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  • 11
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    New method for propagating the square root covariance matrix in triangular form (1975)
    In:  Other Sources
    Details
    Publication Date: 2019-06-27
    Description: A method proposed by Potter of applying the Kalman-Bucy filter to the problem of estimating the state of a dynamic system is described, in which the square root of the state error covariance matrix is used to process the observations. A new technique which propagates the covariance square root matrix in lower triangular form is given for the discrete observation case. The technique is faster than previously proposed algorithms and is well-adapted for use with the Carlson square root measurement algorithm.
    Keywords: NUMERICAL ANALYSIS
    Type: AIAA Journal; 13; May 1975
    Format: text
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  • 12
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    An algorithm for propagating the square-root covariance matrix in triangular form (1976)
    In:  Other Sources
    Details
    Publication Date: 2019-06-27
    Description: A method for propagating the square root of the state error covariance matrix in lower triangular form is described. The algorithm can be combined with any triangular square-root measurement update algorithm to obtain a triangular square-root sequential estimation algorithm. The triangular square-root algorithm compares favorably with the conventional sequential estimation algorithm with regard to computation time.
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: IEEE Transactions on Automatic Control; AC-21; Feb. 197
    Format: text
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  • 13
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    Nonlinear estimation theory applied to orbit determination (1972)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: The development of an approximate nonlinear filter using the Martingale theory and appropriate smoothing properties is considered. Both the first order and the second order moments were estimated. The filter developed can be classified as a modified Gaussian second order filter. Its performance was evaluated in a simulated study of the problem of estimating the state of an interplanetary space vehicle during both a simulated Jupiter flyby and a simulated Jupiter orbiter mission. In addition to the modified Gaussian second order filter, the modified truncated second order filter was also evaluated in the simulated study. Results obtained with each of these filters were compared with numerical results obtained with the extended Kalman filter and the performance of each filter is determined by comparison with the actual estimation errors. The simulations were designed to determine the effects of the second order terms in the dynamic state relations, the observation state relations, and the Kalman gain compensation term. It is shown that the Kalman gain-compensated filter which includes only the Kalman gain compensation term is superior to all of the other filters.
    Keywords: SPACE SCIENCES
    Type: NASA-CR-127326 , AMRL-1038
    Format: application/pdf
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  • 14
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    Nonlinear estimation theory applied to the interplanetary orbit determination problem. (1972)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: The performance of a second order filter which is identical to the algorithm developed by Athans et al. (1968) for the scalar case is evaluated through numerical simulation of a Jupiter flyby mission. The observations used in the simulation are on-board measurements of the angle between Jupiter and a fixed star taken at discrete time intervals. In the numerical study, the influence of each of the second order terms is evaluated.
    Keywords: ELECTRONICS
    Type: Conference on Decision and Control and Symposium on Adaptive Processes; Dec 13, 1972 - Dec 15, 1972; New Orleans, LA
    Format: text
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  • 15
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    Nonlinear estimation theory applied to the interplanetary orbit determination problem. (1972)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: Martingale theory and appropriate smoothing properties of Loeve (1953) have been used to develop a modified Gaussian second-order filter. The performance of the filter is evaluated through numerical simulation of a Jupiter flyby mission. The observations used in the simulation are on-board measurements of the angle between Jupiter and a fixed star taken at discrete time intervals. In the numerical study, the influence of each of the second-order terms is evaluated. Five filter algorithms are used in the simulations. Four of the filters are the modified Gaussian second-order filter and three approximations derived by neglecting one or more of the second-order terms in the equations. The fifth filter is the extended Kalman-Bucy filter which is obtained by neglecting all of the second-order terms.
    Keywords: SPACE SCIENCES
    Type: AD-765232 , AFOSR-73-1436TR , Symposium on Nonlinear Estimation Theory and its Applications; Sep 11, 1972 - Sep 13, 1972; San Diego, CA
    Format: text
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