A Hypothesis Test for Topology Change Detection in Wireless Sensor Networks

The problem of topology change detection in wireless sensor networks (WSNs) is addressed. The network is modeled as a directed graph comprising sensor nodes and edges over which the sensors communicate with each other. The problem, formulated using a linear model of noisy measurements, is to distinguish between hypotheses $H_0$ (null) and $H_1$ (alternative) corresponding to ``no- change'' and ``change'', respectively, in the topology of the network over a period of time. For a fixed probability of false alarm, computable expressions for the test threshold and the probability of detection are derived by efficiently approximating the distribution functions of the test statistic under $H_0$ and $H_1$. The performance of the test is comparable to that of the likelihood ratio test, which requires {\apriori} knowledge of the time of change and the topology of the network after the change. Simulations results are presented to verify the theoretical findings of the paper. The test presented here is especially suited for large- scale WSNs, and is an important component in topology control which has received significant attention in the design of WSNs.