A family of quaternion-valued pipelined second-order Volterra adaptive filters for nonlinear system identification

This paper primarily proposes a family of quaternion Volterra filters based on the feedforward pipelined structure (QPSOVAFs) for nonlinear quaternion system identification to reduce the computational complexity. Then, the strictly nonlinear QPSOVAF (SNL-QPSOVAF), semi-widely nonlinear QPSOVAF(SWNL-QPSOVAF) and widely nonlinear QPSOVAF (WNL-QPSOVAF) are proposed. This architecture consists of several quaternion-valued second-order Volterra (SOV) modules. The structure's nonlinear subsection executes a nonlinear mapping from the input space to an intermediate space using the feedforward SOV; the linear combiner subsection performs a linear mapping from the intermediate space to the output space. Moreover, the theoretical analysis expresses the effectiveness of the proposed QPSOVAFs in a specific condition. Finally, simulation results further prove that the proposed QPSOVAFs have good performance in identifying the quaternion-valued nonlinear system.

Automated summary

This paper proposes a family of quaternion Volterra filters for nonlinear quaternion system identification, which reduces computational complexity. The effectiveness and good performance of the proposed filters are demonstrated through theoretical analysis and simulation results.