Principle Component Analysis on Absolute TEC Values and its Impact on Kalman Filtering when using a Priori Information

J. Jakobsen, P. Knudsen, A.B.O. Jensen

Abstract:	In this work time series from 1999 – 2007 of absolute TECU for an area midpoint as well as a latitudinal and longitudinal variation of the electron density has been calculated using a Kalman filter. Dual frequency data from three reference stations in Denmark (56°N latitude) with a station separation of approximately 130-207 km. has been used. For each year a Singular Value Decomposition (SVD) has been performed on the three variables in order to determine the daily, yearly and 11 year characteristic of the ionosphere. The SVD analysis has shown a very dominant first eigenvalue (approximately 6 times larger than the second eigenvalue) and this eigenvalue correspond clearly to how the daily variation vary over the year. The second eigenvalue correspond to how the width of the daily peak varies over the year and the third eigenvalue show a clear yearly variation of the daily signal with peaks around the equinoxes. For the latitudinal and longitudinal variations the first eigenvalue is less dominant (2-3 times larger than the second eigenvalue), but shows the same characteristic. The eigenvalues for each year show a clear correlation with the sunspot number with a correlation coefficient of approximately 0.95. A power spectrum for the entire time series has been processed and shows a yearly signal as well as a very clear daily signal with amplitude of approximately 7.4 TECU. An a priori model of the ionosphere for the three variables is generated from the signals identified in the SVD analysis using the first three eigenvalues. This model is used to optimize the Kalman filter processing. When using the a priori model the standard deviation on the residuals are reduced especially during years with high ionospheric activity. Furthermore the initialization time of the Kalman filter are reduced significantly using the a priori models as starting values.
Published in:	Proceedings of the 2008 National Technical Meeting of The Institute of Navigation January 28 - 30, 2008 The Catamaran Resort Hotel San Diego, CA
Pages:	884 - 892
Cite this article:	Jakobsen, J., Knudsen, P., Jensen, A.B.O., "Principle Component Analysis on Absolute TEC Values and its Impact on Kalman Filtering when using a Priori Information," Proceedings of the 2008 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2008, pp. 884-892.
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