A Measure-Theoretic Framework and Adaptive Stopping Method for Node-State Quality Monitoring in Dynamic Spatial Networks

Node-state uncertainty in dynamic spatial networks is commonly characterized by posterior covariance. However, under non-Gaussian outliers, unmodeled systematic biases, and geometric degeneracy, a small posterior covariance does not necessarily correspond to high physical reliability and may lead to overconfident assessments of anomalous nodes. To address the inability of a single uncertainty indicator to adequately support node-state quality evaluation and anomaly-related decision making, this paper proposes a measure-theoretic framework for formalizing node-state quality in dynamic spatial networks. First, the conventional node-state is extended to a generalized state tuple comprising the posterior state estimate, covariance structure, observation evidence set, and environmental metadata, and the posterior reliability that the node belongs to the physically valid state domain is defined as the theoretical quality. Second, a four-dimensional evidence vector consisting of residual consistency, posterior uncertainty, geometric constraint balance, and environmental stability is constructed. A computable quality measure is then obtained through direction-consistent normalization and Soft Logical AND product coupling, satisfying boundedness, direction-consistent monotonicity, and the marginal veto property. On this basis, the inheritance of component-wise convergence by the aggregated quality measure is analyzed and an adaptive observation stopping criterion combining the quality level with marginal variation is established. Controllable quality sequences are constructed according to statistically characterized degradation patterns, including heavy-tailed errors and abnormal degradation modes observed in UrbanNav and M2DGR datasets, for numerical verification. The results show that, while maintaining a comparable mean score for normal nodes, the proposed method reduces the mean scores of outlier-contaminated, geometrically degraded, and overconfident-biased nodes from 0.6151, 0.6371, and 0.6569 under the linear model to 0.4910, 0.4303, and 0.4885, respectively. The corresponding false acceptance rates due to overestimation decrease from 10.14%, 23.46%, and 58.04% to 1.22%, 1.94%, and 1.96%, respectively. Under the current parameter settings, 73.74% of the normal nodes trigger adaptive stopping, whereas none of the three anomalous node types incorrectly triggers acceptance-based stopping. These results indicate that the proposed framework limits the compensation of locally failed evidence by high-quality components and provides a unified quantitative basis for node-state quality evaluation, anomalous-node screening, and observation-process management in dynamic networks.