Abstract: The target capture is the key technology of the space-based early warning system. In this paper, the thrust acceleration is analyzed, and then the nonlinear model of ballistic missile in the image is presented. Combined with the Probabilistic Data Association (PDA), the likelihood function is denoted, and the optimal weighted probability is calculated using Lagrange way which causes the logarithmic likelihood ratio maximum. Using the amplitude information of measurement, under low Signal-to-noise (SNR) the detection performance is improved. Via the Monte Carlo simulation, this method has the better detection performance and estimation accuracy than other approaches. It is applicable for the target capture under low SNR in the space-based early warning system.