Distributed Consensus Student-<italic>t</italic> Filter for Sensor Networks With Heavy-Tailed Process and Measurement Noises

Abstract

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 heavy-tailed 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.

Keywords

• t distribution%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> Student-<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">t</italic> distribution
• distributed consensus filter
• distributed sensor networks