H Fusion Estimation for WSNs with Quantization

  • Wen-An Zhang
  • Bo Chen
  • Haiyu Song
  • Li Yu


By quantization, one is able to reduce the size of data packet containing the quantized signal and thus is able to satisfy the bandwidth constraint of the sensor network and reduce communication costs from the sensors to the fusion estimator. In this chapter, a design method for the \(H_{\infty }\) multisensor fusion estimator will be presented for sensor networks with quantized local estimates. The \(H_{\infty }\) estimator does not make any assumption on the statistics of the process and measurement noises; the only assumption is that the external disturbance has bounded energy [1, 2]. A group of finite-level logarithmic quantizers [3] are introduced to deal with the bandwidth constraints, and the corresponding fusion estimation error system model is established. By using the discrete-time bounded real lemma, a convex optimization problem on the choices of the optimal weighting matrices and quantization parameters is established in terms of linear matrix inequalities (LMIs). Moreover, it is proved that the performance of the designed fusion estimator is better than that of each local quantized estimator.


Linear Matrix Inequality Quantization Parameter Fusion Center Convex Optimization Problem Bandwidth Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Gao HJ, Chen TW (2007) \(H_{\infty }\) estimation for uncertain systems with limited communication capacity. IEEE Trans Autom Control 52:2070–2084MathSciNetCrossRefGoogle Scholar
  2. 2.
    He Y, Liu GP, Rees D, Wu M (2009) \(H_{\infty }\) filteirng for discrete-time systems with time-varying delay. Signal Process 89(3):275–282CrossRefzbMATHGoogle Scholar
  3. 3.
    Fu M, Xie L (2005) The sector bound approach to quantized feedback control. IEEE Trans Autom Control 50(11):1698–1711MathSciNetCrossRefGoogle Scholar
  4. 4.
    de Souza CE, Xie L (1992) On the discrete-time bounded real lemma with application in the characterization of static state feedback \(H_{\infty }\) controllers. Syst Control Lett 18(1):61–71CrossRefzbMATHGoogle Scholar
  5. 5.
    Boyd SP, Ghaoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, PhiladelphiaCrossRefzbMATHGoogle Scholar

Copyright information

© Science Press, Beijing and Springer Science+Business Media Singapore 2016

Authors and Affiliations

  • Wen-An Zhang
    • 1
  • Bo Chen
    • 1
  • Haiyu Song
    • 2
  • Li Yu
    • 3
  1. 1.Department of AutomationZhejiang University of TechnologyHangzhouChina
  2. 2.Zhejiang Uni. of Finance & EconomicsHangzhouChina
  3. 3.Zhejiang University of TechnologyHangzhouChina

Personalised recommendations