Incomplete feedback data recovery scheme with Kalman filter for real-time cyber-physical systems

Abstract

Feedback data loss can severely degrade the overall system performance and as well as it can affect the control and computation of the cyber-physical systems (CPS) in the provision of real-time, efficient, dependable, safe, and secure operations of a wide range of emerging applications. In CPS applications, a wide range of data patterns are observed in different applications which make a great challenge in efficient and real-time recovery whenever the data is lost. In this paper, we propose a data recovery scheme called efficient temporal and spatial data recovery scheme with Kalman filter (ETSDR/KF) to ensure efficient and real-time recovery for any data patterns of CPS. In the proposed scheme, the data recovery ETSDR/KF algorithm is presented to recover incomplete feedback data. We identify the temporal model of the pattern using ARIMA model and consider the spatial effect of the neighbors as a data preprocessing step. However, the temporal model, generated from ARIMA has internal errors and the model parameters may not remain constant. Thus, to improve the accuracy of the estimated data, we incorporate a Kalman filter to reduce the error. Before that, we fix the window for Kalman filter to determine the proper process noise co-variance in online. Numerical results reveal that the proposed ETSDR/KF are very promising regardless of the increment percentage of missing data in terms quality of result (QoR).