Tracking Bound of Compressed Distributed Recursive Least Squares with Forgetting Factor

In this paper, we consider the problem of distributed time-varying sparse parameter estimation over sensor networks. By first compressing the regression signals to remove the sparsity, and then estimating the compressed parameters with the compressed signals, a compressed distributed recursive least squares algorithm with forgetting factor (FFLS) is proposed based on compressive sensing theory. Under the compressed cooperative stochastic excitation condition, we analyze the tracking bound of the estimation error and establish the stability of the compressed distributed FFLS algorithm. Our theoretical results do not rely on independency and stationarity of the regression signals, which makes it possible to be applied to the feedback system. Finally, some simulation results are presented to demonstrate the superiority of our proposed algorithm over the compressed distributed least mean squares (LMS) algorithm and the uncompressed distributed FFLS algorithm.