Hierarchical Fusion Estimation for Clustered Asynchronous Sensor Networks

In this paper, the problem of fusion estimation for networked multi-sensor systems with multiplicative noise and correlated noise is studied. First, the state space model is transformed into a new system with fictitious noises and local Kalman filter are obtained. Then the sequential inverse covariance intersection (SICI) fusion algorithm is applied and the SICI fusion estimator is proposed to avoid the computation burden of local estimators. Compared with the Sequential Covariance Intersection (SCI) fusion algorithm, SICI fusion algorithm is less conservative, and its estimation accuracy is higher than that of local filter and SCI fusion estimator. The validity and consistency of the proposed fusion estimator are verified by a simulation example.

Sequential fusion estimation for clustered sensor networks

In several practical applications, an economical processing of multi-sensor data is realised by the fusion of estimates. A very cheap solution, which is also very conservative, is the Covariance Intersection (CI) fusion. Basic information configurations of the estimation system have been inspected by the authors in a preceding paper [1]. This paper provides an extension of the previous discussion to the fusion with memory. It shows that the adding of memory cannot improve the fusions without memory given by partial or full information feedback. Conversely, it shows that the fusion without memory and no information feedback can be in some cases improved by the adding of memory.

For multi-sensor system with colored measurement noises, using the observation transformation, the system can be converted into an equivalent system with correlated measurement noises. Based on this method, using the classical Kalman filtering, this paper proposed a covariance intersection (CI) fusion Kalman estimator, which can handle the fused filtering, prediction and smoothing problems. The advantage of the proposed method is that it can avoid the computation of the cross co-variances among the local filtering errors and can reduce the computational burden significantly, as well as the CI fusion algorithm can be used in the uncertain system with unknown cross covariances. Based on classical Kalman filtering theory, the centralized fusion and three weighted fusion (weighted by matrices, scalars and diagonal) estimators are also presented respectively. Their accuracy comparisons are given. The geometric interpretations based on covariance ellipses are also given. A Monte-Carlo simulation example shows that the accuracy relations.

For the multi-channel ARMA signal with two sensors, by the classical Kalman filtering method and the covariance intersection (CI) fusion method, a covariance intersection fusion steady-state Kalman signal smoother is presented, which is independent of the unknown cross-covariance. It is proved that its accuracy is higher than that of each local Kalman signal smoother, and is lower than that of the optimal signal fuser weighted by matrices. The geometric interpretation of the above accuracy relations are presented based on the covariance ellipses. A simulation example result shows its effectiveness and correctness.

Covariance Intersection fusion is bound-optimal under unknown correlations. Partial knowledge can improve the fusion. An implicit constraint on correlation has been introduced in the literature for full-vector estimates. This paper considers fusion of partial estimates. Weak and strong counterparts of the full-vector assumption are proposed. An analysis of admissible ideal fusions reveals that the considered implicit partial knowledge cannot improve the Covariance Intersection fusion of partial estimates. An exception is found for the strong assumption and fusion of one partial and one full-vector estimate. For this case, an improved fusion rule is presented.

The fusion under unknown correlations tunes a combination of local estimates in such a way that upper bounds of the admissible mean square error matrices are optimised. Based on the recently discovered relation between the admissible matrices and Minkowski sums of ellipsoids, the optimality of existing algorithms is analysed. Simple examples are used to indicate the reasons for the suboptimality of the covariance intersection fusion of multiple estimates. Further, an extension of the existing family of upper bounds is proposed, which makes it possible to get closer to the optimum, and a general case is discussed. All results are obtained analytically and illustrated graphically.

In a distributed estimation system, the local sensor estimates are transferred to fusion center and fused to be an optimal estimation according to some criterion. The well-known best linear unbiased estimation (BLUE) fusion optimally combines the local estimates by minimising the covariance matrix of estimation errors. However, the BLUE fusion need know the cross-covariances of sensor estimation errors exactly, which are not attainable in most of practical applications. In this article, the random matrix is employed to describe the uncertainty of the estimation error covariance among the sensors. By minimising the estimation error covariance only for the most favorable realisations of the random matrix, we model it as an optimisation problem with chance constraint. With appropriate relaxation method, a robust linear unbiased estimation fusion is proposed analytically. Furthermore, an upper bound on the relaxation gap is proposed. Finally, we demonstrate through some numerical simulations that the presented estimation fusion always has smaller absolute estimation error than that of the covariance intersection filter.

Security problems have become obstacles in the practical application of wireless sensor networks (WSNs), and intrusion detection is the second line of defense. In this paper, an intrusion detection based on dynamic state context and hierarchical trust in WSNs is proposed, which is flexible and suitable for constantly changing WSNs characterized by changes in the perceptual environment, transitions of states of nodes, and variations in trust value. A multidimensional two-tier hierarchical trust mechanism in the level of sensor nodes (SNs) and cluster heads (CHs) considering interactive trust, honesty trust, and content trust is put forward, which combines direct evaluation and feedback-based evaluation in the fixed hop range. This means that the trust of SNs is evaluated by CHs, and the trust of CHs is evaluated by neighbor CHs and BS; in this way, the complexity of evaluation is reduced without evaluations by all other CHs in networks. Meanwhile, the intrusion detection mechanism based on a self-adaptive dynamic trust threshold is described, which improves the flexibility and applicability and is suitable for cluster-based WSNs. The experiment simulation and evaluation indicate that the mechanism we proposed outperforms the existing typical system in malicious detection and resource overhead.

