We propose a method for estimating trajectories of objects moving on a world plane. Motivation of this work is to estimate the field trajectories of players and the ball from uncalibrated monocular soccer image sequences. In order to find mappings between images and the plane, four feature points, no three of them are collinear, should exist in each image. However, many soccer images do not satisfy that condition. In that case, the object positions in the given image are mapped to those in the reference image of the sequence, and then mapped again to those in the soccer field. Conventional mapping between given image and the reference image is given by concatenation of homographies between consecutive image pairs. However, small correspondence error is accumulated in the concatenation of homographies over long image sequence. To overcome this problem, we compute globally consistent homographies for all the feature-sufficient images by solving a sparse linear system of equations which consists of consecutive and non-consecutive homographies of feature-sufficient image pairs. Experimental results with real and synthetic soccer data show that the proposed method is more accurate than existing method.