Grid Hopping in Sensor Networks: Acceleration Strategies for Single-Step Estimation Algorithms

In radars, sonars, or for sound source localization, sensor networks enable the estimation of parameters that cannot be unambiguously recovered by a single sensor. The estimation algorithms designed for this context are commonly divided into two categories: the two-step methods, separately estimating intermediate parameters in each sensor before combining them; and the single-step methods jointly processing all the received signals. This paper provides a general framework, coined Grid Hopping (GH), unifying existing techniques to accelerate the single-step methods, known to provide robust results with a higher computational time. GH exploits interpolation to approximate evaluations of correlation functions from the coarser grid used in two-step methods onto the finer grid required for single-step methods, hence “hopping” from one grid to the other. The contribution of this paper is two-fold. We first formulate GH, showing its particularization to existing acceleration techniques used in multiple applications. Second, we derive a novel theoretical bound characterizing the performance loss caused by GH in simplified scenarios. We finally provide Monte-Carlo simulations demonstrating how GH preserves the advantages of both the single-step and two-step approaches and compare its performance when used with multiple interpolation techniques.