Intermittent Kalman filtering with adversarial erasures: Eigenvalue cycles again

We consider intermittent Kalman filtering with adversarial erasures, and characterize the observability condition. Like intermittent Kalman filtering with random erasures, the concept of eigenvalue cycles turns out to be crucial in the characterization. Moreover, the nonuniform sampling which breaks the eigenvalue cycles can also dramatically increase Kalman filtering robustness against adversarial erasures. Precisely, the system becomes observable as long as the ratio of erasures is strictly less than 1.