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.