System Identification Using Adaptive Filters with Affine Projection Algorithm

This paper presents a system identification methodology using adaptive filters based on both full-update and partial-update Affine Projection Algorithm (APA). The approach involves incremental adjustment and updating of input signals to enhance system identification performance. The Affine Projection Algorithm serves as an effective identification method applicable to various system identification scenarios. The implementation typically involves maintaining a projection matrix of recent input vectors and calculating weight updates using matrix inversion or regularization techniques. Key algorithmic steps include: - Collecting a sliding window of input signal vectors - Computing the error between desired and actual outputs - Solving the affine projection equations using efficient matrix operations - Applying full or partial coefficient updates based on convergence requirements A practical implementation in MATLAB might utilize the 'pinv' function for pseudo-inverse calculations or employ regularized versions like R-APA to handle ill-conditioned matrices. The partial-update variant selectively updates filter coefficients to reduce computational complexity while maintaining acceptable convergence rates. The paper elaborates on the algorithm's theoretical foundation and implementation procedures, supported by practical examples demonstrating its application effectiveness. Through studying this content, readers can gain comprehensive understanding of adaptive filter-based system identification methods and learn how to employ Affine Projection Algorithm to improve system identification performance through proper parameter tuning and update strategy selection.