Content deleted Content added
m →Simultaneous solutions: missed a format |
→Simultaneous solutions: expanded with info |
||
Line 19:
====Simultaneous solutions====
Simultaneous solutions are based on solving for both {{math|X}} and {{math|Z}} at the same time (rather than basing the solution of one part off of the other as in seperable solutions), propogation of error is significantly reduced.<ref name="dual-quaternions"> Algo Li, et al. [https://pdfs.semanticscholar.org/225d/e4ea2d3f18b7743bfeabf925fa603fc47bcb.pdf "Simultaneous robot-world and hand-eye calibration using dual-quaternions and Kronecker product."] International Journal of the Physical Sciences Vol. 5(10), pp. 1530-1536, 4 September, 2010. </ref> By formulating the matrices as [[dual quaternion]]s, it is possible to get a linear equation by which {{math|X}} is solvable in a linear format.<ref name="tsapps"/> An alternative way applies the [[least squares| least squares method]] to the [[Kronecker product]] of the matrices {{math|A⊗B}}. As confirmed by experimental results, simultaneous solutions have less error than seperable quaternion solutions.<ref name="dual-quaternions"/>
====Iterative solutions====
| |||