Robust distributed estimation with multi-level quantization and event-triggered communication under unknown inputs

This paper studies robust distributed state estimation over wireless sensor networks when communication is bandwidth-limited, links are unreliable, transmitted data are quantized, and the process is affected by unknown exogenous inputs. The main technical contribution is a unified estimator that combines multi-level quantization (MLQ), chi-square event triggering with an anti-starvation timeout, Bayesian unknown-input marginalization, and covariance-intersection (CI) fusion. The integration is non-trivial because the triggering policy, quantization distortion, stochastic packet losses, and unknown-input uncertainty all enter the local posterior covariance and therefore alter both CI consistency and the attainable mean-square error bound. We derive sufficient conditions for mean-square boundedness and provide an explicit design-oriented sufficient bound whose terms separately quantify the effects of quantization resolution, triggering probability, and link reliability. We also clarify how the triggering threshold determines a non-zero triggering probability through the chi-square law and how a timeout prevents excessively long silent intervals. Simulation results on a communication-constrained networked estimation benchmark show that the proposed method preserves estimation quality close to periodic CI while reducing transmissions, keeps the covariance trace bounded, and exhibits predictable sensitivity to threshold selection, link reliability, and CI weighting.