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:{{math|'''R'''<sub>A</sub>'''R'''<sub>X</sub>{{=}}'''R'''<sub>Z</sub>'''R'''<sub>B</sub>}}
:{{math|'''R'''<sub>A</sub>'''t'''<sub>X</sub>+'''t'''<sub>A</sub>{{=}}'''R'''<sub>Z</sub>'''t'''<sub>B</sub>+'''t'''<sub>Z</sub>}}
The second equation becomes linear if {{math|'''R'''<sub>Z</sub>}} is known. As such, the most frequent approach is to {{clarify|date=June 2020 |reason=seems to be missing a verb here}} {{math|'''R'''<sub>x</sub>}} and {{math|'''R'''<sub>z</sub>}} using the first equation then using it to solve for the second two variables in the second equation. Rotation is represented using [[quaternion]]s, allowing for a linear solution to be found. While separable methods are useful, any error in the estimation for the rotation matrices is compounded when being applied to the translation vector.<ref name="tsapps">Mili Shah, et al. [https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=910651 "An Overview of Robot-Sensor Calibration Methods for Evaluation of Perception Systems."]</ref> Other solutions avoid this problem.
===Simultaneous solutions===
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