Abstract This paper introduces the Multiplicative Measurement Model for observed vectors where the error is modeled as a rigid rotation of the true direction about an axis orthogonal to it. Motivation comes from the fact that the linear additive model, b = Cr + v, where ${\rm v} \sim {cal N}(0,R)$, is in contradiction with nonlinear rotational mechanics. The resulting true-to-nature multiplicative error model highlights a small effect (due to the spherical geometry) affecting any vector observation in space. The consequence of this effect is that the angle between unbiased measurements is biased. This three-dimensional effect, which increases when the sensor accuracy decreases, is here quantified in two direction-based observation systems: a) attitude estimation and b) positioning estimation systems. The multiplicative measurement covariance matrix is derived. Preliminary calculations suggest that the problem of attitude estimation is affected to a small extent because attitude optimality indirectly compensates for the 3D effect. On the other hand, this 3D effect is shown to affect positioning estimation from direction measurements. A comparison between the precision provided by multiplicative and additive models is given for a simple two-measurement case.


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    Title :

    Multiplicative Measurement Model


    Contributors:


    Publication date :

    2009




    Type of media :

    Article (Journal)


    Type of material :

    Print


    Language :

    English



    Classification :

    BKL:    55.60 Raumfahrttechnik
    Local classification TIB:    770/7040



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