Formalising Sensor Topologies for Target Counting

Abstract

We present a formal model developed to reason about topologies created by sensor ranges. This model is used to formalise the topological aspects of an existing counting algorithm to estimate the number of targets in the area covered by the sensors. To that end, we present a first-order logic tailored to specify relations between parts of the space with respect to sensor coverage. The logic serves as a specification language for Hoare-style proofs of correctness of the topological computations of the algorithm, which uncovers ambiguities in their results. Subsequently, we extend the formal model as a step towards improving the estimation of the algorithm. Finally, we sketch how the model can be extended to take mobile sensors and temporal aspects into account.

Target counting with Presburger constraints and its application in sensor networks

“…In this section, we present empirical results of applying our approach to several example topologies. 7 We start with a short description of the implementation. Then, we show with an example, how the addition of weights affects the probabilities of target counts.…”

“…We will then use these distributions to compute the frequencies of the possible target counts and hence infer their probability. This approach builds upon the previous work [7], where such topologies were specified by a formal model based on the first-order logic. However, a crucial difference with the current approach is that previously, sensor readings were not taken into account.…”

“…In both cases, we could reduce the number of feasible target distributions by requiring that only target counts that were previously feasible stay feasible (under the assumption, that no target enters or leaves the sensed area). The possible ways a topology can change within one time-step is restricted by the possible topological changes [7]. Such an extension could be driven further, by taking weights into account.…”

“…A precondition of SCAN is the convexity of the sensor ranges, while we allow for arbitrary shapes of the ranges. Furthermore, in two-dimensional space, minimal topologies are not unique [7]. In particular, different minimal topologies may possess different maximum overlap degrees, which in turn impacts the estimation of SCAN.…”