AlthoughHamilton'squaternionhasbeenintroducedsuccessfullyinestimatingfrequenciesoftwodimensionalharmonics,itwasdifficulttouseittoestimatefrequenciesoftwodimensionalharmonicsinadditivenoisebecausethemultiplicativerulesofHamilton'squaternionwerenotcommutative.Inthispaper,wepresentedanewideatosolvethisproblemandappliedittoarraysignalprocessing.First,wepresentedanotherdefinitionofoperationrulesofquaternion,whosemultiplicativeruleswerecommutative.Second,weappliedthisdefinitiontoconstructcorrelationmatrixofhypercomplexsignalmodelbasedonquaternionsoastorestrainadditivenoise.Finally,wegottheisomorphiccomplexmatrixofcorrelationmatrixofhypercomplexsignalmodeltoestimatefrequencies.Somesimulationsillustratedournewidea.
