Data fusion-based distributed Prony analysis

This paper presents a distributed Prony analysis algorithm using data fusion approach. This classic approach can be found in Kalman filter's measurement update. Distributed optimization algorithms, e.g., alternating direction method of multipliers (ADMM), suitable for constrained optimization problems, have been proposed in the previous literature to develop distributed architecture. In this article, we show that Prony analysis, a non-constrained least square estimation (LSE) problem, can be solved using the classic data fusion approach. Compared to the iterative distributed optimization algorithms (e.g., ADMM and subgradient methods), data fusion takes only one step. There is no need for iteration and there is no issue related to convergence. This approach leads to a distributed Prony analysis architecture which requires a much less demanding communication system (the bandwidth can be less than 0.1 Hz) compared to the conventional centralized Prony analysis for multiple channels which requires a bandwidth of 30 Hz. The application discussed in this paper is to identify oscillation modes from real-world phasor measurement unit (PMU) data and further reconstruct signals. A key technical challenge to implement Prony analysis for signals from multiple channels is the difficulty to identify the noise characteristics of each channel. In this paper, a method is proposed to identify the noise covariances, which leads to the construction of a weighted least square estimation (WLSE) problem. This problem is solved through a distributed architecture. The effectiveness of the proposed distributed Prony analysis is demonstrated through case study results. The accuracy of the estimation is improved in one order compared with the centralized Prony analysis.