摘要
Although Hamilton＇s quaternion has been introduced successfully in estimating frequencies of two dimensional harmonics, it was difficult to use it to estimate frequencies of two dimensional harmonics in additive noise because the multiplicative rules of Hamilton＇s quaternion were not commutative. In this paper, we presented a new idea to solve this problem and applied it to array signal processing. First, we presented another definition of operation rules of quaternion, whose multiplicative rules were commutative. Second, we applied this definition to construct correlation matrix of hypercomplex signal model based on quaternion so as to restrain additive noise. Finally, we got the isomorphic complex matrix of correlation matrix of hypercomplex signal model to estimate frequencies. Some simulations illustrated our new idea.
Although Hamilton＇s quaternion has been introduced successfully in estimating frequencies of two dimensional harmonics, it was difficult to use it to estimate frequencies of two dimensional harmonics in additive noise because the multiplicative rules of Hamilton＇s quaternion were not commutative. In this paper, we presented a new idea to solve this problem and applied it to array signal processing. First, we presented another definition of operation rules of quaternion, whose multiplicative rules were commutative. Second, we applied this definition to construct correlation matrix of hypercomplex signal model based on quaternion so as to restrain additive noise. Finally, we got the isomorphic complex matrix of correlation matrix of hypercomplex signal model to estimate frequencies. Some simulations illustrated our new idea.
