The conventional approaches for measuring battery impedance are characterized by exorbitant implementation expenses and inadequate accuracy. The challenge associated with accurate impedance measuring arises from the intricate nature of signal construction, which inspires us to propose a systematically composed binary sequence (SCBS) for the rapid and precise extraction of broadband impedance responses. The minimum amplitude criteria is first determined by the signal-to-noise ratio (SNR) analysis, combined with the zero-order hold (ZOH) compensation coefficients given for the frequency component design. Subsequently, a novel chaotic optimization algorithm is proposed, capable of evading the pitfall of local minimization, to synthesize a binary sequence that satisfies the SNR requirements while possessing the lowest amplitude. The proposed method is further verified to be superior in terms of optimization performance and frequency response accuracy when compared with existing techniques. The average normalized impedance deviations (NIDs) of the experimental findings across all frequency ranges are lower than the predefined threshold (0.5%), which demonstrates the applicability of the proposed method in various conditions.