Aggregation-Based Remote State Estimation Secrecy With Pseudo-Random Numbers for Networked Systems

This article is concerned with the remote state estimation secrecy problem for networked systems in the presence of eavesdroppers. The majority of current research centers on one kind of eavesdropper that is equipped with predefined estimation structures. To enhance the resistance against eavesdroppers, we simultaneously consider two distinct categories of logical eavesdroppers in this article, namely, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">smart eavesdroppers</i>, who possess the same level of knowledge as legitimate users, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">naive eavesdroppers</i>, who remain oblivious to the encoding process. Moreover, we propose an innovative aggregation-based secrecy code that employs pseudo-random numbers, incorporating both a pseudo-random real-number sequence and a pseudo-random binary scheduler. Also, an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $</tex-math> </inline-formula>-relative secrecy is proposed by introducing a relax variable, which offers higher flexibility than the traditional relative secrecy. Then, both the classical perfect secrecy and the newly proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $</tex-math> </inline-formula>-relative secrecy are proven under specific conditions. Furthermore, the estimation performance for users and eavesdroppers can be tuned by designing the aggregation structure and the probability distribution of the pseudo-random samples, rather than being solely determined by the communication channel characteristics as in previous work. Finally, the effectiveness of the proposed coding method is verified through numerical experiments conducted on two systems with differing stability characteristics.