This site has a great tutorial on how to do it, and includes a helpful bash script that joins the MTS files before starting, as apparently not doing so can cause problems.

If you want to experiment before jumping into his instructions, you can try the following command. This creates an x264 AVI, you can easily change the output format by changing the libx264 part below to mpeg4.

ffmpeg -i your_file.MTS -acodec copy -vcodec libx264 -crf 21 -r 30000/1001 -deinterlace -vpre lossless_medium -y -threads 0 output_file.avi