Multi-task Total Least-Squares Adaptation over Networks

Collaborative parameter estimation is a significant application of distributed multi-agent network. In practical scenarios, there are many multi-task oriented applications that the networks have multiple optimum parameter vectors to be estimated. Considering the condition that the input and output of agents are corrupted by additive noises, the network can be modeled as the multi-task errors-in-variables (M-EIV) problem. Total least-squares (TLS) method is a typical solution to the EIV problem for it can minimize the perturbation both in input and output data. In this paper, we study the problem of unbiased parameter estimation over multi-task networks whose nodes' inputs are corrupted by white noises. We propose a novel multi-task TLS (M-TLS) algorithm which can reach consistent unbiased estimation. Simulation results show that the proposed algorithms can achieve consistent and unbiased estimation.