By The Analytic Sciences Corporation, Arthur Gelb
Written through contributors of the technical employees, Analytic Sciences Corp.
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Extra info for Applied Optimal Estimation
Subtracted) can be defined. This does not suggest that certain constant state variables cannot be considered; as long as their distribution over the ensemble of possible values is unbiased, constant state variables are admissible. It should be pointed out that if the state at some time to isunbiased, the state will remain unbiased. This can be illustrated by taking the ensemble average of both sides of Eq. (kl =0 When r = & Eq. 6-2) defines the c o v a ~ n c eof l; it is simply a matrix whose elements are the second moments of the random components r l , s,.
Self-Contained Orbital Navigation Systems w t h Correlated Measurement Errors," AIAA/ION Guidance and Connol Conference Proceedings, August 1965, pp. 231-247. 7. A. , "Predicted Performance of an Integrated OMEGAIlnertial Navigation System," Prm. N~otionalAerospace Elecnonics Conference, May 1971. 8. A. , F7zysieol Geodesy. H. Freeman, San Francisco, 1967. 9. , "A Geaidal Section in the United States," Bull. , Vol. 65, 1962. 10. A. and Gelb, A,, "Effect of Deflections of the Vertical on the Perfomance of a Terrestrial inertial Na j a t i o n System," I.
These factors are treated analytically in Refs. 12 and 13; brief summaries are given here. S. - A sequence of measurements taken at intervals At over a period T is used to obtain an empirical autocorrelation function N-Q and d is the distance shift parameter. As described in Ref. 10, the fitted function from which Eq. 9-5) is obtained is derived using techniques which compensate for finite data. Thus, it is not unnatural that the function is negative at large distance shifts. In this example the correlation distance D is approximately twice the data interval.
Applied Optimal Estimation by The Analytic Sciences Corporation, Arthur Gelb