The lateral line enables fish to efficiently sense the surrounding environment, thus assisting flow-related fish behaviours. Inspired by this phenomenon, varieties of artificial lateral line systems (ALLSs) have been developed and applied to underwater robots. This article focuses on using the pressure sensor arrays based on ALLS-measured hydrodynamic pressure variations (HPVs) for estimating the relative state between two adjacent robotic fish with leader-follower formation. The relative states include the relative oscillating frequency, amplitude, and offset of the upstream robotic fish to the downstream robotic fish, the relative vertical distance, the relative yaw angle, the relative pitch angle, and the relative roll angle between the two adjacent robotic fish. Regression model between the ALLS-measured and the mentioned relative states is investigated, and regression model-based relative state estimation is conducted. Specifically, two criteria are proposed firstly to investigate not only the sensitivity of each pressure sensor to the variations of relative state but also the insufficiency and redundancy of the pressure sensors. And thus the pressure sensors used for regression analysis are determined. Then four typical regression methods, including random forest algorithm, support vector regression, back propagation neural network, and multiple linear regression method are used for establishing regression models between the ALLS-measured HPVs and the relative states. Then regression effects of the four methods are compared and discussed. Finally, random forest-based method, which has the best regression effect, is used to estimate relative yaw angle and oscillating amplitude using the ALLS-measured HPVs and exhibits excellent estimation performance. This work contributes to local relative estimation for a group of underwater robots, which has always been a challenge.