Locomotion robots with active or passive compliance can show robustness to uncertain scenarios, which can be promising for agricultural, research and environmental industries. However, state estimation for these robots is challenging due to the lack of rigid-body assumptions and kinematic changes from morphing. We propose a method to estimate typical rigid-body states alongside compliance-related states, such as soft robot shape in different morphologies and locomotion modes. Our neural network-based state estimator uses a history of states and a mechanism to directly influence unreliable sensors. We test our framework on the GOAT platform, a robot capable of passive compliance and active morphing for extreme outdoor terrain. The network is trained on motion capture data in a novel compliance-centric frame that accounts for morphing-related states. Our method predicts shape-related measurements within 4.2% of the robot's size, velocities within 6.3% and 2.4% of the top linear and angular speeds, respectively, and orientation within 1.5 degrees. We also demonstrate a 300% increase in travel range during a motor malfunction when using our estimator for closed-loop autonomous outdoor operation.