Diffusion Kalman Filter Research Articles

A distributed diffusion Kalman filter with event‐triggered mechanism and guaranteed stability

AbstractIn this article, a distributed diffusion Kalman filtering algorithm with event‐triggered communication (DDKF‐E) is studied for discrete‐time nonlinear systems. According to the event‐triggered communication protocol, the data between sensors and estimators are transmitted only when the predefined conditions are satisfied. Considering the characteristic of event‐triggered method and truncated error by linearization, an upper bound of the estimation error covariance matrix is obtained by using the variance‐constrained method. The Kalman gain is designed to minimize the upper bound and then two Riccati equations are obtained. Furthermore, the stochastic stability theory is used to prove the stability of DDKF‐E, and it is derived that the estimation error of DDKF‐E is exponentially bounded in mean square. Finally, numerical simulations validate the effectiveness of the DDKF‐E algorithm.

Deep Diffusion Kalman Filter Combining Large-Scale Neuronal Networks Simulation with Multimodal Neuroimaging Data

Using computers to numerically simulate large-scale neuronal networks has become a common method for studying the mechanism of the human brain, and neuroimaging has brought forth multimodal brain data. Determining how to fully consider these multimodal data in the process of brain modeling has become a crucial issue. Data assimilation is an efficient method for combining the dynamic system with the observation data, and many related algorithms have been developed. In this paper, we utilize data assimilation to perform brain state variables estimation, put forward a general form of a diffusion Kalman filter named the deep diffusion Kalman filter, and provide a specific algorithm that is combined with data assimilation. Then, we theoretically demonstrate the deep diffusion Kalman filter’s effectiveness and further validate it by using an experiment in the toy model. Finally, according to the resting state functional magnetic resonance imaging signals, we assimilate a cortex networks model with the resting state brain, where the correlation is as high as 98.42%.

Energy-Efficient Diffusion Kalman Filtering for Multiagent Networks in IoT

Increasing the energy efficiency of an Internet of Things (IoT) system is a major challenge for its successful implementation. To reduce the computation and storage burden and enhance the efficiency of traditional IoT, an energy-efficient diffusion-based algorithm for state estimation in multiagent networks is proposed in this article. In the proposed algorithm [referred to as the reduced-link diffusion Kalman filter (RL-diffKF)] the nodes (agents) can communicate only with a fraction of their neighbors and each node runs a local Kalman filter to estimate the state of a linear dynamic system. This algorithm results in a significant reduction in communication cost during both adaptation and aggregation processes albeit at the expense of possible degradation in the network performance. To justify the stability and convergence of the RL- diffKF algorithm, an in-depth analysis of the performance is reported. We also consider the problem of optimal selection of combination weights and use the idea of minimum variance estimation to analytically derive the adaptive combiners. The theoretical findings are verified through numerical simulations.

Energy-efficient SSD-LMS algorithm for state-space estimation in distributed networks

In a distributed environment, estimation takes place at multiple nodes. The computational complexity at each node can therefore significantly increase the computational cost of the overall network. In this research, we propose a novel energy-efficient state-space diffusion least mean square (SSD-LMS) algorithm for distributed networks. The proposed algorithm minimizes the computational complexity at each node and providing a significant advantage in terms of computational cost and response time of the overall network. Furthermore, the proposed algorithm required less communications for data sharing in the distributed network. Both, the convergence in the mean and the mean square analysis of the proposed algorithm is performed. Furthermore, the transient and the steady-state behavior is also analyzed. As a result of the convergence analysis, recursion is developed to evaluate the transient excess mean square error (EMSE) of the proposed algorithm. The proposed algorithm is evaluated by comparing the theoretical findings with the simulation results. Furthermore, the proposed SSD-LMS and the standard diffusion Kalman filter (D-KF) are compared for two different examples: (1) Channel Estimation, (2) Real-time tracking and (3) estimation of 3-degree-of-freedom piezo-actuator-driven stages. First two examples are a case-studies of small-scale systems while the third one relates to a large-scale system. The results show that the proposed SSD-LMS algorithm provides approximately identical results to the D-KF at a significantly low computational cost.

A novel secure diffusion Kalman filter algorithm against false data injection attacks

A novel secure diffusion Kalman filter algorithm against false data injection attacks

Multi-agent detection and labelling of activity patterns

We address the problem of automatic detection and labelling of far-field activity patterns from target trajectories using vector field abstractions that are estimated by multiple communicating agents in a Kalman filter (KF) framework. We propose a novel 2D application of the diffusion KF. The proposed approach yields multiple vector field abstractions at the same spatial regions by allowing the estimator agents to create a library of states. We compute internal consistency measures to assess the estimated vector fields, and establish thresholds that signal low performance estimates. Experimental results on synthetic and real data sets show that the proposed approach correctly detects activity patterns from training trajectories and, using new test trajectories one at a time, either matches them to previously detected activity patterns or detects new activity patterns that are added to the agents library. Moreover, the internal consistency measures correctly flag the low-performer vector field abstractions.

