Pulse-width modulation (PWM) technolo gy is mainly used to drive LED in intelligent illumination fields,thus the LED emitting signal is approximately rectangular pulse array at normal state ,and unknown parameters (amplitude,frequency offset and phase) are usually contained in the analytical expression. How to estimate these unknown parameters rapidly and effectively is the main res earch contents of this paper.To achieve this purpose,the frequency offset-phase space is firstly discretized into ret iculated grids space along the horizontal and vertical directions,and a sparse model is constructed based on the characteristics that the measured data are sparse in the grids space.Moreover,the latest compressed se nsing technology is involved, and a small number of data are acquired by pseudo random linear measurement.The n,the unknown parameters are rapidly reconstructed by means of basic pursuit (BP) algorithm.Finally,an it erative refinement of grids scheme is also introduced to optimize the sparse model so as to suppress the estimatio n error effectively.Experimental results indicate that the method presented in this paper can fast reconstruct the unknown parameters using only 0.23% of samples,which is needed in the traditional Nyquist sampling theorem i n an ideal situation.After 3times of iterative optimizations,the root mean squared error (RMSE) of our metho d is generally no greater than 10－4.In addition,this algorithm has good anti-noise performance,and it is robust when signal-to-noi se ratio (SNR) is higher than －160dB.