1. 6666666641˙
2. All terms are previously defined except for u and v. There are two variations of both u and v associated with either the transmitter or receiver shown in Eqs. 25-28. Note that for conciseness # is a stand-in variable for the components x;y and z.
3. The simplest solution necessitates that both T1=T2=0. Thisconditionissatisfiedwhenthereferenceand calibrator positions are coincident, rrtr =rttr. This is a non-physical solution and therefore disregarded, see condition 3 in Table 1. There are a number of other solutions possible but they would require assumptions 1-3 to be violated in Table 1 except for the following solution to Eq. 35,
4. F1δr1+J1δv1+F2δr2+J2δv2 =0: (37) Again the most straightforward solution is for F1= F2= J1= J2= 0. Using Eqs. 23 - 30 we find this solution to be non-physical as well. Two solutions are found that do not violate assumptions 1 and 3, they are, F1 =-δr~2 & F2=~δr~1 & J1=-δv~2 & J2=~δv~1 or,
5. (43) Eq. 43 is substituted into Eqs. 38 and 39 to obtain a comprehensive solution to the necessary conditions from rows 1-3.