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Distributed Fusion Estimation with Sensor Gain Degradation and Markovian Delays

Author

Listed:
  • María Jesús García-Ligero

    (Departamento de Estadística e I. O., Universidad de Granada, Avda Fuentenueva s/n, 18071 Granada, Spain
    These authors contributed equally to this work.)

  • Aurora Hermoso-Carazo

    (Departamento de Estadística e I. O., Universidad de Granada, Avda Fuentenueva s/n, 18071 Granada, Spain
    These authors contributed equally to this work.)

  • Josefa Linares-Pérez

    (Departamento de Estadística e I. O., Universidad de Granada, Avda Fuentenueva s/n, 18071 Granada, Spain
    These authors contributed equally to this work.)

Abstract

This paper investigates the distributed fusion estimation of a signal for a class of multi-sensor systems with random uncertainties both in the sensor outputs and during the transmission connections. The measured outputs are assumed to be affected by multiplicative noises, which degrade the signal, and delays may occur during transmission. These uncertainties are commonly described by means of independent Bernoulli random variables. In the present paper, the model is generalised in two directions: ( i ) at each sensor, the degradation in the measurements is modelled by sequences of random variables with arbitrary distribution over the interval [0, 1]; ( i i ) transmission delays are described using three-state homogeneous Markov chains (Markovian delays), thus modelling dependence at different sampling times. Assuming that the measurement noises are correlated and cross-correlated at both simultaneous and consecutive sampling times, and that the evolution of the signal process is unknown, we address the problem of signal estimation in terms of covariances, using the following distributed fusion method. First, the local filtering and fixed-point smoothing algorithms are obtained by an innovation approach. Then, the corresponding distributed fusion estimators are obtained as a matrix-weighted linear combination of the local ones, using the mean squared error as the criterion of optimality. Finally, the efficiency of the algorithms obtained, measured by estimation error covariance matrices, is shown by a numerical simulation example.

Suggested Citation

  • María Jesús García-Ligero & Aurora Hermoso-Carazo & Josefa Linares-Pérez, 2020. "Distributed Fusion Estimation with Sensor Gain Degradation and Markovian Delays," Mathematics, MDPI, vol. 8(11), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1948-:d:439722
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    References listed on IDEAS

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    1. Hongli Dong & Zidong Wang & Steven X. Ding & Huijun Gao, 2014. "A Survey on Distributed Filtering and Fault Detection for Sensor Networks," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-7, January.
    2. Shang, Yilun, 2016. "Consensus seeking over Markovian switching networks with time-varying delays and uncertain topologies," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1234-1245.
    3. R. Caballero-Águila & A. Hermoso-Carazo & J. Linares-Pérez, 2017. "Least-Squares Filtering Algorithm in Sensor Networks with Noise Correlation and Multiple Random Failures in Transmission," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-9, August.
    4. M. J. García-Ligero & A. Hermoso-Carazo & J. Linares-Pérez, 2020. "Least-squares estimators for systems with stochastic sensor gain degradation, correlated measurement noises and delays in transmission modelled by Markov chains," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(4), pages 731-745, March.
    5. Wangyan Li & Zidong Wang & Guoliang Wei & Lifeng Ma & Jun Hu & Derui Ding, 2015. "A Survey on Multisensor Fusion and Consensus Filtering for Sensor Networks," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-12, October.
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    Cited by:

    1. Huijuan Zhao & Jiapeng Xu & Fangfei Li, 2022. "Event-Triggered Extended Kalman Filtering Analysis for Networked Systems," Mathematics, MDPI, vol. 10(6), pages 1-12, March.
    2. María Jesús García-Ligero & Aurora Hermoso-Carazo & Josefa Linares-Pérez, 2022. "Distributed Fusion Estimation in Network Systems Subject to Random Delays and Deception Attacks," Mathematics, MDPI, vol. 10(4), pages 1-17, February.

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