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• A cost-efficient LFE-ASQC algorithm with similar or even better control accuracy than the ANE and ASP algorithms is proposed. • The proposed algorithm reduces the computational complexity more than one order of magnitude compared to the ANE or ASP algorithms. • The proposed LSP modeling methods A and B have significantly higher modeling accuracy. • Simulated and experimental studies confirm the equalization capability of the proposed algorithm in both stationary and non-stationary cases. Current active noise equalization or active sound profiling algorithms with a parallel structure are typically used for sound quality improvement of multi-harmonic noise. The computational efficiency and system performance may, however, be severely degraded due to an increase in the length of estimated secondary path or the number of controlled frequencies. To alleviate this problem, a local secondary path estimation and filtered-error structure based active sound quality control (LFE-ASQC) algorithm is proposed in this paper. The algorithm utilizes a set of low-order local secondary path (LSP) models to perform filtering operations and uses the filtered pseudo-error signals instead of usual filtered reference signals to update control filter weights, thus it not only has good spectral reshaping capability but also requires notably low computational effort. Two new LSP modeling methods are also proposed. Moreover, a computational complexity analysis of the proposed LFE-ASQC algorithm is provided. