Gaussian Filtering With False Data Injection and Randomly Delayed Measurements

Sumanta Kumar Nanda, Guddu Kumar, Amit Kumar Naik, Mohammed Abdel-Hafez, Vimal Bhatia, Ondrej Krejcar, Abhinoy Kumar Singh

Research output: Contribution to journalArticlepeer-review


State estimation in cyber-physical systems is a challenging task involving integrating physical models and measurements to estimate dynamic states accurately in practical machine-to-machine and IoT deployments. However, integrating advanced wireless communication and intelligent measurements has increased vulnerability of external intrusion through a centralized server. This study addresses the challenge of Gaussian filtering for a specific type of stochastic nonlinear system vulnerable to cyber attacks and delayed measurements. These attacks occur randomly when data is transmitted from sensor nodes to remote filter nodes. To address this issue, a new cyber attack model is proposed that combines false data injection attacks and delayed measurement into a unified framework. The study also analyzes the stochastic stability of the proposed filter and establishes sufficient conditions to ensure that the filtering error remains bounded even in the presence of randomly occurring cyber attacks and delayed measurements. The proposed methodology is demonstrated and compared with other widely used approaches using simulated data to highlight its effectiveness and usefulness.

Original languageEnglish
Pages (from-to)88637-88648
Number of pages12
JournalIEEE Access
Publication statusPublished - 2023


  • Delay measurement
  • FDI
  • Gaussian filtering
  • nonlinear Bayesian filtering

ASJC Scopus subject areas

  • General Computer Science
  • General Materials Science
  • General Engineering


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