Formation of the Criterion of Estimation of Navigation Systems Accuracy for Different Stages of the Flight and High Precision Navigation for the Systems of Automatic Landing

V. L. Leonidov

Abstract:	Due to the requirements to the navigation accuracy, especially to high precision navigation it comes necessary to develop the criterion for analyzing tests and simulation results taking into consideration into account selective variability. While analyzing account series of results based on statistical hypotheses theory the 1st order error can to the rejection of the system which is acceptable in terms of accuracy. The upper boundary of the critical domain defines the alpha significance level. The 2nd order error beta signifies that the system is not rejected, though it is unacceptable in terms of accuracy. The Neumann-Pearson lemma can be applied for one parameter laws and binomial distribution ; the corresponding uniform power full criterion minimizes the probability of the 2nd order error. The y2 distribution is used for analyzing samples data of the navigation error independent and normal (in the lateral deviation from the track or landing strip axis. Asymptotic properties of the 1st and the 2nd order error depending on the distribution parameter and sample number are studied. Boundary statistics values have been defined for the given a and a number of tests n in terms of the mean-root-square value delta Z for all stages of plane’s flight (Oceanic, Enroute, Terminal, Approach) and 5m for automatic landing. It is fulfilled for adoption of the Ho hypothesis in presence of the H1 : 01 > 00 completing hypothesis. A similar task of definition of the 1st and the 2nd order errors is solved also for binomial distribution. For space plane “Buran” errors of the inertial system and of the azimuth based on system’s correction are taken into account. The number of error cases has been defined on the basis of statistical experiment (n=1000) when lateral deviations are less or equal to the given delta Z* values. The significance value alpha corresponds to the Ho : P > PO = 0,997 hypothesis in presence of the competing Hl : Pl < P hypothesis. When delta Z* = 12m , the value of error the 2nd order, tends zero. In the real flight of the space shuttle “Buran” this quantity was about 3m.
Published in:	Proceedings of the 52nd Annual Meeting of The Institute of Navigation (1996) June 19 - 21, 1996 Royal Sonesta Hotel Cambridge, MA
Pages:	127 - 135
Cite this article:	Leonidov, V. L., "Formation of the Criterion of Estimation of Navigation Systems Accuracy for Different Stages of the Flight and High Precision Navigation for the Systems of Automatic Landing," Proceedings of the 52nd Annual Meeting of The Institute of Navigation (1996), Cambridge, MA, June 1996, pp. 127-135.
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