Accurate online identification of battery internal resistance is vital for the performance and reliability of electric vehicles (EVs). This paper proposes a Trace-Enhanced Adaptive Forgetting Recursive Least Squares (TEAF-RLS) algorithm for internal resistance identification. The algorithm adaptively adjusts the forgetting factor by jointly considering the instantaneous prediction error and the trace of the covariance matrix, thereby enhancing adaptability to dynamic system variations while maintaining numerical stability. In practical applications, direct measurement of internal resistance is often infeasible. To address this, we established a discrete-time battery model by deriving a recursive parameter identification structure through Laplace transform of the equivalent circuit, focusing on the identification of ohmic internal resistance. Based on the identified resistance parameters, Euler discretization was applied to derive a terminal voltage prediction formula. The deviation between predicted and measured terminal voltage is then used as an indirect measure of internal resistance identification accuracy, thus enabling model evaluation without requiring ground truth values of resistance. The accuracy of the proposed approach under different sampling frequencies was also validated by experimental results based on real-world driving data.