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Exact(14)
So are the two route elements across-track.
The two route elements along-track are equally long.
Positions and hence the route elements have no uncertainty (Medium Orbit Determination MOD, ~1 m).
Points Q1, …, Q4 are positions on the orbit tracks of satellites SwA and SwB connected by route elements dℓ.
Hence the variation of the ICR uncertainty depends entirely on the variation of the cross-track route elements dℓ2.
The route elements are estimated from the Cartesian position vectors: (5)The route elements, dℓ, mark the path from one quad point to the next one; for example, dℓ1 marks the path from point Q1 to point Q2. Figure 3 top) shows the evolution of the route elements' size on one full orbit.
Similar(46)
The second term is constant, since the route element dℓ1 doesn't vary along the orbit.
The angle α describes the angle between an along-track route element and the direction towards the pole, whereas β denotes the angle between a route element transverse to the flight direction and the poleward direction.
dℓ is a route element along the integration path, B is the measured magnetic field vector (B x, B y, B z ) in the coordinate frame of the flight direction (VHQ).
dℓ is a route element along the integration path, B is the residual magnetic field vector (B x, B y, B z ) in the coordinate frame of the flight direction (VHQ, Velocity-Oriented Horizontal Quad, see Section 7), A is the encircled area, and μ0 is the magnetic permeability.
Along-track-route elements along track, dℓ1,3, are constant, whereas those between the satellites, dℓ2,4, are smallest close to the geographic poles, where the satellites' orbits cross.
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