Motion estimation is an effective way to rectify the distortion of linear array images of moving target in linear measurement system. However, the non-cooperation and motion complexity of instability space targets make it difficult to precisely estimate their motion parameters. In order to improve the estimation accuracy, a feature-driven high-precision motion estimation for instability space targets was presented. Firstly, a self-constrained motion model of instability space targets by means of the spherical coordinate was established, which transformed the motion estimation into an unconstrained nonlinear optimization problem in high dimensional space. Then, according to the existence and uniqueness of global solutions, an effective way was devised to judge the validity of obtained solutions via comparing the similarity of two solutions calculated via two solving processes under different selections of frame number, which evidently improved the effectiveness and robustness of our method. Finally, the solving efficiency among different non-linear solution methods in the view of our problem was numerically analyzed and an efficient solution scheme in terms of the accuracy of initial values was presented to improve the efficiency of our method. Experimental results illustrate that only needing a maximum of 15 frames of linear array images the estimation accuracy of motion parameters all reach (<10^-5) and thus achieve the high performance of rectification for distorted linear array images in our research background.