Mathematics – Probability
Scientific paper
Dec 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992acm..proc..429m&link_type=abstract
In Lunar and Planetary Inst., Asteroids, Comets, Meteors 1991 p 429-432 (SEE N93-19113 06-90)
Mathematics
Probability
Asteroids, Bayes Theorem, Error Analysis, Orbit Calculation, Orbital Elements, Covariance, Errors, Probability Density Functions, Random Noise
Scientific paper
We present a rigorous Bayesian theory for asteroid orbital error estimation in which the probability density of the orbital elements is derived from the noise statistics of the observations. For Gaussian noise in a linearized approximation the probability density is also Gaussian, and the errors of the orbital elements at a given epoch are fully described by the covariance matrix. The law of error propagation can then be applied to calculate past and future positional uncertainty ellipsoids (Cappellari et al. 1976, Yeomans et al. 1987, Whipple et al. 1991). To our knowledge, this is the first time a Bayesian approach has been formulated for orbital element estimation. In contrast to the classical Fisherian school of statistics, the Bayesian school allows a priori information to be formally present in the final estimation. However, Bayesian estimation does give the same results as Fisherian estimation when no priori information is assumed (Lehtinen 1988, and reference therein).
Bowell Edward
Muinonen Karri
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