Sparse Reconstruction of 3-D Regional Ionospheric Tomography Using Data From a Network of GNSS Reference Stations

3-D computerized ionospheric tomography (CIT) is an ill-posed problem due to the insufficient amount of observations, it remains challenging for practical applications. In this article, we proposed an ionospheric tomography method that combined data-driven methods with compressed sensing (CS) to deal with the ill-posed problem. First, slant total electron content (STEC) data were extracted by undifferenced and uncombined precise point positioning (UCPPP) with known fixed station coordinates. Second, data-driven methods were adopted to construct the projection matrix from the ionospheric model. Third, compressed sensing was used to derive the sparse solution based on
$L_{1}$
norm. The ionospheric tomography can be achieved well by using observations during the shorter time interval and in a sparse receiver distribution based on the property of compressed sensing. Results of experiment based on real Global Positioning System (GPS) observation data verified the effectiveness of the proposed methods. By comparing with the colocated ionosonde, it is found that the CS methods are more consistent with the actual ionospheric fluctuation than the modified constrained algebraic reconstruction technique (CART). In terms of the differential STEC (dSTEC) analysis, the error of the tomography model by Compressed Sensing-Principal Component Analysis (CS-PCA) is less than 0.2 TEC unit (TECU), and the time resolution is 5 min. The UCPPP with constraint by CS-PCA shows the best performance of 12.2%, 40.9% and 0.31% improvement in positioning accuracy, convergence time, and fixed rate over the UCPPP with constraint by modified CART. The proposed data-driven methods may be important for high-resolution 4-D ionospheric tomography in the future.