Acharya & Fleck's gain normalization restores contraction in learned observers

In a new arXiv preprint accepted at IEEE CDC 2026, Aditi Acharya and Andrew Fleck tackle a hidden failure mode in learning-enabled state estimation. Modern nonlinear observers increasingly rely on learned perception models—neural networks that map high-dimensional sensory inputs (images, LiDAR) to low-dimensional measurements for tracking position or orientation. Unlike handcrafted analytic measurement functions, these learned maps come with state-dependent Jacobians whose influence on observer stability is rarely analyzed. The authors show that this learned measurement geometry enters the error dynamics explicitly and effectively rescales Euclidean contraction margins. For fixed observer gains, higher measurement sensitivity shrinks the certifiable contraction region and can completely eliminate exponential convergence guarantees—meaning the observer may diverge even in benign conditions.

To counter this, Acharya and Fleck introduce a representation-aware gain normalization that compensates for geometry-induced amplification using only local Jacobian information. The method treats the learned measurement model as a black box—no retraining or architectural modification is required—preserving the simple observer structure while removing the dominant sensitivity dependence and restoring a uniform Euclidean contraction bound. Numerical simulations and real-data experiments validate the predicted sensitivity-convergence relationship and demonstrate improved robustness in learning-enabled observer architectures. The work has immediate implications for safety-critical applications such as autonomous navigation, robotic manipulation, and any system where neural perception feeds a state estimator, offering a cheap, drop-in fix that guarantees stability without touching the learned model.