Energy-efficient SSD-LMS algorithm for state-space estimation in distributed networks

In a distributed environment, estimation takes place at multiple nodes. The computational complexity at each node can therefore significantly increase the computational cost of the overall network. In this research, we propose a novel energy-efficient state-space diffusion least mean square (SSD-LMS) algorithm for distributed networks. The proposed algorithm minimizes the computational complexity at each node and providing a significant advantage in terms of computational cost and response time of the overall network. Furthermore, the proposed algorithm required less communications for data sharing in the distributed network. Both, the convergence in the mean and the mean square analysis of the proposed algorithm is performed. Furthermore, the transient and the steady-state behavior is also analyzed. As a result of the convergence analysis, recursion is developed to evaluate the transient excess mean square error (EMSE) of the proposed algorithm. The proposed algorithm is evaluated by comparing the theoretical findings with the simulation results. Furthermore, the proposed SSD-LMS and the standard diffusion Kalman filter (D-KF) are compared for two different examples: (1) Channel Estimation, (2) Real-time tracking and (3) estimation of 3-degree-of-freedom piezo-actuator-driven stages. First two examples are a case-studies of small-scale systems while the third one relates to a large-scale system. The results show that the proposed SSD-LMS algorithm provides approximately identical results to the D-KF at a significantly low computational cost.