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Tuning of coning algorithms to gyro data frequency response characteristics

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2001年第4期24卷 641-647页

作者： Mark, JG Tazartes, DA Litton Guidance & Control Syst Woodland Hills CA 91367 USA

Substantial efforts have gone into the development of sophisticated algorithms that reduce system drift errors in the presence of coning motion. Present-day algorithms form high-order coning correction terms using multiple incremental angle outputs from the gyros. These algorithms assume a hat transfer function for the processing of the incremental angle outputs and are structured to yield very high-order responses. However, these algorithms do not address the issue of nonideal gyro frequency response or of filtered gyro data. Many gyros exhibit complex frequency responses and violate the assumptions used in deriving the previously developed coning algorithms. The mismatch between the assumed and actual frequency response of the gyro data leads to degradation of performance in a coning environment as well as amplification of pseudoconing errors. A method of deriving algorithms that are tailored to the frequency response of the particular type of gyros used is presented. These algorithms can be designed to arbitrarily high order and can also supply an extremely sharp high-frequency cutoff to minimize pseudo-coning errors. Additionally, this method can be used to design coning algorithms that are tuned to deliberately filtered gyro data. The technique developed equally applies to mechanical, fiber-optic, and other types of gyros.

关键词： Frequency Response Functions Quaternions Laser Gyroscopes integration algorithm Taylor Series Strapdown Inertial Navigation System Navigation Performance Strapdown System Angular Motion

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Unconditionally stable time-step-integration algorithms based on Hamilton's principle

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AIAA JOURNAL 2000年第8期38卷 1453-1464页

作者： Fung, TC Nanyang Technol Univ Sch Civil & Struct Engn Singapore 639798 Singapore

Unconditionally stable time-step-integration algorithms derived from Hamilton's principle are presented. The corresponding constrained variations are assumed to be in the form of Sigma alpha(k)tau(k)(1 - T) to ensure vanishing variations at the ends of a time interval. The initial conditions are strongly enforced in the formulation. The order of accuracy can be 2n - 1 or 2n, where n is the number of unknown variables. The ultimate spectral radii of the algorithms can be controlled directly. The approximate solutions are in fact equivalent to the generalized Pade approximations for linear second-order differential equations. Hence, Hamilton's principle can be used to construct unconditionally stable higher-order-accurate time-step-integration algorithms directly as well, provided the appropriate constrained variations are used.

关键词： integration algorithm Second Order Differential Equations Critical Damping Ratio Lagrange Multipliers Kinetic Energy Hu Washizu Principle Linear Interpolation Solid Mechanics Modal Analysis Cramers Rule

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Strapdown inertial navigation integration algorithm design Part 2: Velocity and position algorithms

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1998年第2期21卷 208-221页

作者： Savage, PG Strapdown Associates Inc Maple Plain MN 55359 USA

This series of two papers (Parts 1 and 2) provides a rigorous comprehensive approach to the design of the principal software algorithms utilized in modern-day strapdown inertial navigation systems: integration of angular rate into attitude, acceleration transformation/integration into velocity, and integration of velocity into position. The algorithms are structured utilizing the two-speed updating approach originally developed for attitude updating;an analytically exact equation is used a moderate speed to update the integration parameter (attitude, velocity, or po sition) with input provided from sr high-speed algorithm measuring rectified dynamic motion within the parameter update time interval [coming far attitude updating, sculling for velocity updating, and scrolling (writer's terminology) for high-resolution position updating]. The algorithm design approach accounts for angular rate/specific force acceleration inputs from the strapdown system inertial sensors, as well as rotation of the navigation frame used for attitude referencing and velocity integration. The Pare 1 paper (Savage, P. G., "Strapdown Inertial Navigation integration algorithm Design Part 1: Attitude algorithms," Journal of Guidance Control, and Dynamics, Vol. 21, No, 1, 1998, pip 19-28) defined the overall design requirement for the strapdown inertial navigation integration function and developed the attitude updating algorithms. This paper, Part 2, deals with design of the acceleration transformation/velocity integration and position integration algorithms. Although Parts I and 2 often cover basic concepts, the material presented is intended for use by the practitioner who is already familiar with inertial navigation fundamentals.

