The sequential fusion estimation algorithms based on Gauss-Newton method over multi-agent networked systems

In multi-agent networked systems, parameter estimation problems arising in many practical applications are often required to solve Non-Linear Least Squares (NLLS) problems with the usual objective function (i.e., sum of squared residuals). The aim is to estimate a global parameter of interest across the network, such that the discrepancy between the estimation model and the real output of the system is minimized. There are challenges to face when applying the conventional Gauss-Newton method, such as non-cooperation and prosaic learning behavior. In this paper, we propose two Gauss-Newton type fusion estimation algorithms for solving overdetermined NLLS optimization problems arising frequently in multi-agent networked environment. One is the cycle-based Gauss-Newton (CGN) algorithm that is more attractive in performance due to its distributed nature than its peer: the known centralized Gauss-Newton algorithm. On the basis of CGN, we put emphasis on developing a simple but effective learning scheme leveraging an incremental technique, which is distributed on each computing agent over network. Such scheme results in the Incremental Gauss-Newton (IGN) algorithm that achieves a clear increase on convergence rate at the expense of higher computation cost than the CGN algorithm as well as the centralized one by deeper learning over the networking cycle. Both algorithms utilize Gauss-Newton iteration update in a cyclic cooperative manner, which offers the flexibility in exploiting the network topology. We provide the detailed analysis and the sufficient conditions for convergence of proposed IGN algorithm. By applying to target localization in wireless sensor networks, the numerical results confirm our convergence analysis and show that the proposed incremental scheme outperforms the centralized one in term of convergence performance.