Minimal Persistent Measurements for Time-Varying Unobservable Subspaces

This preprint studies the minimum fixed and adaptive measurements needed to track time-varying unobservable subspaces. It develops a Grassmannian and common-complement formulation, proves persistent-memory bounds and sharp examples, analyzes adaptive basis handoffs along algebraic trajectories, and connects the theory to resolved geometric singularities, historical measurements, future probing, and low-rank rigid-body updates.