The paper introduces a unified affine-projection-like adaptive (UAPLA) algorithm designed for system identification. The UAPLA algorithm is derived from a generalized cost function that incorporates data-reusing methods to handle colored input signals and impulsive noises. This cost function can approximate several affine-projection (AP) algorithms, making the UAPLA algorithm flexible and effective in various applications. The algorithm's performance is evaluated through simulations, demonstrating superior convergence rates and reduced estimation errors compared to other popular AP algorithms. The UAPLA algorithm is particularly effective in channel estimation and echo cancellation tasks, showing faster convergence and smaller steady-state misalignment under impulsive noise conditions. The paper also provides a detailed analysis of the algorithm's convergence and computational complexity, highlighting its robustness and efficiency.The paper introduces a unified affine-projection-like adaptive (UAPLA) algorithm designed for system identification. The UAPLA algorithm is derived from a generalized cost function that incorporates data-reusing methods to handle colored input signals and impulsive noises. This cost function can approximate several affine-projection (AP) algorithms, making the UAPLA algorithm flexible and effective in various applications. The algorithm's performance is evaluated through simulations, demonstrating superior convergence rates and reduced estimation errors compared to other popular AP algorithms. The UAPLA algorithm is particularly effective in channel estimation and echo cancellation tasks, showing faster convergence and smaller steady-state misalignment under impulsive noise conditions. The paper also provides a detailed analysis of the algorithm's convergence and computational complexity, highlighting its robustness and efficiency.