2.1.2.2 Measured orientation angles (IMU)
GPS / IMU systems are available for nearly all camera types. These systems perform direct measurements of photo orientation positions and angles during the photo flight. For terrestrial photos, many of the cameras are also equipped with angle measurement devices, allowing to measure the orientation angles for ϕ and ω and partly also for κ. In cases of terrestrial exposures even the angle κ can adopt predefined, known values, namely by means of levels or by rotating the camera in fixed notches.
These measured values or known angle values can be used as further observations in the adjustment. But the measured orientations will deviate from the real values by constant direction differences. The angle differences, resulting of the orientation differences, cannot be added to the angle values, but have to be combined with them by a three-dimensional rotation, even in case of very small correction angles. The equation is defined as follows:
with
Rotation from ground to instrument (measurement values Φ, Ω, Κ of the IMU or of a photo theodolite).
Rotation matrix of the photo. Rotation from ground to photo (orientation angles ϕ ω κ)
Rotation from photo to instrument (calibration angles dϕ dω dκ)
As soon as the equation according to 2.1.2/2 is used, the calibration angles are automatically introduced into the adjustment as additional unknowns. They are constant for the photo camera and belong to its calibration values. If dφ, dω and dκ are known, they can be introduced into the adjustment as additional observations.
For terrestrial applications, a standard deviation of ¼ of the level indication is suggested to calculate the weight of the measured angles.
Restrictions:
The chosen equation does not consider eventual rotation axes errors of the angle measurement system, but requires strictly orthogonal rotations. A probable meridian convergence has to be corrected beforehand; otherwise the results are definitively wrong!