In this abstract, we present a modular state estima- tion framework for legged robots that decouples floating-base orientation estimation—handled via an invariant EKF—from the estimation of physical quantities such as contact forces and inertial parameters using a Moving Horizon Estimation (MHE) approach. This design leverages system symmetries and naturally incorporates robot dynamics and deterministic constraints. Build- ing on prior hardware validation, we further integrate recent advances in differential dynamics and numerical optimization to model contact interactions within the estimation process.