Partial Observation Amplifies Model Mismatch in MAP Estimation via Information-Curvature Margins

Abstract

This paper theoretically analyzes how system model mismatch displaces finite-horizon maximum a posteriori (MAP) initial-state estimates in controlled dynamical systems under partial observation. From pathwise sensitivity analysis, the initial-state nominal-oracle displacement called MAP shift is decomposed into a model-side mismatch injection and an estimator-side curvature resistance to identify a sensor-dependent information-curvature margin as the amplification bottleneck. The margin is governed by the weakest posterior-curvature direction, so that sensor configurations that maximize aggregate information can still be fragile to mismatches. We connect the margin to nominal Gauss-Newton curvature and to the Bayesian Fisher information matrix, distinguishing instance-wise mismatch robustness from design-time inferability. The margin admits a computable nominal proxy in nonlinear systems, becomes explicit in the linear time-invariant case, and is validated through two numerical examples.