The paper includes a correlation analysis of the orbit parameters, Earth rotation parameters and the geopotential coefficient C20, based on covariance matrices from weekly solutions.
However, we find that first finding the optimal rotation parameters and keeping it fixed, as described in [33] leads to errors in subsequent optimization steps when the rotation estimate is flawed.
The range measurements are used for precise orbit determination (POD), study of tectonic plate motion, as well as determination of Earth's gravity field, Earth rotation parameters, and geocenter position (Moore and Wang 2003).
Preprocessing included slice-time correction, rigid body movement correction (three translation, three rotation parameters), and normalization of the functional images by directly registering the mean functional image to the standard Montreal Neurological Institute (MNI) echo-planar-imaging template image provided by SPM8, with a resulting interpolated spatial resolution of 3 × 3 × 3 mm.
The first type yields values of (R_{L1}), (Omega_{1}), (X_{2}), (Omega_{2}), (X_{3}), (Omega_{3}), (R_{bk}), (R_{y}), (R_{z}), A, V and (R_{eq}), where the various symbols are defined above, given input values of mass ratio, q, stellar rotation parameter, p, and stellar fill-out factor, F. The second type gives the Roche radius in any direction specified by the user.
Therefore, we used a repeated-measures ANOVA (analysis of variance) for each individual translation and rotation parameter, with time as the within-subject factor and with/without screws as between-subjects factor.
The Lorenz-Stenflo equation is regarded as an extended Lorenz equation since it reduces to the Lorenz equation [1] when the rotation parameter s is zero, and it also can be obtained from the rotating thermal convection equations.
Assuming an arbitrary scale parameter h and rotation parameter θ that produces the candidate function Φ c, both the current image frame I and the candidate function Φ c are transformed according to: Φ ~ c ( x, y ) = Φ c ( x ~, y ~ ) (33) I ~ ( x, y ) = I ( x ~, y ~ ), (34).
Head motion was restricted with foam padding and straps over the forehead and under the chin (estimated translation and rotation parameters were inspected and never exceeded 2 mm or 2°).
However, as described above, if the transformation for directly above viewpoint has been added, the posture variables can be thought of as a total of three degrees of freedom; two parallel movement parameters (x, y) and a rotation parameter (theta) on the plane.
