bundle block adjustment with 3d natural cubic splines

5.2 Experiments with error free EOPsSince spline parameters and spline location parameters are dependent with respectto other parameters, the unknowns can be obtained by the combined model ofthe extended collinearity equations and the arc-length parameterization equations ofsplines. Splines in the object space are considered as tie lines in the same fashionas tie points in conventional bundle block adjustment. Information about the exteriororientation parameters is considered as control information in this experiment.A well-known fact of least squares system is that the good initial estimates to truevalues make the system convergent to the correct solution quickly and correctly. Theequation system of integrated model is described as⎡⎢⎣A k SPA i t⎤ ⎡⎥ ⎢⎦ ⎣ξ i SP⎤⎥⎦ = [ y ki ] (5.1)A i ALξ i tA i SP =A kit =A kiAL =⎡Mi7 1 Mi8 1 · · · M 1 ⎤i18.M i7 m Mi8 m · · · M m i18N 1 i7 Ni8 1 · · · Ni181 ⎢⎥⎣ .⎦Ni7 m Ni8 m · · · Ni18m⎡Mi19 1 Mi20 1 · · · Mi18+n1.M i19 m Mi20 m · · · M m i18+nN 1 i19 Ni20 1 · · · Ni18+n1 ⎢⎥⎣ .⎦Ni19 m Ni20 m · · · Ni18+nm ⎡A k1⎤i1⎢⎣.A kmi1A k1i2 · · · A k1i20A kmi2 · · · A kmi20⎥⎦⎤78