Patent ID: 6842702

Claim:
A method of multivariate spectral analysis, comprising the steps of: a) obtaining an estimate of spectral error covariance E A for measured set of multivariate spectral data A; b) decomposing the spectral error covariance E A according to E A =TP+E, where T is a set of n×r scores and P is a set of r×p loading vectors obtained from factor analysis of the spectral error covariance E A , and E is a set of n×p random errors and spectral variations not useful for prediction; c) guessing pure-component spectra K for the set of multivariate spectral data A; d) predicting a set of component values Ĉ according to ĈAK T ( KK T ) −1 =A ( K T ) + ; e) augmenting the set of predicted component values Ĉ with at least one vector of the T scores to obtain a first set of augmented component values C ~ ^ ; f) estimating augmented pure-component spectra K ~ ^ according to K ~ ^ = ( C ~ T ⁢ C ~ ) - 1 ⁢ C ~ T ⁢ A = C ~ ^ ⁢ + ⁢ A ; g) testing for convergence according to  A - C ~ ^ ⁢ K ~ ^  ⁢ 2 ⁢ ; h) predicting a second set of augmented component values C ~ ^ according to C ~ ^ = A ⁢ K ~ ^ T ⁡ ( K ~ ^ ⁢ K ~ ^ T ) - 1 = A ⁡ ( K ~ ^ T ) + ; i) replacing the augmented portion of the second set of augmented component values C ~ ^ with the at least one vector of the T scores to obtain a third set of augmented component values C ~ ; ^ and j) repeating steps f) through i) at least once.