TY - JOUR
T1 - Time Series Analysis of 3D Coordinates Using Nonstochastic Observations
AU - Velsink, Hiddo
PY - 2016/3/1
Y1 - 2016/3/1
N2 - Adjustment and testing of a combination of stochastic and nonstochastic observations is applied to the deformation analysis of a time series of 3D coordinates. Nonstochastic observations are constant values that are treated as if they were observations. They are used to formulate constraints on the unknown parameters of the adjustment problem. Thus they describe deformation patterns. If deformation is absent, the epochs of the time series are supposed to be related via affine, similarity or congruence transformations. S-basis invariant testing of deformation patterns is treated. The model is experimentally validated by showing the procedure for a point set of 3D coordinates, determined from total station measurements during five epochs. The modelling of two patterns, the movement of just one point in several epochs, and of several points, is shown. Full, rank deficient covariance matrices of the 3D coordinates, resulting from free network adjustments of the total station measurements of each epoch, are used in the analysis.
AB - Adjustment and testing of a combination of stochastic and nonstochastic observations is applied to the deformation analysis of a time series of 3D coordinates. Nonstochastic observations are constant values that are treated as if they were observations. They are used to formulate constraints on the unknown parameters of the adjustment problem. Thus they describe deformation patterns. If deformation is absent, the epochs of the time series are supposed to be related via affine, similarity or congruence transformations. S-basis invariant testing of deformation patterns is treated. The model is experimentally validated by showing the procedure for a point set of 3D coordinates, determined from total station measurements during five epochs. The modelling of two patterns, the movement of just one point in several epochs, and of several points, is shown. Full, rank deficient covariance matrices of the 3D coordinates, resulting from free network adjustments of the total station measurements of each epoch, are used in the analysis.
KW - 3D Coordinates
KW - Full
KW - Geodetic Deformation Analysis
KW - Nonstochastic Observations
KW - S-basis Invariant Testing
KW - Singular Covariance Matrices
KW - Time Series
UR - http://resolver.tudelft.nl/uuid:c6049c97-c213-4a51-9d9f-bb1069291b7f
UR - http://www.scopus.com/inward/record.url?scp=84960962335&partnerID=8YFLogxK
U2 - 10.1515/jag-2015-0027
DO - 10.1515/jag-2015-0027
M3 - Article
AN - SCOPUS:84960962335
SN - 1862-9016
VL - 10
SP - 5
EP - 16
JO - Journal of Applied Geodesy
JF - Journal of Applied Geodesy
IS - 1
ER -