Estimating frequencies of two dimensional harmonics with extended quaternion matrix pencil

In this paper, we proposed a novel algorithm to estimate frequency pairs of two dimensional harmonics, whose frequency pairs might share the common frequency. First, we presented a new math model of two dimensional harmonics signal, which was based on quaternion. Then, we presented operation rules definitions of Hamilton´s quaternion and Ma´s quaternion. After analyzing the properties of two kind of quaternion, we computed correlation function of quaternion data model using Ma´s operation rules and constructed extended quaternion matrix of correlation function data. At last, we proposed our estimation method using Hamilton´s operation rules. Some simulations illustrated our idea.