Sparse Robust Learning From Flipped Bits

Abstract

In wireless sensor networks (WSNs), distributed sensors are often constrained by their limited battery energy and radio spectrum for transmission. This paper investigates an on-line parameter estimation problem of linear regression in a WSN, where each sensor is restricted to send a one-bit message $+1/-1$ to a fusion center in order to satisfy the spectrum and power constraints. Moreover, sensor nodes communicate with the fusion center over noisy links, which can randomly flip the binary message sent from each sensor to the fusion center. With the flipped bit stream, robust and sparse-robust learning algorithms respectively are proposed. In the proposed algorithms, the parameter estimation over a WSN with the imperfect binary communication is formulated hierarchically as Bayesian learning, and is equivalent to an expectation maximization realized by using the recursive least-squares methods. Theoretical and empirical research is carried out to assess the performance of the proposed algorithms, and a practical application of the proposed algorithms in estimation and tracking of frequencies of multiple sinusoids is also presented. These theoretical analysis and experimental results demonstrate the effectiveness of the proposed algorithms.