With excellent resolution and estimation performance, The super-resolution array processing methods have shown their prospect of application in many fields. Nevertheless , because the excellence performances of the methods are based on the accurate knowledge of the data model , the performance of super-resolution methods degraded extremely when the signal-to-noise-ratio is not very high , and the snapshots is not very more or the system errors are existing in the array. This prevent greatly their application in practical system. So , the study of the robust processing methods are main subject in the current .This dissertation is focused on proposing a category of the signals separation, and lay the foundation on the category and drive on the study about the algorithm that can relaxation the h~othcsis of the additive noise and the system errors . The content can be outlined as follows:?A genemlintion of thc(DD-)RELAX from the data domain to the correlation domain , i.e the CD-RELAX, was provided . The equivalence of the iterative subtraction and the recursion iterative of the definite matrix operators was proved , the tranuibrmation of the recursion iterative fitting between the azimuth and the waveform to the analytical form of the waveform and the iterative fitting of the azimuth was made . With the analysis of the RELAX in the correlation domain, the theory of the signals resolution that based on the signals separation was established, and the effect of the signal separation with the projection of the iterative matrix operators was also proved.?Under the hypothesis of the given matrix operators satisfying the signals separation, the multi-dimensional optimum about the signal azimuth, and the multidimensional(MD-)RELAX , was established. To establish the Alternating Separation (AS)algorithm of the (MD-)RELAX , that same one dimensional optinluni as the CDRELAX was derived and the recurrent iterative operators relation was replaced by the operators liner equation . By comparing the CD-RELAX with the Alternating Projection of the Maximum Likelihood(ML-AP) , the opinion of the exact fitting and the non-exact fitting was proposed . Based on the discussion , the improved RELAX was proposed , that it is the RELAX-AS.~.On the characteristic of the RELAX , some functions was defined, the regularity and irregularity , as in the ideal case and the non ideal case, are discussed, respectively.C?The comparison is made about the RELAX and ML , the RELAX-AS and the ML-AP , The weightiest characteristic of the current estimation of the signal parameter in getting the new estimation in the RELAX-AS was found . The character is relative to the convergent slowness and the restraint of the local extreme ; The慍indirect relation of the current estimation of the signal parameter in getting the new estimation in the ML-AP was also point out . The method about rid ofthe shortcoming and usc the characters of the ML-AP and RELAX-AS , the RELAX-AS and ~AP approach, w also ??The discussion of the relative algorithm of the Maximum Likelihood ii made , the conchnion abont that IMP. ANPA and Al?are all one dimensional algorithm of the Maximum Likelihood, the intrinsic of the IMP and ANPA are same as that of the AP was derived.?The asymptotic of the two dimensional MUSIC of the spatial and temporal processing is established, The effect of the two dimensional processing under the spatial or the temporal wmcx is proved, and the optimum length of the temporal filtering is provided.晘 The statistical fitting of the gain and phase errors is discussed , on guaranteeing the aitariom of the least squares , using the separation and elimination approach , making the dimension of the errors fitting equal to the number of the sensors .Under the different hypothesis of the statistical characteristic of the errors, the different constrains are proposed, which make the errors fitting as a constrains optimum Since the complicate algorithm can be done for definite array before the app cati