Distributed synchronization in wireless networks

Synchronization in complex networks of phase oscillators: A survey

“…Since alternating current (AC) circuits are naturally modeled by equations similar to (1), some electric applications are found in structure-preserving (Bergen and Hill, 1981;Sauer and Pai, 1998) and networkreduced power system models (Chiang et al, 1995;Dörfler and Bullo, 2012b), and droop-controlled inverters in microgrids (Simpson-Porco et al, 2013). Algorithmic applications of the coupled oscillator model (1) include limit-cycle estimation through particle filters (Tilton et al, 2012), clock synchronization in decentralized computing networks (Simeone et al, 2008;Baldoni et al, 2010;, central pattern generators for robotic locomotion (Aoi and Tsuchiya, 2005;Righetti and Ijspeert, 2006;Ijspeert, 2008), decentralized maximum likelihood estimation (Barbarossa and Scutari, 2007), and human-robot interaction (Mizumoto et al, 2010). Further envisioned applications of oscillator networks obeying equations similar to (1) include generating music (Huepe et al, 2012), signal processing (Shim et al, 2007), pattern recognition (Vassilieva et al, 2011), and neuro-computing through micromechanical (Hoppensteadt and Izhikevich, 2001) or laser (Hoppensteadt and Izhikevich, 2000;Wang and Ghosh, 2007) oscillators.…”

“…A natural approach to clock synchronization is to treat each clock as an oscillator and follow a diffusion-based (or pulse-coupling) protocol to synchronize them, see the surveys (Lindsey et al, 1985;Simeone et al, 2008) and the interesting recent results (Hong and Scaglione, 2005;Baldoni et al, 2010;Mallada and Tang, 2011;Wang and Doyle, 2012).…”

“…These clocks need to be synchronized for distributed computing and network routing tasks. As discussed in the surveys by Lindsey et al (1985) and Simeone et al (2008), we consider only analog clocks with continuous coupling since digital clocks are essentially discretized analog clocks, and pulse-coupled clocks can be modeled continuously after a phase reduction and averaging analysis. For our purposes, the clock of processor i is a voltage-controlled oscillator (VCO) generating a harmonic waveform s i (t) = sin(θ i (t)), where θ i (t) is the accumulated instantaneous phase.…”

“…Also, in many applications the diffusive coupling includes a phase shift (Izhikevich, 1998). For instance, mutual excitatory or inhibitory synaptic organizations in neuroscience (Crook et al, 1997), time delays in sensor networks (Simeone et al, 2008), or transfer conductances in power networks (Chiang et al, 1995) lead to a shifted coupling of the form sin(θ i − θ j − ϕ ij ) with ϕ ij ∈ [−π/2, π/2]. In these cases and also for other "skewed" or "symmetry-breaking" interactions among the oscillators, many of the presented analysis schemes either fail or lead to overly conservative results.…”

An Overview of a Class of Clock Synchronization Algorithms for Wireless Sensor Networks: A Statistical Signal Processing Perspective

“…In the literature, surveys for clock synchronization in WSNs have been presented by [9,10,16,17]. The focus of [10,16] lies in the clock synchronization protocols that are applied in WSNs.…”