This work demonstrates simultaneous pose (position and orientation) and shape estimation for a free-floating, bioinspired multi-link robot with unactuated joints, link-mounted thrusters for control, and a single gyroscope per link, resulting in an underactuated, minimally sensed platform. Because the inter-link joint angles are constrained, translation and rotation of the multi-link system requires cyclic, reciprocating actuation of the thrusters, referred to as a gait. Through a proof-of-concept hardware experiment and offline analysis, we show that the robot's shape can be reliably estimated using an Unscented Kalman Filter augmented with Gaussian process residual models to compensate for non-zero-mean, non-Gaussian noise, while the pose exhibits drift expected from gyroscope integration in the absence of absolute position measurements. Experimental results demonstrate that a Gaussian process model trained on a multi-gait dataset (forward, backward, left, right, and turning) performs comparably to one trained exclusively on forward-gait data, revealing an overlap in the gait input space, which can be exploited to reduce per-gait training data requirements while enhancing the filter's generalizability across multiple gaits. Lastly, we introduce a heuristic derived from the observability Gramian to correlate joint angle estimate quality with gait periodicity and thruster inputs, highlighting how control affects estimation quality.