Sparse representation of tropospheric grid data using compressed sensing

With the widespread application of global navigation satellite system, increasing amounts of gridded tropospheric data have been generated, increasing the difficulty of real-time transmission. We present that the global tropospheric grid data (GTGD) provided by Vienna mapping functions open access data have approximate sparse characteristics, and the compressed sensing (CS) method is used for sparse reconstruction for the first time. To reduce the memory and number of calculations required for the K-SVD (K-means and SVD) algorithm, the mini-batch K-SVD algorithm is proposed to speed up the calculation process. This article discusses several key problems of CS processing and application in GTGD, such as signal sparsity, reconstruction accuracy, iteration times, etc. We use mini-batch K-SVD algorithm train 1436 GTGD historical files from 2018 to establish a sparse representation model. To evaluate the accuracy of the new model, sparse reconstruction is performed on 1460 GTGD files from 2019. The experimental results show that the average root-mean-square (RMS) error, the BIAS, the maximum absolute error (MAAE), and the mean absolute error (MAE) of the compressed sensing are 2.16, 2.00E-04, 17.99, and 1.44 mm, respectively. The average RMS, BIAS, MAAE, and MAE of the spherical harmonic expansion (72-degree) are 27.39, − 9.71E-14, 273.93, and 16.67 mm. The results show that the CS approach yields a more accurate solution than spherical harmonic expansion. In summary, the established sparse representation model saves real-time transmission cost and enables high-precision sparse reconstruction and can achieve data encryption and compression simultaneously.