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.
Multiplicative Measurement Model
The Journal of the Astronautical Sciences ; 57 , 1-2
2009
Aufsatz (Zeitschrift)
Englisch
Multiplicative Measurement Model
Springer Verlag | 2009
|Multiplicative Measurement Model
Online Contents | 2009
|Position Estimation Using Multiplicative Measurement Model (AAS 11-143)
British Library Conference Proceedings | 2011
|Attitude Estimation Using Multiplicative Measurement Model (AAS 11-133)
British Library Conference Proceedings | 2011
|Multiplicative Measurement Model and Single-Point Attitude Estimation (AAS 08-263)
British Library Conference Proceedings | 2008
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