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arXiv:physics/9903013v1 [physics.geo-ph] 8 Mar 1999
GIST: A tool for Global Ionospheric Tomography using GPS ground and LEO data and sources of opportunity with applications in instrument calibration A. Flores, G. Ruffini, A. Rius, and E. Cardellach February 10, 2018 Abstract Ionospheric tomography using GPS data has been reported in the literature and even the application to radar altimeter calibration was succesfully carried out in a recent work ( ). We here present a new software tool, called Global Ionospheric Stochastic Tomography software (GIST), and its powerful capability for ingesting GPS data from different sources (ground stations, receivers on board LEO for navigation and occultation purposes) and other data such as altimetry data to yield global maps with dense coverage and inherent calibration of the instruments. We show results obtained including 106 IGS ground stations, GPS/MET low rate occultation data, TOPEX/POSEIDON GPS data from the navigation antenna and NASA Radar Altimeter with the additional benefit of a direct estimation of the NRA bias. The possibility of ingesting different kinds of ionospheric data into the tomographic model suggest a way to accurately monitor the ionosphere with direct application to single frequency instrument calibration.
Radio waves traversing the ionosphere suffer a delay of a well-known dispersive nature and it is common to suppress this effect by using a combination of signals at two separated frequencies. However, there are two aspects here to be considered: first, the electronic equipment of on board instrumentation has to be periodically calibrated, and second, duplicating systems to operate at two frequencies adds cost and complexity to the instruments. Therefore it is desirable to have a system able to reproduce the status of the ionosphere, and use it for monitoring, and single- and dual-frequency instrument calibration. Tomographic techniques are applied to this end ingesting data from different sources. In previous references , ,  we have discussed the tomographic methodology and some different implementations, which we will here briefly summarize. This work intends to highlight the successful elaboration of a software package that implements those techniques and also to emphasize the possibility of ingesting data other than GPS to densify the receivers network.
The ionospheric delay can be determined in a bistatic dual-frequency system from phase measurements following the equation: Z dlρ(~r, t) + cr + ct , (2.1) LI (~r, t) = L1 − L2 = γ ray
where we have noted the phase measurements with L. The factor γ depends on the frequencies in use (for GPS γ = 1.05 · 10−17 m3 /el) and ρ is the electron density. The two
constants cr and ct are the biases associated to the transmitter and receiver ( ). Tomographic analysis consist in obtainting the solution fields (ρ) from the integrated value along the ray paths and Equation 2.1 is termed as the “tomographic equation”. If ρ is expressed P as a linear combination of a set of basis functions ρ = j xj (t)Ψj (~r)+ ǫ(~r, t) then the above R P equation becomes LI = yi = J xJ (t) s.l. ΨJ (~r)d~l + ζ(~r, t) + cr + ct and can be written for each ray to obtain a set of linear equations such as y = A · x. In our tomographic system, we choose voxels as the basis functions. Voxels are 3-D pixels or fuctions valued 1 inside the volume of the voxel and 0 elsewhere. Empirical Orthogonal Functions can also be used as shown in .The system, however, may not have a solution because data are not uniformly distributed, and thus we seek to minimize the functional χ2 (x) = (y − Ax)T · (y − Ax).
In  we discussed the use of a correlation functional to confine the spatial spectrum of the solution to the low portion of the frequency space. The same concept can be expressed by adding new equations (constraints) that impose that the density in a voxel be a weighted average of its neighbours ( ). To take into account variation in time, a Kalman filter is implemented, considering the density to behave as a random walk stochastic process. Instrumental constants are also considered and resolved as constants or eliminated by differencing , . While differencing reduces the number of unknowns, estimation furnishes the solution with more information and provides nuisance parameters to absorb noise from the system.
The GIST tool for ionospheric tomography
The software tool GIST implements the above described technique including differencing and constant estimation strategies (for a block diagram see Figure 1). In addition, since the previous equations are valid for any dual-frequency system, different sources of data should be used. It has to be remembered, however, that the tomographic solution is possible thanks to the different directions of the rays received from different satellites which permit the system to distinguish between layers. Therefore, GPS data serve as the basic source on which the solution is based and any additional data such as altimetric data (which is always in the same direction) should be fed as an aiding source of information and with the main goal of constraining the values of ρ to obtain the calibration constants. In monostatic systems the two constants are merged into one. In this fashion, we can calibrate the instrument as part of the overall solution. The package GIST shares common modules with the package LOTTOS, oriented to Tropospheric Tomography (see ) and has the following features: • Raw RINEX data conditioning: cycle slip detection, phase alignment, and data decimation. • Altimeter Data conditioning • Linear System Construction • Kalman Filtering with Random Walk Stochastic Process. • Different Constraints Strategies The input data are GPS raw phases and pseudoranges, precise orbits for all the satellites in ECI format and time-tagged Total Electron Contents data from other sources. In  we discussed the convenience of the constant estimation in the data processing due to the robustness of the system and the existence of systematic noise sinks. However, this approach is computationally intensive and in some cases, for system testing, it is interesting to have a rapid solution even if it is with low accuracy. In such cases, differencing is an attractive approach because it reduces the number of unknowns and it is hence included as an option in the GIST package; it has to be advised, however, that this technique is more sensitive to systematic noise in the data or mismodeling.
