scholarly journals Distributed weighted least squares estimation with fast convergence in large-scale systems

2013 ◽  
Author(s):  
Damin Marelli ◽  
Minyue Fu
Keyword(s):  
Least Squares ◽  
Large Scale ◽  
Weighted Least Squares ◽  
Least Squares Estimation ◽  
Fast Convergence ◽  
Large Scale Systems ◽  
Weighted Least Squares Estimation

scholarly journals Distributed Weighted Least-Squares and Gaussian Belief Propagation: An Integrated Approach

2021 ◽  
Author(s):  
Dino Zivojevic ◽  
Muhamed Delalic ◽  
Darijo Raca ◽  
Dejan Vukobratovic ◽  
Mirsad Cosovic
Keyword(s):  
Least Squares ◽  
Large Scale ◽  
Belief Propagation ◽  
Weighted Least Squares ◽  
Measurement Data ◽  
Integrated Approach ◽  
Factor Graph ◽  
State Variables ◽  
Large Scale Systems ◽  
Distributed Approach

The purpose of a state estimation (SE) algorithm is to estimate the values of the state variables considering the available set of measurements. The centralised SE becomes impractical for large-scale systems, particularly if the measurements are spatially distributed across wide geographical areas. Dividing the large-scale systems into clusters (\ie subsystems) and distributing the computation across clusters, solves the constraints of centralised based approach. In such scenarios, using distributed SE methods brings numerous advantages over the centralised ones. In this paper, we propose a novel distributed approach to solve the linear SE model by combining local solutions obtained by applying weighted least-squares (WLS) of the given subsystems with the Gaussian belief propagation (GBP) algorithm. The proposed algorithm is based on the factor graph operating without a central coordinator, where subsystems exchange only ``beliefs", thus preserving privacy of the measurement data and state variables. Further, we propose an approach to speed-up evaluation of the local solution upon arrival of a new information to the subsystem. Finally, the proposed algorithm provides results that reach accuracy of the centralised WLS solution in a few iterations, and outperforms vanilla GBP algorithm with respect to its convergence properties.

Effects of errors-in-variables on weighted least squares estimation

2014 ◽  
Vol 88 (7) ◽  
pp. 705-716 ◽  
Author(s):  
Peiliang Xu ◽  
Jingnan Liu ◽  
Wenxian Zeng ◽  
Yunzhong Shen
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Least Squares Estimation ◽  
Errors In Variables ◽  
Weighted Least Squares Estimation
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