With the nonlinearity of bi-directional mirror scan

motion of spacecraft and attitude variability

the model of the line of sight and Projection for Landsat 7 are very complex

and it cost much time during systematically geometric correction. In order to solve this problem

a method to simplify the model and speed up the calculation process is introduced. Image distortion is decomposed into nominal distortions and perturbation caused by seven deviations from nominal motions including one mirror-scan component

three spacecraft-motion components and three attitude components. The nominal mirror scan is selected as an estimated linear model. The nominal spacecraft motions are selected as three forecast orbit components. Three nominal attitudes are all selected as zero. The nominal line of sight can be calculated in advance which cost a great amount of time

and real-time calculation will cost only a little part of time. The whole process is modeled in detail. A new method is introduced in this paper when only partial components can be described. At last

through the analysis in theory and the experiments with real data

the speed and precision of the model are discussed

and the model is validated.