A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 5) Algorithm 5. Kalman-Based Filtering III: <s> In this technical note, the distributed filtering problem is investigated for a class of discrete time-varying systems with an event-based communication mechanism. Each intelligent sensor node transmits the data to its neighbors only when the local innovation violates a predetermined Send-on-Delta (SoD) data transmission condition. The aim of the proposed problem is to construct a distributed filter for each sensor node subject to sporadic communications over wireless networks. In terms of an event indicator variable, the triggering information is utilized so as to reduce the conservatism in the filter analysis. An upper bound for the filtering error covariance is obtained in form of Riccati-like difference equations by utilizing the inductive method. Subsequently, such an upper bound is minimized by appropriately designing the filter parameters iteratively, where a novel matrix simplification technique is developed to handle the challenges resulting from the sparseness of the sensor network topology and filter structure preserving issues. The effectiveness of the proposed strategy is illustrated by a numerical simulation. <s> BIB001 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 5) Algorithm 5. Kalman-Based Filtering III: <s> This paper is concerned with the distributed filtering problem for a class of discrete time-varying systems with stochastic nonlinearities and sensor degradation over a finite horizon. A two-step distributed filter algorithm is proposed where the sensor nodes collaboratively estimate the states of the plant by exploiting the information from both the local and the neighboring nodes. The goal of this paper is to design the distributed filters over a wireless sensor network subject to given sporadic communication topology. Moreover, a resilient operation is guaranteed to suppress random perturbations on the actually implemented filter gains. An upper bound is first derived for the filtering error covariance by utilizing an inductive method and such an upper bound is subsequently minimized via iteratively solving a quadratic optimization problem. To account for the topological information of the sensor networks, a novel matrix simplification technique is utilized to preserve the sparsity of the gain matrices in accordance with the given topology, and the analytical parameterization is obtained for the gain matrices of the desired suboptimal filter. Furthermore, a sufficient condition is established to guarantee the mean-square boundedness of the estimation errors. Numerical simulation is carried out to verify the effectiveness of the proposed filtering algorithm. <s> BIB002
In the above algorithm, all innovations are summed together with given weights and then employed to update the prediction. Such an algorithm cannot adequately identify the effect on filtering performance from different neighbors' information, especially, for the case with heterogeneous sensors. As such, a more general structure is designed in BIB002 , and removing gain uncertainties leads to the following simplified version: where the formula K ij k , dependent on global error covariance P i,k , can be derived along the same line in BIB002 and BIB001 and hence omitted in this survey paper for the simplicity of presentation. Obviously, in comparison with Algorithms 3 and 4, the gain K ij k provides more design freedom although the calculation burden is increased. The pseudocode is provided in Algorithm 5. 