Fast distributed smoothing of relative measurements

Nikolaos M. Freris, Anastasios Zouzias

Research output: Contribution to journalConference articlepeer-review


We consider the problem of estimation from noisy relative measurements in a network. In previous work, a distributed scheme for obtaining least-squares (LS) estimates was developed based on the Jacobi algorithm; in a synchronous version, the algorithm was shown to converge exponentially and bounds on the rate of convergence have been obtained. In this paper, we design and analyze a new class of distributed asynchronous smoothing algorithms based on a randomized version of Kaczmarz algorithm for solving linear systems. One of the proposed schemes applies Randomized Kaczmarz directly to the noisy linear system, whereas the other one operates on the normal equations for LS estimation. We analyze the expected convergence rate of the proposed algorithms depending solely on properties of the network topology. Inspired by the analytical insights, we propose a distributed smoothing algorithm, namely Randomized Kaczmarz Over-smoothing (RKO), which has demonstrated significant improvement over existing protocols in terms of both convergence speedup and energy savings.

Original languageEnglish (US)
Article number6427110
Pages (from-to)1411-1416
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - 2012
Event51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States
Duration: Dec 10 2012Dec 13 2012


  • Clock synchronization
  • Distributed algorithms
  • Least Squares Estimation
  • Randomized algorithms
  • Sensor networks
  • Smoothing
  • Wireless Networks

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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