A unified affine-projection-like adaptive (UAPLA) algorithm is proposed for system identification. The UAPLA algorithm uses a generalized cost function that encompasses data-reusing methods to handle colored input signals. It approximates several affine-projection algorithms by deriving the algorithm based on the new cost function. The UAPLA algorithm can approximate classical adaptive filters as special cases, allowing flexibility to achieve low estimation errors under impulsive noise. Simulation results show that the UAPLA algorithm outperforms other popular AP algorithms in terms of convergence rate and misalignment. The UAPLA algorithm is derived by constructing a generalized cost function within a data-reusing scheme. The cost function is designed to be flexible, allowing the algorithm to approximate various algorithms such as LMS, AP, and APS by selecting different shaping factors. The algorithm's convergence is analyzed, and it is shown that the UAPLA algorithm can achieve faster convergence and smaller misalignment when the shaping factor is set to -2. The computational complexity of the UAPLA algorithm is analyzed, and it is shown that the algorithm has lower computational burden compared to other AP-like algorithms. Simulation results demonstrate that the UAPLA algorithm performs well in echo cancellation and system identification tasks, especially under impulsive noise conditions. The algorithm outperforms other algorithms in terms of convergence rate and steady-state misalignment. The UAPLA algorithm is versatile and can be used for various applications, including system identification and echo cancellation.A unified affine-projection-like adaptive (UAPLA) algorithm is proposed for system identification. The UAPLA algorithm uses a generalized cost function that encompasses data-reusing methods to handle colored input signals. It approximates several affine-projection algorithms by deriving the algorithm based on the new cost function. The UAPLA algorithm can approximate classical adaptive filters as special cases, allowing flexibility to achieve low estimation errors under impulsive noise. Simulation results show that the UAPLA algorithm outperforms other popular AP algorithms in terms of convergence rate and misalignment. The UAPLA algorithm is derived by constructing a generalized cost function within a data-reusing scheme. The cost function is designed to be flexible, allowing the algorithm to approximate various algorithms such as LMS, AP, and APS by selecting different shaping factors. The algorithm's convergence is analyzed, and it is shown that the UAPLA algorithm can achieve faster convergence and smaller misalignment when the shaping factor is set to -2. The computational complexity of the UAPLA algorithm is analyzed, and it is shown that the algorithm has lower computational burden compared to other AP-like algorithms. Simulation results demonstrate that the UAPLA algorithm performs well in echo cancellation and system identification tasks, especially under impulsive noise conditions. The algorithm outperforms other algorithms in terms of convergence rate and steady-state misalignment. The UAPLA algorithm is versatile and can be used for various applications, including system identification and echo cancellation.