A Distributed Zonotopic Set-Membership Filtering for RSSI-Based Indoor Localization

This work proposes a distributed zonotope set-membership filtering (DZSMF) to mitigate non-line-of-sight (NLOS)-induced uncertainties while ensuring the computational efficiency for robust real-time localization. First, a zonotope set-membership filtering is designed for received signal strength (RSSI)-based localization, in which process noise, measurement noise, and higher order Taylor-series residuals are jointly confined within a zonotope ensemble. The filter gain is analytically obtained by minimizing the Fradius of the posterior error zonotope. Second, a compact zonotope refinement mechanism is established by intersecting three zonotopes generated from each anchor-node group's iterative updates. These locally optimized zonotopes are subsequently integrated through a fully distributed, hierarchical information fusion strategy to produce a global state estimate accompanied by rigorous, easy-to-interpret uncertainty intervals. DZSMF uses observable sensor signals and the deployment and selection of multianchor node groups to alleviate NLOS faced in positioning. Finally, experimental results validate the accuracy and effectiveness of the proposed method. The present study represents a substantial improvement over initial estimates, with a 90.38% enhancement in performance. In comparison to existing methods, it demonstrates a 17.93%, 48.95%, 41.82%, and 1.99% improvement in terms of accuracy when evaluated against the extended kalman filtering (EKF), classical ellipsoidal set membership filtering (CESMF), interval ellipsoidal set membership filtering (IESMF), nonlinear dual set membership filtering (NDSMF) algorithms, respectively.