Exact or Least-Squares Solution 5 Equations

Hello;

I've tried a number of techniques to solve 5 equations in 5 unknowns
with no avail!! I hope someone might have either come across a
similar problem or has the appropriate analytical tools and would be
kind enough to share his/her expertise.

Here's a brief discription of the problem.

5 UNKNOWNS: B, C, D, F, G

SQRT { (x2-F)^2 + (y2-G)^2 } = { a + B.t2 + C.t22 + D.t23 } Exp(m.t2)
SQRT { (x3-F)^2 + (y3-G)^2 } = { a + B.t3 + C.t32 + D.t33 } Exp(m.t3)
SQRT { (x4-F)^2 + (y4-G)^2 } = { a + B.t4 + C.t42 + D.t43 } Exp(m.t4)
SQRT { (x5-F)^2 + (y5-G)^2 } = { a + B.t5 + C.t52 + D.t53 } Exp(m.t5)
SQRT { (x6-F)^2 + (y6-G)^2 } = { a + B.t6 + C.t62 + D.t63 } Exp(m.t6)

All other quantities in the above equations are known.

Q1: What are the exact expressions for B, C, D, F, G ??

Q2: In the event that such exact expressions are defficult/impossible
to derive (I certaily hope not!), then what are the least-squares
regression formulas ??

Your expert help would be greatly appreciated.
Monir

.

Loading