Constructive updating/downdating of oblique projectors: a generalization   of the Gram-Schmidt process
  A generalization of the Gram-Schmidt procedure is achieved by providing equations for updating and downdating oblique projectors. The work is motivated by the problem of adaptive signal representation outside the orthogonal basis setting. The proposed techniques are shown to be relevant to the problem of discriminating signals produced by different phenomena when the order of the signal model needs to be adjusted. 
Laura Rebollo-Neira