We provide three examples to show that we can solve complex problems in sensor networks even with minimalist observation and communication models.

First, we propose a scheme to maintain synchrony in a Time Division Multi-plexed network with minimal overhead. Each node estimates the offset in its clock phase with its neighbors based on the differences between the expected and actual times at which it receives communication packets. Using such estimates, the nodes adjust their clock phases every time they receive a packet and also adjust their clock frequencies on a slower timescale. We provide insight by analyzing a simpler "averaged" system and use simulations to demonstrate the efficacy of the algorithm.

Next, we consider the problem of localizing multiple events that are closely spaced in time, based solely on their Times of Arrival (ToAs) at different sensors. The challenge is to identify and group the ToAs belonging to a given event. The naive approach of trying all possible groupings suffers from excessive complexity. We design a three-stage algorithm to sidestep such bottlenecks. The simplification comes from the first stage, where we discretize the times at which events occur to reduce the set of event candidates considerably. However, some of these candidates are "phantoms" that arise because we do not know the correct groupings. We refine the estimates in a Bayesian manner and solve a matching problem on a graph to reject the phantoms and group the ToAs. We use simulations to illustrate the near-optimal localization performance.

Finally, we consider the problem of estimating an unknown signal recorded at multiple sensors through an unknown dispersive environment. We parallelize the problem by solving it in the frequency domain. We first estimate the signal over small bands efficiently, up to a scale factor. We then estimate the scale factors by choosing the small bands to have significant overlap. We show via experiments and simulations that the algorithm is effective in reconstructing signals with "moderate" bandwidths. For signals with larger bandwidths, we demonstrate fundamental ambiguities in the form of multiple source signals explaining the recorded observations.