Forward and Backward Filtering (MATLAB's `filtfilt()`)
My opinion is that the trimming isn't necessary.  

The method in the paper is based on a simple idea, if we filter the signal $ x [n] $ forward and then backward, the result should be equal to the result of doing it backward and then forward.

The paper shows how to chose the initial conditions which minimize the $ {\ell}_{2} $ norm between the the different approaches.