Remote State Estimation

In this chapter, we address remote state estimation strategies. In the first part, we consider a remote state estimation process under an active eavesdropper for cyber-physical system. A smart sensor transmits its local state estimates to a remote estimator over an unreliable network, which is eavesdropped by an adversary. The intelligent adversary can work in passive eavesdropping mode and active jamming mode. An active jamming mode enables the adversary to interfere the data transmission from sensor to estimator, and meanwhile improve the data reception of itself. To protect the transmission data from being wiretapped, the sensor with two antennas injects noise to the eavesdropping link with different power levels. Aiming at minimizing the estimation error covariance and power cost of themselves while maximizing the estimation error covariance of their opponents, a two-player nonzero-sum game is constructed for sensor and active eavesdropper. For an open-loop case, the mixed Nash equilibrium is obtained by solving an one-stage nonzero-sum game. For a long-term consideration, a Markov stochastic game is introduced and a Nash Q-learning method is given to find the Nash equilibrium strategies for two players. In the second part, the partial-nodes-based (PNB) state estimation issue is investigated for a class of discrete-time complex networks with constrained bit rate and bounded noises. Measurements from only a fraction of nodes in a complex network are acquired and used for state estimation. The communication between sensor nodes and estimators is accomplished over a wireless digital communication network with limited bandwidth. A bit rate constraint model is introduced to reflect the bandwidth allocation rules of partially accessible nodes. A sufficient condition is proposed under which the PNB state estimation error system is guaranteed to be ultimately bounded, and then a bit rate condition assuring a specific estimation performance is presented. The estimator gains are derived by solving two optimization problems in order to ensure two estimation performance metrics (i.e., the smallest ultimate bound and the fastest decay rate). Furthermore, the co-design issue of the bit rate allocation protocol and the estimator gains is addressed by means of particle swarm optimization and linear matrix inequalities. Finally, three numerical simulations are provided to verify the validity of the proposed PNB state estimation approach.