  We discuss a robust projection method for the extraction of excited-state
masses of the nucleon from a matrix of correlation functions. To illustrate the
algorithm in practice, we present results for the positive parity excited
states of the nucleon in quenched QCD. Using eigenvectors obtained via the
variational method, we construct an eigenstate-projected correlation function
amenable to standard analysis techniques. The method displays its utility when
comparing results from the fit of the projected correlation function with those
obtained from the eigenvalues of the variational method. Standard nucleon
interpolators are considered, with $2\times 2$ and $3\times 3$ correlation
matrix analyses presented using various combinations of source-smeared,
sink-smeared and smeared-smeared correlation functions. Using these new robust
methods, we observe a systematic dependency of the nucleon excited-state masses
on source- and sink-smearing levels. To the best of our knowledge, this is the
first clear indication that a correlation matrix of standard nucleon
interpolators is insufficient to isolate the eigenstates of QCD.
