Abstract: For multiple-input single-output finite impulse response (MISO-FIR) systems with unknown time delays, we combine the matching pursuit method and the gradient search principle, according to the sparsity of the parameterized model based on the compressed sensing theory, and propose a gradient pursuit algorithm for simultaneously estimating parameters and time delays with limited sampling data. The proposed method reduces the associated computational burden compared with that of the orthogonal matching pursuit algorithm. The simulation results show the effectiveness of the proposed algorithm.