A novel robust multivariate Laplace distribution-based distributed consensus information fusion

Authors:
raw_author_name: Zihao Jiang
raw_affiliation_string: College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin, 150001, People's Republic of China; Department of Information Engineering, University of Florence, Florence, 50139, Italy; Engineering Research Center of Navigation Instruments, Ministry of Education, Harbin, 150001, People's Republic of China
raw_author_name: Weidong Zhou
raw_affiliation_string: College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin, 150001, People's Republic of China; Engineering Research Center of Navigation Instruments, Ministry of Education, Harbin, 150001, People's Republic of China
raw_author_name: Yu Guo
raw_affiliation_string: College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin, 150001, People's Republic of China; Engineering Research Center of Navigation Instruments, Ministry of Education, Harbin, 150001, People's Republic of China
raw_author_name: Chao Zhang
raw_affiliation_string: College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin, 150001, People's Republic of China; Engineering Research Center of Navigation Instruments, Ministry of Education, Harbin, 150001, People's Republic of China
raw_author_name: Lu Tian
raw_affiliation_string: College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin, 150001, People's Republic of China; Engineering Research Center of Navigation Instruments, Ministry of Education, Harbin, 150001, People's Republic of China

Abstract: The multivariate Laplace distribution (MLD) possesses a lesser set of prior parameters compared to the Student's t-distribution, thus simplifying the modeling of measurement data subject to heavy-tailed noise corruption. This short communication introduces a novel distributed hybrid consensus fusion algorithm utilizing the MLD modeling and variational Bayesian approach. Firstly, we formulate the measurement noise associated with individual sensor nodes and introduce the hierarchical Gaussian form of MLD to enhance the feasibility of variational inference. Secondly, we opt for the inverse-Wishart (IW) distribution to serve as the conjugate prior to the positive definite matrix, enabling adaptive parameter learning within the MLD context. As a result, a novel hierarchical Gaussian state–space model (SSM) is established for multi-sensors network. Subsequently, we derive a novel local information filter to acquire higher precision information and innovation vector–matrix pairs, outperforming the Student's t distribution-based filter. These derivations are grounded in the new hierarchical SSM, and the vector–matrix pairs aid in information fusion across the network. Lastly, we present a distributed robust consensus filter for fusing local information using a hybrid consensus approach that devoid of a central fusion node. Simulation results demonstrate that the proposed consensus filter can obtain better estimation accuracy under the interference of heavy-tailed measurement outliers.