Sensor deployment optimization based on optimal recovery interpolation

摘要

Obtaining the desired signals in wireless sensor networks can be challenging due to various constraints on sensor placement or deployment. Retrieving the information accurately from sensors placed at non-uniform locations, is a problem of sensor communication and signal interpolation. In this research, the optimal recovery (OR) method, a deterministic framework that can use a priori bandwidth or spectral shape information, is used to interpolate from the given non-uniformly spaced samples. The error to be minimized is the maximum possible norm difference over a set of feasible signals. In the OR problem formulation and solution, the role of worst case feasible signals can be recognized but these signals are very difficult to find analytically. Computer simulations of feasible signals can help to produce estimates of the theoretical minimal worst-case error bounds. In this paper, monitoring of OR error bounds serves to assess sensor deployment configuration quality and to optimize the placement of additional sensors. Starting from an initial configuration of sensors, optimal deployment of additional sensors is clearly a more powerful option than random deployment of such sensors. These two approaches are compared and contrasted to show the improvement that is possible using the OR framework for one-dimensional and two-dimensional signals