关键词： Strapdown Inertial Navigation System integration algorithm Inertial Sensor Strapdown System Earth Accelerometer Synthetic Aperture Radar Resonance Frequencies Software Architecture Taylor Series

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Strapdown inertial navigation integration algorithm design part 1: Attitude algorithms

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1998年第1期21卷 19-28页

作者： Savage, PG Strapdown Associates Inc Maple Plain MN 55359 USA

This series of two papers provides a rigorous comprehensive approach to the design of the principal software algorithms utilized in modern-day strapdown inertial navigation systems: integration of angular rate into attitude, acceleration transformation/integration into velocity, and integration of velocity into position, The algorithms are structured utilizing the two-speed updating approach originally developed for attitude updating in which an analytically exact equation is used at moderate speed to update the integration parameter (attitude, velocity, or position) with input provided from a high-speed algorithm measuring dynamic angular rate/acceleration effects within the parameter update time interval [coning for attitude updating, sculling for velocity updating, and scrolling (writer's terminology) for high-resolution position updating], The algorithm design approach accounts for angular rate/specific force acceleration measurements from the strapdown system inertial sensors as well as rotation of the navigation frame used for attitude referencing and velocity integration. This paper, Part 1, defines the overall design requirement for the strapdown inertial navigation integration function and develops direction cosine and quaternion forms for the attitude updating algorithms, Part 2 [Savage, P. G., "Strapdown Inertial Navigation integration algorithm Design Part 2: Velocity and Position algorithms," Journal of Guidance, Control, and Dynamics (to be published)] deals with design of the velocity and position integration algorithms, Although Parts 1 and 2 often cover fundamental inertial navigation concepts, the material presented is intended for use by the practitioner who is already familiar with basic inertial navigation concepts.

关键词： integration algorithm Strapdown Inertial Navigation System Quaternions Inertial Sensor Strapdown System Earth Angular Motion Taylor Series Linear Vibrations Power Spectral Density

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Local block relaxation method for the solution of equations of gasdynamics

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AIAA JOURNAL 2000年第8期38卷 1377-1384页

作者： de Nicola, C Tognaccini, R Puoti, V Univ Naples Federico II Dipartimento Progettaz Aeronaut I-80125 Naples Italy Ctr Italiano Ric Aerospaz Dipartimento Caicoio Numer & Parallelo I-81043 Capua CE Italy

A new explicit pseudo-time-integration algorithm, termed local block relaxation, for the solution of the equations of gasdynamics in block-structured domains is proposed. The aim of the method is to reduce the computational costs in obtaining the numerical solution of complex flowfields. Attention is given to the definition of proper interface boundary conditions that ensure stability even if the smoothing of the solution is not synchronized in time among the blocks. Once stability is guaranteed, oversmoothings can be performed in a restricted number of blocks, namely, those that exhibit a slower rate of convergence. The method proposed is closely coupled with a standard multigrid cycle. A theoretical analysis of the savings in computational work is presented so that the convergence speed up can be estimated a priori. The strategy is shown to be effective in both two-dimensional and three-dimensional Navier-Stokes simulations. The present algorithm can be extended to a broad variety of numerical schemes based on explicit time integrations.

关键词： Gasdynamics Navier Stokes Calculations Courant Friedrichs Lewy integration algorithm Boundary Value Problems Computing Baldwin Lomax Turbulence Model Interprocessor Communication Numerical integration Freestream Conditions

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Integrating heterogeneous OO schemas

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JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 2000年第4期16卷 555-591页

作者： Chen, YJ GMD GmbH IPSI Inst D-64293 Darmstadt Germany

A key problem in providing enterprise-wide information is the integration of databases that have been independently developed. A major requirement is to accommodate heterogeneity and at the same time preserve the autonomy of component databases. This article addresses this problem and presents a strategy to integrate heterogeneous OO schemas. As compared to the existing methodologies, this approach integrates local schemes into a deduction-like global schema. In this way, more semantic relationships of component schemas can be captured, and more complete integration can be obtained. In addition, an efficient algorithm is proposed which can do the integration almost automatically, based on the correspondence assertions supplied by designers. This algorithm is efficient in the sense that the characteristics of assertions are utilized to avoid useless matchings.

