Sparse identification for stochastic systems with binary-valued observations

This paper studies the identification of finite impulse response systems with binary observations, where the system parameters are sparse. Inspired by the least square method, a sparse parameter identification algorithm based on L-2 norm and L-1 regularization in the binary case is given, where adaptive weights are used for the optimization variables of the L-1 term. Also, the convergence of the parameters of the proposed algorithm is proved. Finally, a numerical example is given to support the theoretical analysis.