity/position algorithms' design that makes the comprehension of the inertial navigation computation principle more accessible to practitioners, and different approximations to the integrals involved give birth to various velocity/position update algorithms. Two-sample velocity and position algorithms are derived to exemplify the design process. In the context of level-flight airplane examples, the derived algorithm is analytically and numerically compared with the typical algorithms that exist in the literature. The results throw light on the problems in existing algorithms and the potential benefits of the derived algorithm.

  • velocity position Integration Formula i application to in flight alignment
    arXiv: Robotics, 2013
    Co-Authors: Xianfei Pan
    Abstract:

    The in-flight alignment is a critical stage for airborne INS/GPS applications. The alignment task is usually carried out by the Kalman filtering technique that necessitates a good initial attitude to obtain satisfying performance. Due to the airborne dynamics, the in-flight alignment is much difficult than alignment on the ground. This paper proposes an optimization-based coarse alignment approach using GPS position/velocity as input, founded on the newly-derived velocity/position Integration Formulae. Simulation and flight test results show that, with the GPS lever arm well handled, it is potentially able to yield the initial heading up to one degree accuracy in ten seconds. It can serve as a nice coarse in-flight alignment without any prior attitude information for the subsequent fine Kalman alignment. The approach can also be applied to other applications that require aligning the INS on the run.

  • velocity position Integration Formula ii application to inertial navigation computation
    arXiv: Robotics, 2012
    Co-Authors: Xianfei Pan
    Abstract:

    Inertial navigation applications are usually referenced to a rotating frame. Consideration of the navigation reference frame rotation in the inertial navigation algorithm design is an important but so far less seriously treated issue, especially for ultra-high-speed flying aircraft or the future ultra-precision navigation system of several meters per hour. This paper proposes a rigorous approach to tackle the issue of navigation frame rotation in velocity/position computation by use of the newly-devised velocity/position Integration Formulae in the Part I companion paper. The two Integration Formulae set a well-founded cornerstone for the velocity/position algorithms design that makes the comprehension of the inertial navigation computation principle more accessible to practitioners, and different approximations to the integrals involved will give birth to various velocity/position update algorithms. Two-sample velocity and position algorithms are derived to exemplify the design process. In the context of level-flight airplane examples, the derived algorithm is analytically and numerically compared to the typical algorithms existing in the literature. The results throw light on the problems in existing algorithms and the potential benefits of the derived algorithm.

Dubussy Christophe - One of the best experts on this subject based on the ideXlab platform.

  • Convolution cohomologique holomorphe, transformation de Laplace enrichie et applications
    Université de Liège ​Liège ​​Belgique, 2019
    Co-Authors: Dubussy Christophe
    Abstract:

