Consensus filtering is an effective method for distributed state estimation of distributed sensor networks and the assumption of white measurement noise is widely used. However, when the measurement noise is colored, the traditional consensus filter cannot work well. In this paper, we first propose a consensus-based distributed filter for colored measurement noise by augmenting the state to include the colored measurement noise. To improve the efficiency of the filter, only local colored measurement noise is integrated into the augmented state for each local filter. Furthermore, another consensus-based distributed filter based on measurement differencing scheme is developed to eliminate the ill-conditioned computations of the augmented state approach. In addition, this method does not need to augment the state and thus has lower dimension than the augmented state filter. Simulation results demonstrate the superiority of the proposed methods.
In the estimation of distributed sensor networks, process noise and measurement noise may have outliers which have heavy-tailed characteristics. To solve this problem, this paper proposes a distributed consensus estimating method for sensor networks based on Student-t distribution. In the state space model, both process noise and measurement noise are modeled as Student-t distributions with heavytailed characteristics. First, for the assumption that the process noise and measurement noise have the same degree of freedom parameters, an exact distributed consensus Student-t filtering algorithm is derived. In practical applications, this assumption is often not true, and due to the increasing degrees of freedom, the method will quickly converge to the traditional distributed consensus Kalman filter. Therefore, it is necessary to relax the assumption of the same degree of freedom and keep the degree of freedom unchanged within a certain range. Based on this, an approximate distributed consensus Student-t filter algorithm is proposed. Simulation results verify the effectiveness of the proposed algorithm.
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