Geometry Induced Contraction Degradation and Stabilization of Learning Enabled Observers

Abstract: Learned perception models are increasingly used as measurement maps within nonlinear observers, mapping high dimensional sensory inputs to low dimensional quantities for state estimation. Unlike analytic measurement functions, learned models introduce state dependent Jacobians whose effect on observer stability is rarely characterized. We show that learned measurement geometry enters the observer error dynamics explicitly and rescales Euclidean contraction margins. Under fixed gains, increased measurement sensitivity reduces the certifiable contraction region and can eliminate exponential convergence guarantees. To address this effect, we introduce a representation aware gain normalization that compensates for geometry induced amplification using only local Jacobian information. The proposed approach treats the learned measurement model as a black box and requires no retraining or architectural modification. The normalization removes the dominant sensitivity dependence and restores a uniform Euclidean contraction bound while preserving a simple observer structure. Numerical and real data experiments validate the predicted sensitivity convergence relationship and demonstrate improved robustness and stability in learning enabled observer architectures.