  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.
