Abstract We address the problem of constructing the probability density function (pdf) of a random attitude when there is no a priori knowledge of the attitude of any kind. We first define generally, on the basis of purely physical arguments, what is meant by such a uniform pdf of the attitude and develop a general expression from which the pdf for most three-dimensional attitude representations can be determined. We then calculate explicit expressions for this completely a priori pdf for the attitude quaternion, both for the vectorial components alone and as a function of all four components treated independently in R4. On the basis of this last pdf we develop a universal expression for the uniform pdf of any three-dimensional representation of the attitude. Explicit expressions for the uniform pdf of the more useful attitude representations are presented and also methods for computing samples of these uniformly distributed attitude representations. The possible consequences of this work for attitude estimation are discussed briefly. The connection of the present work to the classical mathematical literature is also discussed briefly.
Uniform Attitude Probability Distributions
2003
Aufsatz (Zeitschrift)
Englisch
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