1. Example: Earth Rotation
G51A-0604
Filtering techniques to enhance signal extraction
from geodetic time series
Lomonosov Moscow State University
Leonid Zotov
Sternberg Astronomical Institute, MSU, Russia; Geodetic Science, School of Earth Sciences, Ohio State University, USA
From the mathematical point of view we can extract useful information from the signal only if we are able to find a basis (functional, vectorial, etc.), where it is separable from the undesirable systematic errors and noise.
Dynamic system u y x
input (cause)
output (consequence)
state
principal components
basis (SSA)
Fourier basis
wavelet basis
The more difficult aim is to separate useful components from the signal, which has been non-uniformly transformed by a dynamic system. In this case a system model should be build and an inverse problem can be formulated. Additional filtering is needed to regularize the solution and to prevent the inadmissible strengthening of observation noises. We suggest Panteleev corrective smoothing as such a procedure.
Example: Earth Rotation
years
frequency
Correlation analysis is an important step needed for linear filtering, which allows projection of the signal onto the selected basis and finding out its features. Operation of filtering consists of weighing. If we need to separate useful components, we need to transform all the signals into the characteristic space, where desirable components have specific differences (e.g., frequency band), and build a procedure of separation, or to build a filter which gives higher weights to valuable components and smaller weights to undesirable ones.
hat means Fourier transform
SSA-components of observations
Reconstructed excitation
Normal equations allows to project the object on the space of linear estimations (normal system in LSM, LS Collocation, Wiener-Hopf equation, etc.)
It looks like the Chandler oscillation is decreasing in the last years.
We find important developing the methods of generalized transfer function modeling and proper functions search for the cases of different, may be nonlinear systems. It means, that we should find a set of signals, which involves all the interior of the system, making it to response by all its essence. Sometimes it is possible to find a transformation, which converts the nonlinear filtering problem to the linear case (holomorph filtering).
Acknowledgement: Sponsored by C.K.Shum, RFBR grants and