Abstract: In the parameter estimation over wireless sensor networks（WSNs）, each node's ability in data acquisition, storage, processing and transmission is limited. In a binary sensor network, each node only can provide low-precision One-bit observations. Compared with the measurement value sensors that can provide analog measurements (infinite accuracy), the binary sensors have lower cost. How to use low-cost binary sensor networks to obtain better parameter estimation performance have attracted extensive attention in recent years. Based on this binary sensor network, an adaptive least mean square (LMS) algorithm for distributed sparse parameter estimation is proposed. The algorithm adopts sparse penalty maximum likelihood optimization, combined with expectation maximization (EM) and Least Mean Square (LMS) method, to obtain the online estimation of sparse signal. Simulation experiment results show that the proposed algorithm, though only using 1-bit measurements, has good convergence, is comparable to the existing algorithms based on analog measurements (infinite accuracy).