GPS World, February 2014

Algorithms Methods INNOVATION FIGURE 2 The network of the four stations used in the evaluation procedures estimate for each station a constant term one to describe the longitude variations and one for the latitude variations The mapping function used in the model is the standard geometric mapping function which computes the secant of the zenith angle of the signal geometric ray path at the IPP DW D VSHFL HG VKHOO KHLJKW HFDXVH RI WKH GHSHQGHQFH RI WKH LRQRVSKHUH RQ VRODU UDGLDWLRQ DQG WKH JHRPDJQHWLF HOG WKH solar geomagnetic reference frame is used to compute the TEC over each station in this technique Since the ionosphere FKDQJHV PRUH VORZO LQ WKH VXQ HG UHIHUHQFH IUDPH WKDQ LQ WKH DUWK HG RQH VXFK D UHIHUHQFH IUDPH LV LGHDO IRU producing more accurate TEC estimates 7KH LQLWLDO YHUVLRQ RI 81 07 LJQRUHG WKH QRQ OLQHDU spatial variation of the ionosphere Non linear terms are H SHFWHG WR EH DEOH WR DEVRUE PRUH FRPSOH YDULDELOLW RI WKH ionosphere and thus more properly describe the ionosphere in disturbed conditions Regarding this issue the drawbacks of some modeling methods based on linear models have EHHQ UHSRUWHG IRU H DPSOH WKH KLJKO YDULDEOH LRQRVSKHUH PLJKW EH DEVRUEHG E WKH HVWLPDWHG V PDNLQJ WKH UHSHDWDELOLW RI WKH HVWLPDWHG V GD WR GD YDULDELOLW correlated with the variability of the ionosphere To enhance WKH SHUIRUPDQFH RI 81 07 HVSHFLDOO XQGHU GLVWXUEHG LRQRVSKHULF FRQGLWLRQV 81 UHVHDUFKHUV H WHQGHG WKH OLQHDU YHUVLRQ RI 81 07 WR D TXDGUDWLF RQH DQG DVVHVVHG LW E using a wide area regional network in North America This PRGL HG DSSURDFK UHGXFHG WKH SRVW W UHVLGXDOV VLJQL FDQWO by better modeling the ionospheric variations with the help of WKH DGGLWLRQDO VHFRQG RUGHU QRQ OLQHDU WHUPV To better use a priori information in the development of 3D 81 07 ZH VHSDUDWH WKH 7 LQWR D EDFNJURXQG UHIHUHQFH or known part and a perturbation or to be modeled part The background reference part of TEC could be calculated from an a priori source of electron density such as any kind of ionospheric model including empirical and theoretical ionospheric models The density as a function of latitude longitude height and time is integrated along the raypath between the receiver and a satellite Then the perturbation part of the electron density is modeled by the inner product of EOFs and polynomial IXQFWLRQV ZLWK DVVRFLDWHG HVWLPDWHG FRHI FLHQWV WR GHSLFW WKH variability of the ionosphere in the vertical and horizontal directions respectively And this part is similarly integrated along the raypath and added to the reference part along with WKH V Empirical Orthogonal Functions The EOF method is a method RI FKRLFH IRU DQDO LQJ WKH YDULDELOLW RI D VLQJOH HOG ZLWK RQO RQH VFDODU YDULDEOH 9DULDELOLW RI WKH LRQRVSKHUH ZLWK respect to height is needed for the 3D models The method QGV WKH VSDWLDO SDWWHUQV RI YDULDELOLW EDVHG RQ KLVWRULFDO GDWD VHWV DV UHÀHFWHG LQ HPSLULFDO RU WKHRUHWLFDO PRGHOV Q RWKHU words the modes of variability decomposed by the method are primarily data modes and not necessarily physical or actual real time models Due to its noted ability in describing the background ionosphere the data sets output from the empirical Ionospheric Reference Ionosphere 2007 were utilized to form the EOFs in our technique Thus the data sets of electron densities are realized by uniform sampling at the following variant time scale intervals DQG VSHFL F JHRJUDSKLF ORFDWLRQV 6RODU F FOH @ HDU 6HDVRQ RI HDU HF 0DU XQ 6HS @ PRQWK 7LPH RI GD @ KRXU D RI PRQWK @ GD RI PRQWK HRJUDSKLF ODWLWXGH @ GHJUHH HRJUDSKLF ORQJLWXGH @ GHJUHH where the numbers separated by colons correspond to PLQLPXP LQFUHPHQW PD LPXP 7KH GDWD VHWV FRYHU WKH ZKROH spatial area of interest The data sets of a whole solar cycle in W SLFDO HTXLQR DQG VROVWLFH PRQWKV DUH XVHG WR HQVXUH WKDW WKH 2 V VSDQ WKH UDQJH RI SUR OH YDULDWLRQV WKDW LQFOXGH WKH YDULDWLRQ LQ VRODU 89 DQG UD RXWSXW DFK HOHFWURQ GHQVLW SUR OH ZLWK UHVSHFW WR KHLJKW DW WKHVH ORFDWLRQV DQG WLPH SRLQWV LV VDPSOHG LQ WKH YHUWLFDO GLPHQVLRQ DW @ NP FIGURE 1 VKRZV WKH UVW WKUHH WKLUG RUGHU QRUPDOL HG 2 V EDVHG RQ WKH GDWD VHWV 7KH UVW WKUHH HLJHQYDOXHV DFFRXQW for 9222 669 and 078 percent of the total respectively Provided the solution is nonsingular the choice of the highest order of EOFs is a trade off between processing time and PRGHOLQJ DFFXUDF DV WR WKH VSHFL F QHWZRUN DQG FDSDELOLW RI FRPSXWHU V Q RXU FXUUHQW ZRUN WKH KLJKHVW RUGHU RI WKUHH was chosen In this case the neglected vertical variation of the ionosphere corresponding to higher order EOFs is 031 percent Once the modeling approach has been constructed the IROORZLQJ WDVN LV WR HVWLPDWH WKH FRHI FLHQWV RQVLGHULQJ WKH SRWHQWLDO UHDO WLPH DSSOLFDWLRQV D DOPDQ OWHU LV HPSOR HG WR VROYH WKH 7 REVHUYDWLRQ HTXDWLRQ 7R EH VSHFL F WKH following settings are used The correlation time is set to YH PLQXWHV ZKLFK FRUUHVSRQG WR WKH 6 XSGDWH LQWHUYDO for ionospheric grid points The uncertainty of the dynamic www gpsworld com February 2014 GPS World 61