meetings - Space Flight Mechanics Committee

Feb 11, 2013 Kauai Salon 1
SESSION 1: ORBIT DETERMINATION AND ESTIMATION THEORY -- I
Chair: Dr. Michael Gabor, TASC
8:00 AAS Nonlinear filtering based on Taylor differential algebra
13-200 Roberto Armellin, Politecnico di Milano
Nonlinear filtering plays an important role in various space-related applications. An
innovative filter based on Taylor differential algebraic (DA) technique is proposed. This is
based on updating the entire conditional probability density function whenever a new
measurement becomes available. The update is performed applying Bayes' rule. The
probability density function is represented as an arbitrary order Taylor series. The process is
enabled by the DA evaluation of the involved probability density functions. The case of an
Earth orbiting satellite with realistic initial orbit uncertainties and nonlinear measurements
is presented to discuss the performances of the proposed filtering algorithm.
8:20 AAS Chebyshev Interpolation for VLS
13-201 James Wright, Analytical Graphics, Inc.; William Chuba, Analytical Graphics, Inc.
The variable lag smoother (VLS) is a forward running filter-smoother for sequential orbit
determination. Multiple smoothed state estimates are updated at distinct fixed epochs
simultaneously with each filter state estimate update. But smoothed estimates must be
interpolated. Uniform time-grid Lagrange interpolation is unacceptably slow due to required
computation of many fixed-epoch smoothers. But the number of VLS fixed epoch
smoothers required for non-uniform Chebyshev series interpolation is far fewer. Thus
computer wall time through-put is significantly faster with Chebyshev. The results of a
LEO simulation with an interpolation interval of five hour duration is presented.
8:40 AAS On the Expected Value of Sensed Data
13-477 James D. Turner, Texas A&M University; Ahmad Bani Younes, Texas A&M
University
Tensor-based state transition power series solutions are developed for propagating the
uncertainty in the system initial conditions and parameters for nonlinear systems. The
tensor power series are used to develop analytic models for the nonlinear statistical
moments of the system behavior. A second-order expansion is developed for the system
observation equation that accounts for the initial condition and parameter uncertainty. An
analytic expectation operator is used to evaluate the expected value of the system
observation equation, thereby producing a nonlinear prediction of the current value of the
observed state that accounts for system dynamics.
9:00 AAS Analytic Characterization of Measurement Uncertainty and Initial Orbit
13-203 Determination on Orbital Element Uncertainty and Correlation
Ryan Weisman, Texas A&M University; Manoranjan Majji, University at Buffalo,
State University of New York; Kyle T. Alfriend, Texas A&M University
23 rd AAS / AIAA Space Flight Mechanics Meeting Page 17