Robust Distributed Parameter Estimation of Nonlinear Systems With Missing Data Over Networks

Distributed parameter estimation of linear systems has received much attention in the past two decades. However, the complicated dynamics of some real systems is difficult to characterize with linear models. Nonlinear models, may instead, be good candidates for complex system modeling. But, due to the nonlinearity of the systems, the existing distributed parameter estimation algorithms are not directly applicable. Besides, due to various physical and man-made reasons, some measurements are missing in practice. Considering this, in this article, two robust distributed estimation algorithms are proposed for estimating the parameters of nonlinear Hammerstein systems with missing data. In the proposed algorithms, a Bayesian hypothesis testing is used to justify whether the incoming measurement is missing or not. Then, the parameters are updated and combined via an adaptive combiner according to the status of the measurements. The performance of the proposed algorithms is analyzed theoretically and verified by some simulations. Results show that the proposed algorithms are very robust to different probabilities of data missing. Although the convergence rates of the proposed algorithms decrease as the probability of data missing increases, the performance of estimation approaches the case when there is no data missing.