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Visual SLAM techniques have proven to be effective methods for estimating robust position and attitude in the field of robotics. However, current monocular SLAM algorithms cannot guarantee timeliness of system startup due to the problematic initialization time and the low success rates. This paper introduces a rectilinear platform motion hypothesis and thereby converts the estimation problem into a verification problem to achieve fast monocular SLAM initialization. The proposed method is simulation tested on a fixed-wing UAV. Tests show that the proposed method can produce faster initialization of visual SLAM and that the advantages are more profound on systems with sparse image features.