It has been demonstrated that an estimate of an empirical Green's function (EGF) can be extracted from the ocean ambient noise cross-correlation functions, which can provide an alternative method for ocean acoustic tomography. However, the requirement for a long recording time to obtain EGFs with a high signal-to-noise ratio limits the application. This article focuses on using array signal processing to accelerate the convergence rate of EGFs between two horizontally separated arrays. With the extracted EGFs and data assimilation, ocean sound speed profiles (SSPs) can be inverted every 2 h in shallow water. The experimental results indicate that the variation in ocean SSPs can be reconstructed with reasonable agreement using an average variance of 1.14 m/s over three months.