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Did you try a simple background subtraction, with history? The logo should be in the area, where pixels are less changing. With your prior, you can only get background subtraction in the 4 corners where it is supposed to be.
For the subtraction, I think you will have better results with absdiff than with Mixture of Gaussian subtraction. After finding the logo in the first video, you can either used SIFT/SURF or template matching for others video to directly detect the logo, maybe also the corner position of first video.