For networked sensor systems (NSSs) with hard and soft sensors including five uncertainties, two universal approaches of solving the robust fusion estimation problems are presented. It includes an integrated sequential covariance intersection (SCI) fusion minimax robust Kalman filtering approach with cross‐covariance information and a generalized Lyapunov equation approach with four pairs of Lyapunov equations. Applying them, the robust local and SCI fused time‐varying and steady‐state Kalman filters are presented in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. The equivalent batch SCI fusers are also presented. Their robustness and accuracy relations are proved, and the sensitivity of the SCI fuser with respect to the fused orders of sensors is analyzed. Applying the dynamic error system analysis method and the dynamic variance error system analysis method, a new convergence and absolute asymptotic stability theory of robust fusion Kalman filtering is presented. The classical Kalman filtering convergence and stability theory is developed. Compared with the original covariance intersection fuser, they significantly reduced the computational complexity and burden. Compared with the optimal and conservative SCI fusers, they significantly improved the robust accuracies. They are suitable to deal with asynchronous or random delayed data and are suitable for real‐time applications. A simulation applied to the two‐mass spring damper mechanical system shows their effectiveness.

SummaryFor networked mixed uncertain time‐varying systems with uncertain noise variances, random one‐step measurement delay, state‐dependent and noise‐dependent multiplicative noises, and linearly dependent additive white noises, the robust local, centralized, and distributed fusion estimation problems are addressed. Three new approaches are presented, which include a new augmented state approach with fictitious white noises, an extended Lyapunov equation approach with two Lyapunov equations, and a universal integrated covariance intersection (ICI) fusion approach of integrating the minimax robust local Kalman estimators and their conservative cross‐covariances. They constitute a new important methodology of solving robust fusion estimation problems. Applying them, the local, centralized, and distributed ICI fusion time‐varying and steady‐state robust Kalman estimators (predictor, filter, and smoother) are presented in the sense that for all admissible uncertainties, their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. Their robustness, convergence, and accuracy relations are proved. Specially, the proposed ICI fusers improve the robust accuracies of the original covariance intersection fusers, and overcome their drawbacks, such that the local estimators and their conservative variances are assumed to be known, and the conservative cross‐variances are ignored. A simulation example with application to a vehicle suspension system shows the effectiveness of the proposed approaches and results.

This article is concerned with the nonlinear state estimation for the multisenor networked system with uncertain bounded noise. Traditional distributed methods only pay attention to the information fusion of state estimations, but neglect the fusion of noise statistics. The difference of noise statistics among sensor nodes usually affects the precision of state estimation in wireless sensor networks, especially for the distributed state estimation. In this article, in order to improve the accuracy of noise statistic estimations, a distributed noise statistic estimator is derived based on covariance intersection criterion and modified Sage–Husa maximum posterior. Then, distributed adaptive cubature information filtering (DACIF) is founded based on weighted average consensus to obtain accurate state estimation. Two‐step information fusion, including the information fusion of state estimations and noise statistics, is derived to enhance the precision of state estimations. Meanwhile, a novel weighted rule is devised based on the state and measurement innovation vectors to improve the accuracy of distribution information fusion. Next, the estimation errors of DACIF are proved to be bounded in mean square. Simulations and semisimulation experiments are conducted to verify the effectiveness of the proposed algorithm.

Multi-constraint multi-objective QoS aware routing heuristics for query driven sensor networks using fuzzy soft sets

Cluster formation and cluster head selection are important problems in sensor network applications and can drastically affect the network's communication energy dissipation. However, selecting of the cluster head is not easy in different environments which may have different characteristics. In order to deal with this problem, we propose a power reduction algorithm for sensor networks based on fuzzy logic and node movement. The proposed system uses 3 input linguistic parameters: remaining battery power of sensor, degree of number of neighbor nodes and sensor speed for cluster-head decision. By considering the moving speed of the sensor node, we are able to find the nodes which leave the cluster. We evaluate the proposed system by simulations and show that the proposed system has a good cluster-head selection.

Devices with sensors are rapidly becoming indispensable. As the technology behind sensors has improved, a wide variety of sensor-based automated systems have emerged. By relaying data from sensors to actuators, these systems can perform actions automatically. Researchers face difficulties in obtaining long-lasting efficacy from sensor nodes into wireless sensor networks (WSNs) because of inadequate resources, energy constraints, and interference. For WSNs to continue operating for as long as possible, it is essential that their limited supply of energy be conserved. technique to organize groups of sensor nodes into clusters of varying sizes, each of which will then send its data on to the central station. First, the CEOMS algorithm build energy density task of the network nodes, & using the energy density function, it designates the sensor nodes having maximum left-over energy like cluster heads.