    The Hadamard product of power series has been studied for more than one hundred years and has become a classical tool in complex analysis. Nonetheless, this product only concerns functions which are holomorphic near the origin. In 2009, T. Pohlen studied an extension of this Hadamard product on functions defined on open subsets of the Riemann sphere, which do not necessarily contain the origin. Using ad-hoc and explicit constructions, he could define this product thanks to a contour Integration Formula. However, his construction is non-symmetric with respect to 0 and the infinity. The first part of this thesis consists in the study of a generalization of Pohlen's extended Hadamard product. Using singular homology theory, we introduce more symmetric cycles and define a generalized Hadamard product which is equivalent to Pohlen's product when the functions vanish at infinity. Then, we show that this generalized Hadamard product is a particular case of a more general phenomenon called "holomorphic cohomological convolution". We study this convolution in detail on the multiplicative complex Lie group C^* and provide a contour Integration Formula to compute it. The second part of the thesis is devoted to the study of holomorphic Paley-Wiener type theorems due to Polya (in the compact case) and to Méril (in the non-compact case). These theorems use a contour Integration version of the Laplace transform. Thanks to the theory of enhanced subanalytic sheaves developed by A. D'Agnolo and M. Kashiwara as well as the enhanced Laplace transform introduced by M. Kashiwara and P. Schapira, we show that such theorems can be understood from a cohomological point of view. Under some convex subanalytic conditions, we are even able to provide stronger Laplace isomorphisms between spaces which are described by tempered growth conditions. It appears that these spaces can be linked to certain spaces of analytic functionals. In the non-compact case, we define a convolution product between analytic functionals and conjecture that it is compatible with the additive version of the previously studied holomorphic cohomological convolution. Thanks to our results on the enhanced Laplace transform, we prove the conjecture in the subanalytic case.Le produit d'Hadamard entre séries de puissances entières a été étudié depuis plus de cent ans et est devenu un outil classique de l'analyse complexe. Néanmoins, ce produit concerne uniquement les fonctions holomorphes au voisinage de l'origine. En 2009, T. Pohlen a étudié une extension de ce produit d'Hadamard pour des fonctions définies sur des ouverts de la sphère de Riemann, qui ne contiennent pas nécessairement l'origine. En utilisant des constructions ad-hoc et explicites, il a pu définir ce produit via une intégrale de contour. Cependant, cette construction n'est pas symétrique par rapport à 0 et à l'infini. La première partie de cette thèse consiste en l'étude d'une généralisation du produit d'Hadamard étendu par Pohlen. Au moyen de la théorie de l'homologie singulière, nous introduisons des cycles plus symétriques et définissons un produit d'Hadamard généralisé, équivalent à celui de Pohlen quand les fonctions s'annulent à l'infini. Nous montrons ensuite que ce produit d'Hadamard généralisé est un cas particulier d'un phénomène plus général appelé "convolution cohomologique holomorphe". Nous étudions en détail cette convolution dans le cas du groupe de Lie complexe multiplicatif C^* et fournissons une formule à base d'intégrales de contour pour la calculer. La deuxième partie de la thèse est consacrée à l'étude de théorèmes de type Paley-Wiener holomorphes dus à Polya (dans le cas compact) et à Méril (dans le cas non compact). Ces théorèmes utilisent une version de la transformation de Laplace à base d'intégrales de contour. Grâce à la théorie des faisceaux sous-analytiques enrichis développée par A. D'Agnolo et M. Kashiwara, ainsi qu'à la transformation de Laplace enrichie introduite par M. Kashiwara et P. Schapira, nous montrons que ces théorèmes peuvent être compris d'un point de vue cohomologique. Sous certaines hypothèses de convexité et de sous-analyticité, il est même possible de prouver de plus forts isomorphismes de Laplace entre des espaces décrits par des conditions de croissance tempérée. Ces espaces peuvent être liés à certains espaces de fonctionnelles analytiques. Dans le cas non compact, nous définissons un produit de convolution entre fonctionnelles analytiques et conjecturons que ce produit est compatible avec la version additive de la convolution cohomologique holomorphe précédemment étudiée. Grâce à nos résultats sur la transformation de Laplace enrichie, nous prouvons cette conjecture dans le cas sous-analytique

  • Convolution cohomologique holomorphe, transformation de Laplace enrichie et applications
    Université de Liège ​Liège ​​Belgique, 2019
    Co-Authors: Dubussy Christophe
    Abstract:

    audience: researcherThe Hadamard product of power series has been studied for more than one hundred years and has become a classical tool in complex analysis. Nonetheless, this product only concerns functions which are holomorphic near the origin. In 2009, T. Pohlen studied an extension of this Hadamard product on functions defined on open subsets of the Riemann sphere, which do not necessarily contain the origin. Using ad-hoc and explicit constructions, he could define this product thanks to a contour Integration Formula. However, his construction is non-symmetric with respect to 0 and the infinity. The first part of this thesis consists in the study of a generalization of Pohlen's extended Hadamard product. Using singular homology theory, we introduce more symmetric cycles and define a generalized Hadamard product which is equivalent to Pohlen's product when the functions vanish at infinity. Then, we show that this generalized Hadamard product is a particular case of a more general phenomenon called "holomorphic cohomological convolution". We study this convolution in detail on the multiplicative complex Lie group C^* and provide a contour Integration Formula to compute it. The second part of the thesis is devoted to the study of holomorphic Paley-Wiener type theorems due to Polya (in the compact case) and to Méril (in the non-compact case). These theorems use a contour Integration version of the Laplace transform. Thanks to the theory of enhanced subanalytic sheaves developed by A. D'Agnolo and M. Kashiwara as well as the enhanced Laplace transform introduced by M. Kashiwara and P. Schapira, we show that such theorems can be understood from a cohomological point of view. Under some convex subanalytic conditions, we are even able to provide stronger Laplace isomorphisms between spaces which are described by tempered growth conditions. It appears that these spaces can be linked to certain spaces of analytic functionals. In the non-compact case, we define a convolution product between analytic functionals and conjecture that it is compatible with the additive version of the previously studied holomorphic cohomological convolution. Thanks to our results on the enhanced Laplace transform, we prove the conjecture in the subanalytic case.Le produit d'Hadamard entre séries de puissances entières a été étudié depuis plus de cent ans et est devenu un outil classique de l'analyse complexe. Néanmoins, ce produit concerne uniquement les fonctions holomorphes au voisinage de l'origine. En 2009, T. Pohlen a étudié une extension de ce produit d'Hadamard pour des fonctions définies sur des ouverts de la sphère de Riemann, qui ne contiennent pas nécessairement l'origine. En utilisant des constructions ad-hoc et explicites, il a pu définir ce produit via une intégrale de contour. Cependant, cette construction n'est pas symétrique par rapport à 0 et à l'infini. La première partie de cette thèse consiste en l'étude d'une généralisation du produit d'Hadamard étendu par Pohlen. Au moyen de la théorie de l'homologie singulière, nous introduisons des cycles plus symétriques et définissons un produit d'Hadamard généralisé, équivalent à celui de Pohlen quand les fonctions s'annulent à l'infini. Nous montrons ensuite que ce produit d'Hadamard généralisé est un cas particulier d'un phénomène plus général appelé "convolution cohomologique holomorphe". Nous étudions en détail cette convolution dans le cas du groupe de Lie complexe multiplicatif C^* et fournissons une formule à base d'intégrales de contour pour la calculer. La deuxième partie de la thèse est consacrée à l'étude de théorèmes de type Paley-Wiener holomorphes dus à Polya (dans le cas compact) et à Méril (dans le cas non compact). Ces théorèmes utilisent une version de la transformation de Laplace à base d'intégrales de contour. Grâce à la théorie des faisceaux sous-analytiques enrichis développée par A. D'Agnolo et M. Kashiwara, ainsi qu'à la transformation de Laplace enrichie introduite par M. Kashiwara et P. Schapira, nous montrons que ces théorèmes peuvent être compris d'un point de vue cohomologique. Sous certaines hypothèses de convexité et de sous-analyticité, il est même possible de prouver de plus forts isomorphismes de Laplace entre des espaces décrits par des conditions de croissance tempérée. Ces espaces peuvent être liés à certains espaces de fonctionnelles analytiques. Dans le cas non compact, nous définissons un produit de convolution entre fonctionnelles analytiques et conjecturons que ce produit est compatible avec la version additive de la convolution cohomologique holomorphe précédemment étudiée. Grâce à nos résultats sur la transformation de Laplace enrichie, nous prouvons cette conjecture dans le cas sous-analytique.Holomorphic Cohomological Convolution, Enhanced Laplace Transform and Application

