发表机构
Purdue University（普渡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对学习型观测器中测量几何导致的收缩退化问题，提出仅用局部雅可比信息的感知器增益归一化方法，恢复收缩界并提升观测器稳定性，经实验验证有效。
AI 中文摘要
学习型感知模型越来越多地被用作非线性观测器中的测量映射，将高维感官输入映射到低维量以进行状态估计。与解析测量函数不同，学习型模型会引入依赖状态的雅可比矩阵，其对观测器稳定性的影响鲜有被表征。我们表明，学习型测量几何会显式进入观测器误差动力学并重新缩放欧氏收缩裕度。在固定增益下，测量灵敏度增加会减小可验证的收缩区域，可能消除指数收敛保证。为解决该问题，我们提出一种感知器增益归一化方法，仅利用局部雅可比信息补偿几何诱导的放大效应。该方法将学习型测量模型视为黑箱，无需重新训练或修改架构。该归一化消除了主导的灵敏度依赖关系，恢复了均匀的欧氏收缩界，同时保留了简单的观测器结构。数值和真实数据实验验证了预测的灵敏度-收敛关系，并证明学习型观测器架构的鲁棒性和稳定性得到提升。
英文摘要
Learned perception models increasingly serve as measurement maps within nonlinear observers. Their state-dependent Jacobians introduce measurement geometry that measurement-value accuracy does not constrain. Even when measurements satisfy standard accuracy criteria, the corresponding one-step Euclidean error operator can be noncontractive. Improving measurement accuracy or retuning the correction strength may leave this observer-level contraction failure unresolved. We derive the exact estimation-error operator and use it to determine whether scalar-gain adjustment can restore contraction or the correction structure must change. The analysis separates three distinct cases: a conservative certificate may be inconclusive, the nominal gain may be exactly noncontractive, or the correction geometry may lie beyond scalar-gain repair. Convexity makes this recovery boundary exactly computable. When scalar recovery remains possible, uncertainty-aware envelopes define a safe projection that changes the nominal gain only when contraction and same-state improvement are certified. Uniform local certification yields exponential error decay and explicit disturbance-dependent bounds. The method uses local composite-Jacobian information or a certified approximation and requires no retraining. Scalar experiments demonstrate certified contraction recovery and improved tracking when the geometry permits. Controlled real-image experiments provide numerical evidence of scalar-unrecoverable contraction loss despite accurate learned measurements
CommentsIEEE CDC 2026 preprint (Accepted), Authors have equal contribution, 8 pages and 3 figures
