For the identification problem of nonlinear systems, the accuracy and stability of the nonlinear compression measurement identification algorithm were proved in the simulation experiment, and the complete signal was obtained accurately only by using constant multiple measurement times of the signal sparsity. Compared with the least square method, the proposed algorithm has greatly reduced the needed measurements, therefore, it is possible for the identification of high-order Volterra series. Furthermore, the influence of all factors on the accuracy of system identification was analyzed, such as signal sparsity, measurement noise, measurement matrix form, etc.