Lueyung Chow Chiu - One of the best experts on this subject based on the ideXlab platform.

  • multicenter molecular integrals of spherical gaussian functions by fourier transform convolution theorem
    Journal of Chemical Physics, 1996
    Co-Authors: Mohammad Moharerrzadeh, Lueyung Chow Chiu
    Abstract:

    The two‐electron four‐center integral of the homogeneous solid spherical harmonic Gaussian‐type functions (GTF’s), r2n+lYlm(r)exp(−αr2), has been evaluated analytically by decomposing it into a linear combination of two‐center integrals through coincidence of centers. The two‐electron two‐center integrals are integrated analytically through the Fourier transformation convolution theorem. A compact Integration Formula is obtained for a general two‐electron irregular solid spherical harmonic operator [4π/(2L+1)]1/2YLM (r12)/r(L+1)12. This Formula is applied to evaluate two‐center integrals of the Coulomb repulsion, the spin–other–orbit interaction and the spin–spin interaction by letting L=0, 1, and 2, respectively. The Integration results are in terms of the spherical Laguerre GTF’s, Ln′l′+1/2(σR2)Rl′Yl′m′ ()exp(−σR2), of the relative nuclear coordinate plus one error‐type F‐function term. One‐electron multicenter integrals have also been evaluated through Fourier transformation convolution theorem. The...

Mohammad Moharerrzadeh - One of the best experts on this subject based on the ideXlab platform.

  • multicenter molecular integrals of spherical gaussian functions by fourier transform convolution theorem
    Journal of Chemical Physics, 1996
    Co-Authors: Mohammad Moharerrzadeh, Lueyung Chow Chiu
    Abstract:

    The two‐electron four‐center integral of the homogeneous solid spherical harmonic Gaussian‐type functions (GTF’s), r2n+lYlm(r)exp(−αr2), has been evaluated analytically by decomposing it into a linear combination of two‐center integrals through coincidence of centers. The two‐electron two‐center integrals are integrated analytically through the Fourier transformation convolution theorem. A compact Integration Formula is obtained for a general two‐electron irregular solid spherical harmonic operator [4π/(2L+1)]1/2YLM (r12)/r(L+1)12. This Formula is applied to evaluate two‐center integrals of the Coulomb repulsion, the spin–other–orbit interaction and the spin–spin interaction by letting L=0, 1, and 2, respectively. The Integration results are in terms of the spherical Laguerre GTF’s, Ln′l′+1/2(σR2)Rl′Yl′m′ ()exp(−σR2), of the relative nuclear coordinate plus one error‐type F‐function term. One‐electron multicenter integrals have also been evaluated through Fourier transformation convolution theorem. The...

Barry J Cummins - One of the best experts on this subject based on the ideXlab platform.