Recursive Identification of Binary-Valued Systems Under Uniform Persistent Excitations

This article investigates the online identification problem of binary-valued moving average systems. A stochastic approximation-based algorithm without projections or truncations is proposed. To analyze the convergence property of the algorithm, the distribution tail of the parameter estimate is proved to be exponentially convergent through an auxiliary stochastic process. Under uniform persistent excitations, the almost sure and mean square convergence of the algorithm is obtained. When the step-size coefficient is properly selected, the almost sure and mean square convergence rates are proved to reach O(root ln lnk/k) and O(1/k), respectively, where k is the sample size. A numerical example is given to demonstrate the effectiveness of the proposed algorithm and theoretical results.