Scalars:
   b = bearing (device)
   i = inclination (device)
   r = rotation (device)
   dip = dip of magnetic field of vertical. negative if north pointing into ground


Vectors:
   Mr = Magnetic field vector in real world, usually (0,cos(dip),sin(dip))
   Gr = Gravitatinal field vector in real world (0,0,-1)
   Dr = Device Laser vector in real world (cos(b)*cos(i),sin(b)*cos(i),sin(i))

(cos(b)^2*cos(i)^2) + (sin(b)^2 * cos(i)^2) + sin(i)^2
= (cos(b)^2 + sin(b)^2)(cos(i)^2) + sin(i)^2
= cos(i)^2 + sin(i)^2
Tick - adds up...
Offshoot1 = O1 = Dr dot Gr - gives us a horizontal field
Offshoot 2 = O2 = Gr dot O1 - gives us our third orthogonal field

Rotational conversion matrix R(D)=

   
( Dr O1 O2)^-1 . ( sin(-r) cos(-r))
                 (-cos(-r) sin(-r))

Next we need a calibration matrix
Mx,My,Mz = Vectors of Magnetometers in Device coords eg (0.9,0.1,0.1), multiplied by scaling error
Mt = translation error (typically +512 or whatever)
Gx etc for accels

Mc = (Mx My Mz Mt)^-1
     ( 0  0  0  1)
Gc = (Gx Gy Gz Gt)^-1
     ( 0  0  0  1)

Final data = Md = Mr x R x Mc
           = Gd = Gr x R x Gc



Convert Realworld co-ords of device vector into a matrix

Device operation
Gc' = Mc' = devices calibration thingy - should be inverses of Mc and Gc

G = Gd.Gc'
M = Md.Mc'

D(own) = G
E(ast) = G.M
N(orth)= E.G
Translation matrix T = (E N D)^-1
Dr = (1 0 0) T


b = tan(Dr.x/Dr.y)
i = tan(Dr.z/sqrt(Dr.x^2 + Dr.y^2))

Sweet