Method for correcting non-orthogonal coordinate axes of three-dimensional coordinate system
A calibration method and coordinate system technology, applied to measurement devices, instruments, navigation through velocity/acceleration measurement, etc., can solve the problem that the external signal source cannot be covered, and achieve the effect of mutual orthogonality
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[0025] In the plane coordinate system, let the X-axis and the Y-axis be an orthogonal coordinate system, and the coordinates are x, y; the X' axis and the Y' axis are a non-orthogonal coordinate system, and the coordinates are x', y'. When the X axis coincides with the X' axis, the non-orthogonal angle between the Y' axis and the X axis or X' axis is θ XY ,exist figure 1 (a), figure 1 (b) is two non-orthogonal cases.
[0026] Depend on figure 1 (a):
[0027]
[0028] Depend on figure 1 (b):
[0029] y'=(y-x'tanθXY )cosθ XY
[0030] (2) Because the non-orthogonal angle is very small, approximately: cosθ XY ≈1 sinθ XY ≈tanθ XY ≈θ XY , and ignoring the second-order infinitesimal, formula (1) and formula (2) can be simplified as:
[0031] y=y'-x'θ XY (3)
[0032] y=y'+x'θ XY (4)
[0033] In the three-dimensional orthogonal coordinate system, O-XYZ is the orthogonal index system, and O-X'Y'Z' is the actual non-orthogonal coordinate system. Taking the X axis as...
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