After net-adjustments of old and new triangulation networks in which the same fixed stations are assumed, we can obtain displacement vector (V) of an arbitrary station by subtracting the old coordinates (X″) from the new coordinates (X′) and the variances and covariances (Σ
x″, Σ
x′) of the station are
After rotating the coordinate system with the angle 6, we obtain the following vari-ances
σ
2θ″=TΣx″T
t, σ
2θ′TΣx′T
t where T is [cos θ sin θ] and T
t is transpose of T.
Because the new and old observations are uncorrelate, variance of V(σ
2v) in the direction θ is given by (σ
2θ″+σ
2θ′). Substituting the proper values of θ gives the maximum or minimum values of σ
2v, which may be reduced to
maximum=1/2(σ
2x+σ
2y+ω)
minimium=1/2(σ
2x+σ
2y-ω)
ω-{(σ
2x-σ
2y)
2+4σ
2xy}
1/2,
where
Direction of principal axis ψ is given by
φ=1/2 tan
-12σxy/(σ
2X-σ
2Y)
By using this method, we estimate the errors of the displacement vectors in KANTO-TOKAI district. As a result of the estimation we fined that the obtained dis-placement vectors are reliable. But we do not consider error of the displacement vector due to error of the fixed stations in this paper.
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