Abstract
The LB-planning is a construction of the dependence between three variables k, m, and Δ, where k is the number of parameters of the linear dynamic system (LDS) under study, m is the specified number of measurements (communication sessions), and Δ (defect) is the maximum value of failure (set of all criterion functions) in a chosen m-point measurement program relative to the optimal program. The problem is reduced to the solution of an extremal problem, which, at m = k + 1, is found rather simply by maximization of the Tchebyshev determinant (TD-planning).
Similar content being viewed by others
REFERENCES
Bakhman, F. and Shmidt E., N-ugol'niki (Polygons), Moscow: Mir, 1969, p. 34.
Belousov, L.Yu., Multi-Purpose Planning within the Model of Measurement Errors with Arbitrary Correlation, Kosm. Issled., 1980, vol. 18, no. 5, p. 790.
Belousov, L.Yu., Tchebyshev Approximation as a Solution to the Problem of Multi-Purpose Planning at Arbitrary Correlated Errors of Measurement, Kosm. Issled., 1982, no. 6, p. 808.
Belousov, L.Yu. and Panyushin, A.N., Modified Method of Solving the Problem of Multi-Purpose Planning under the Tchebyshev Approximation, Kosm. Issled., 1981, vol. 29, no. 2, p. 163.
Belousov, L.Yu., On the Problem of Evaluation Taking the Influence of Unmodeled Accelerations into Account, Kosm. Issled., 1994, vol. 32, no. 4, p. 66.
Belousov, L.Yu., Processing of Noninterrogative Distance Measurements with Error of Onboard Time Scale and Uncertainty of Light Pressure Forces Taken into Account, Kosm. Issled., 2000, vol. 38, no. 3, pp. 286–295.
Global'naya sputnikovaya radionavigatsionnaya sistema “GLONASS” (Global Satellite System GLONASS for Radio Navigation), Kharisov, V.N., Perov, L.I., and Boldin, V.A., Eds., Moscow: IPRZhR, 1998.
Kieffer, J., Optimal Plans of Regression Experiments, Matematika, 1974, vol. 18, no. 2.
Kieffer, J. and Wolfowitz, J., The Equivalence to Two Extremum Problems, Can. J. Math., 1960, no. 12, p.363.
Matematicheskaya teoriya planirovaniya eksperimenta (Mathematical Theory of Experiment Design), Ermakov, S.M., Ed., Moscow: Nauka, 1983, p. 125.
Marcus, M. and Minc, H., A Survey of Matrix Theory and Matrix Inequalities, University of California Santa Barbara, Boston: Aliyn and Bacon, 1964, p. 96.
Nevol'ko, M.P., Drobin, I.S., and Belousov, L.Yu., Planning Navigation Measurements Using the TD-Criterion for Determination of Spacecraft Motion by the Least Squares Method, Kosm. Issled., 1984, vol. 22, no. 2, p.159.
Sachov, V.N., Kombinatornye metody diskretnoi matematiki (Combinatorial Methods of Discrete Mathematics), Moscow: Nauka, 1977, p. 73.
Podinovskii, V.I. and Nogin, V.D., Pareto-optimal'nye resheniya mnogokriterial'nykh zadach (Pareto-Optimal Solutions to Multicriteria Problems), Moscow: Nauka, 1982.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Belousov, L.Y. Application of LB-Planning for Designing the Programs of Trajectory Measurements. Cosmic Research 40, 455–466 (2002). https://doi.org/10.1023/A:1020694800959
Issue Date:
DOI: https://doi.org/10.1023/A:1020694800959