We have taken data from 106 IGS ground stations for 21st February 1997, GPS/MET low rate data and TOPEX/POSEIDON data from the on-board GPS receiver (zenith-looking for navigation purposes) and the on-board NRA altimeter data. A global grid with 20 divisions in longitude, 10 divisions in latitude and 6 layers (5 below the TOPEX/POSEIDON orbit and 1 above to absorbe the protonosphere) has been used and the data divided into 3-hour batches for Kalman filtering. The data were weighted according to the sigma value of the measurements (0.1 m for GPS data and 1 TECU for TOPEX/POSEIDON , ) and the orbits for the LEO were estimated using the GIPSY-OASIS II software . In Figures 2 and 3 we see the 6 layers of the ionosphere, and in Figure 4 the residues for the T/P altimeter data. The bias constant is 2.98 TECU with a formal error of 2.58 mTECU for the T/P Radar Altimeter, which agrees fairly well with what was reported in .
We have successfully developed a solid software tool GIST for ionospheric tomography and applied it to one day of data to yield 4D ionospheric maps. These maps are consistent with previous work and, in addition, the ingestion of altimeter data into the model permits the direct calibration of the instrumentation. We foresee this technique to be a very useful technique particularly when other sources of opportunity such as GPS data from satellites or airplanes are included because of the great densification of measurements.
The authors would like to thank N. Picot (CNES), B. Haines (JPL) and C. Rocken (UCAR) for providing the data. This work was supported by the EC grant WAVEFRONT PL-952007 and the Comissionat per a Universitats i Recerca de la Generalitat de Catalunya.
References  G. Ruffini, E. Cardellach, A. Flores, L. Cucurull, and A. Rius. Ionospheric calibration of radar altimeters using GPS tomography. Geophysical Research Letters, 25(20):3771– 3774, 1998.  A. Rius, G. Ruffini, and L. Cucurull. Improving the vertical resolution of ionospheric tomography with GPS occultations. Geophysical Research Letters, 24(18):2291–, 1997.  G. Ruffini, A. Flores, and A. Rius. GPS tomography of the ionospheric electron content with a correlation functional. IEEE Transactions on Geoscience and Remote Sensing, 36(1), January 1998.  E. Sardon, A. Rius, and N. Zarraoa. Estimation of the transmitter and receiver differential biases and the ionospheric total electron content from global positioning system observation. Radio Science, 29(3):577–586, May-June 1994.  B. Howe, K. Runciman, and J.A. Secan. Tomography of the ionosphere: Fourdimensional simulations. Radio Science, 33(1):109–128, January-February 1998.  M. Hernandez-Pajares, J.M. Juan, J. Sanz, and J.G. Sole. Global observation of the ionospheric electronic response to solar eventsusing ground and LEO GPS data. Journal of Geophysical Research, 103(49):20789–20796, September 1998.  A. Flores, G. Ruffini, and A. Rius. 4D tropospheric tomography using estimated GPS slant delays. http://xxx.lanl.gov/physics, 1998.
Figure 1: Block Diagram of the GIST software.
T/P NRA Altimetry Data
T/P GPS Data
LOTTOS/GIST Tomography Modules
IGS Ground Stations GPS Data
GIST Data Preconditioner
4-D Ionospheric Tomographic Fields GPS/MET Low Rate GPS Data
Figure 3: Representation of the electron density in layers at 7175 Km, 7525 Km, and 8250 Km shells from the center of the Earth (from bottom to top).
0 -16 -14 -12 -10
Figure 4: Histogram of the residues of the altimeter TEC measurements (x-axis in TECU).
 D. A. Imel. Evaluation of the topex/poseidon dual-frequency ionosphere correction. Journal of Geophysical Research, 99(C12):24895–248906, December 1994.  F.H. Webb and J.F. Zumberge. An Introduction to GIPSY-OASIS II. Jet Propulsion Laboratory, California Institute of Technology, 1997.