  In contrast to conventional robots, accurately modeling the kinematics and
statics of continuum robots is challenging due to partially unknown material
properties, parasitic effects, or unknown forces acting on the continuous body.
Consequentially, state estimation approaches that utilize additional sensor
information to predict the shape of continuum robots have garnered significant
interest. This paper presents a novel approach to state estimation for systems
with multiple coupled continuum robots, which allows estimating the shape and
strain variables of multiple continuum robots in an arbitrary coupled topology.
Simulations and experiments demonstrate the capabilities and versatility of the
proposed method, while achieving accurate and continuous estimates for the
state of such systems, resulting in average end-effector errors of 3.3 mm and
5.02{\deg} depending on the sensor setup. It is further shown, that the
approach offers fast computation times of below 10 ms, enabling its utilization
in quasi-static real-time scenarios with average update rates of 100-200 Hz. An
open-source C++ implementation of the proposed state estimation method is made
publicly available to the community.
