The Application of Quaternion-valued Nonlinear Adaptive Algorithm in Vector-Sensor Arrays

Abstract

In the optimization process of adaptive filtering algorithms, nonlinear objective functions are often encountered. Quaternion is used as a new mathematical model in the adaptive filtering algorithm based on vector sensing. A nonlinear adaptive filtering algorithm and its application based on quaternion-valued chain rules are proposed and implemented. Then the quaternion-valued hyperbolic tangent function is employed as the output nonlinear constraint function, the gradient of its cost function is solved, and then the iterative formula of the weight coefficient vector of array is obtained. As the input signal receiver of the vector sensor array, the crossed dipole antenna pairs have been used in the quaternion-valued nonlinear adaptive beamforming algorithm to form an array system to process incident signals. Through Matlab simulation results, it is verified that the quaternion-valued nonlinear adaptive beamforming algorithm can be applied in the vector-senor array to receive desired signals and suppress interferences.