 The double-adaptive adjustment algorithm, DAAA, was developed to improve the accuracy and efficiency of ionospheric tomography. This algorithm uses adaptive multiplicative algebraic reconstruction techniques, AMART, which can be used to reduce the effects of noisy data and smooth the reconstructions. Additionally, the algorithm allows for adaptive adjustments of the constraining matrix elements, which improves the accuracy and efficiency of the reconstruction. The DAAA algorithm has been tested using both simulated and real GNSS data, and it has been shown to produce accurate and reliable results. This article was authored by Debayowin, Enghao-Tang, Shiqin, and others.