Bounds on coverage time and node density for multi-modality sensing

In wireless sensor networks, nodes may employ multiple sensing modalities to improve the robustness of covering a region. Multi-modality coverage requires that every point in the region be covered by at least one node for each sensing modality. In this paper, we study the problem of maximizing the multi-modality coverage time and the relationship between node density and the probability of coverage. To this end, for the coverage time, we (1) derive lower and upper bounds on the achievable coverage time; (2) formulate the multi-modality coverage time maximization problem as a linear program; and (3) develop a heuristic to compute the achievable coverage time when the network is operated in phases. Through simulations, we show that the heuristic approach attains coverage time close to the optimal for a random network when large number of phases are employed. For the node density estimation, we evaluate the probability that a point is covered by at least one node for each modality for a given density of deployment by considering the possible correlation in the sensed information.