Distributed recursive binary identification under tampering and non-persistent excitation

Abstract

In this paper, we consider distributed parameter estimation with binary observations under measurement-side tampering: each node observes a thresholded output whose label may be flipped and exchanges information over a communication graph. We develop a distributed recursive projection algorithm based on the diffusion strategy. Without imposing independence, stationarity, or Gaussian assumptions, we establish almost sure upper bounds of both the accumulated regrets of the adaptive predictor and the distributed estimation error. Under a mild cooperative excitation condition, all nodes' estimate are consistent, even when each node is individually non-exciting. Simulations on a jointly exciting network corroborate the theory and show that the proposed algorithm converges, whereas non-cooperative and tampering-unaware baselines do not.