Distributed detection of Gauss–Markov signals using diffusion Kalman filtering

Abstract This paper addresses the problem of distributed detection of Gauss–Markov signals in adaptive networks, where nodes make individual decisions by exchanging information with their neighbours and no fusion centre is used. Relying on the connection between the log-likelihood ratio (LLR) and the innovations process, a distributed detection algorithm for Gauss–Markov signals is proposed based on diffusion Kalman filtering. To perform hypothesis testing, a LLR is constructed using the innovations estimated by the diffusion Kalman filter. The detection performance of the new algorithm is analysed by deriving approximate expressions for the probability of false alarm and detection. The mean and mean-square value of the test statistic, and the probability of detection and receiver operating characteristics of the algorithm are demonstrated by way of Monte Carlo simulations, where a good agreement between theoretical and simulation results is observed. Simulations also confirm the improved detection performance of the proposed algorithm over non-cooperative detection and show that the performance of the algorithm converges to that of the centralized scheme.

Diffusion nonlinear Kalman filter with intermittent observations

In this article, we consider the distributed nonlinear state estimation over sensor networks under the diffusion Kalman filter paradigm, where data only exchanges among the neighbourhoods of sensors. We first obtain a novel nonlinear Kalman filter with intermittent observations based on cubature Kalman filter. After that, its equivalent information filter is derived, and the proposed diffusion cubature Kalman filter with intermittent observations is designed based on this information filter. The effectiveness of proposed algorithms is demonstrated by a typical target tracking example, and our algorithm has similar estimation accuracy when comparing with existing algorithms while consuming less computation and communication resources.

Diffusion Kalman filtering with multi-channel decoupled event-triggered strategy and its application to the optic-electric sensor network

Recently the distributed estimation problem with communication constraints has been widely studied for sensor network application. Our work focus on the diffusion Kalman filter with communication constraints. To satisfy finite communication resources constraints, this paper presents a multi-channel decoupled event-triggered strategy which improves the utilization of the network communication resources. With this strategy, only some entries of sensors’ measurements are transmitted if their triggering criteria are satisfied. We apply this strategy to the step 1 of the diffusion Kalman filter and analyze its performance. The analysis shows that the multi-channel decoupled event-triggered diffusion Kalman filter is unbiased in mean sense and is convergent in mean-square sense. The theoretical steady-state mean-square deviation (MSD) and communication cost are also given in this article. Simulation results demonstrate a good match between the theory analysis and experiment. Finally this algorithm is applied to the optic-electric sensor network, and the results verify the effectiveness of the proposed strategy in terms of the communication resources utilization.

Diffusion Strategies for Distributed Kalman Filter with Dynamic Topologies in Virtualized Sensor Networks

Network virtualization has become pervasive and is used in many applications. Through the combination of network virtualization and wireless sensor networks, it can greatly improve the multiple applications of traditional wireless sensor networks. However, because of the dynamic reconfiguration of topologies in the physical layer of virtualized sensor networks (VSNs), it requires a mechanism to guarantee the accuracy of estimate values by sensors. In this paper, we focus on the distributed Kalman filter algorithm with dynamic topologies to support this requirement. As one strategy of distributed Kalman filter algorithms, diffusion Kalman filter algorithm has a better performance on the state estimation. However, the existing diffusion Kalman filter algorithms all focus on the fixed topologies. Considering the dynamic topologies in the physical layer of VSNs mentioned above, we present a diffusion Kalman filter algorithm with dynamic topologies (DKFdt). Then, we emphatically derive the theoretical expressions of the mean and mean-square performance. From the expressions, the feasibility of the algorithm is verified. Finally, simulations confirm that the proposed algorithm achieves a greatly improved performance as compared with a noncooperative manner.

Diffusion Strategies for Distributed Kalman Filtering and Smoothing

We study the problem of distributed Kalman filtering and smoothing, where a set of nodes is required to estimate the state of a linear dynamic system from in a collaborative manner. Our focus is on diffusion strategies, where nodes communicate with their direct neighbors only, and the information is diffused across the network through a sequence of Kalman iterations and data-aggregation. We study the problems of Kalman filtering, fixed-lag smoothing and fixed-point smoothing, and propose diffusion algorithms to solve each one of these problems. We analyze the mean and mean-square performance of the proposed algorithms, provide expressions for their steady-state mean-square performance, and analyze the convergence of the diffusion Kalman filter recursions. Finally, we apply the proposed algorithms to the problem of estimating and tracking the position of a projectile. We compare our simulation results with the theoretical expressions, and note that the proposed approach outperforms existing techniques.