关键词： federated databases correspondence assertion schema integration derivation assertion integration algorithm

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Efficiency improvement of unified implicit relaxation/time integration algorithms

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AIAA JOURNAL 1999年第1期37卷 125-128页

作者： Fujii, K Inst Space & Astronaut Sci Space Trasportat Res Div Sagamihara Kanagawa 2298510 Japan

A new implicit time-integration/relaxation scheme was proposed. The method is based on the two-factored relaxation-type scheme in which streamwise direction is chosen as a sweep direction. A new implicit scheme was constructed by adopting the approximation of the flux Jacobian matrices used in the lower-upper-symmetric Gauss-Seidel (LU-SGS) scheme for the streamwise direction and lower-diagonal-upper (LDU) approximate decomposition of lower-upper alternating direction implicit (LU-ADI) scheme. It was shown that the implicit operations in this scheme can be obtained by simply adding the spectral radius of the streamwise direction to the existing LU-ADI operations and is easy to develop from the existing code.

关键词： integration algorithm Freestream Mach Number Vortex Structure Angle of Attack Reynolds Averaged Navier Stokes Rockets Turbulence Models Computational Fluid Dynamics NACA 0012 Continuity Equation

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New constraint stabilization technique for dynamic systems with nonholonomic constraints

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1999年第3期22卷 497-499页

作者： Wu, SD Chiou, JC Yang, JY Natl Chiao Tung Univ Dept Elect & Control Engn Hsinchu 300 Taiwan

A new constraint stabilization technique based on the velocity correction method is proposed for solving multibody dynamic systems with nonholonomic constraints. By propagating the velocity errors into a nonholonomic constraint equation, a modified velocity vector is obtained that consists of a constraint Jacobian matrix and the original calculated velocity. The present method does not require one to choose parameters that greatly affect the performance in simulating MBD systems. A computational procedure based on this finding is developed to suppress the constraint violation during the process of numerical integration. (AIAA)

关键词： Numerical integration integration algorithm Numerical Simulation Convex Optimization Energy Conservation Aircraft Control Control Surfaces Linear Mapping Heading Angle Robot Arms

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Discontinuous time-integration method for dynamic contact impact problems

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AIAA JOURNAL 1999年第7期37卷 874-880页

作者： Cho, JY Kim, SJ Seoul Natl Univ Dept Aerosp Engn Kwanak Ku Seoul 151742 South Korea

A new time-integration method is proposed using the generalized derivative concept to simulate the dynamic phenomena with sudden constraint occurring in dynamic contact/impact problems. By the adoption of the generalized derivative concept and the jump assumption, discontinuity can be incorporated in time integration, and as a result, the algorithm does not need any other special consideration of jumps in dynamic field variables due to sudden constraint, such as dynamic contact-release conditions. To observe the characteristics of the proposed time-integration method, stability and convergence analyses are carried out. The analyses prove that the proposed method with linear approximation in the time domain yields unconditional stability and third-order accuracy In numerical tests, several dynamic contact/impact problems are analyzed by straightforward application of the proposed time-integration method with the exterior penalty method. From the tests, it is shown that the proposed time-integration method can be used successfully with the penalty method in numerical simulations of dynamic contact/impact problems.

关键词： Numerical Simulation Finite Element Approximation Composite Structures integration algorithm Material Properties Structural System Numerical integration Poisson's Ratio Plane Strain Dirac Delta Function

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Stability analysis of Baumgarte constraint stabilization technique in multibody dynamic systems

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1999年第1期22卷 160-162页

作者： Chiou, JC Yang, JY Wu, SD Natl Tsing Hua Univ Dept Elect & Control Engn Hsinchu 300 Taiwan

A guideline was developed to determine the stabilization parameters of Baumgarte constraint stabilization technique. The guideline, based on the stability limits of the employed numerical algorithms and the chosen integration step size, was used to systematically determine the stabilization parameter. Numerical results indicated that the current guideline yields a more accurate and robust solution than arbitrarily determined stabilization parameters in simulating multibody dynamics (MBD) systems.

关键词： Probability Density Functions integration algorithm Numerical algorithms Numerical integration Variable Structure System Holonomic Constraints Robot Arms Viscosity

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