A mathematical model of the airborne light detection and ranging (LiDAR) system based on the GM-APD arrays is established in the behavioral level. The model adopts Poisson probability distribution to calculate the intensity of the echo-laser-signal. After the detection, the range of the target is obtained by the time-of-flight (ToF) method. Then, the system outputs the range and intensity images taking advantages of the peak-value algorithm. The sources and the impact of the noise are analyzed in the model. In condition of 3km distance, 33uJ laser pulse energy, 20 KHz repetition frequency and 200 accumulations each period, the simulation results show that the system is capable to get clear pictures of the target in distance with 1 miscount per frame time. The standard deviation of the calculated range is 0.0219m. The model also demonstrates the validity of capturing the moving target. The proposed model is suitable in systematic design of the airborne LiDAR, which is promising in civil and military applications.
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