MULTIPLICATIVE MEASUREMENT MODEL AND SINGLE-POINT ATTITUDE ESTIMATION
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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, b̃ = C r + v, where v ∼ 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. Consequence of this effect is that the angle between unbiased measurements is biased. This 3-Dimensional effect, which increases when the sensor accuracy decreases, has important consequences to all direction-based observation systems (e.g., triangulation and positioning systems, optical navigation systems, etc.). In particular, the problem of attitude determination is affected to a small extent because attitude optimality indirectly compensates for it. This study shows how to modify the problem of optimal attitude estimation and formulates an unconstrained least squares and a constrained iterative technique to solve for the single-point attitude estimation case. The error in positioning systems caused by disregarding this effect is quantified.
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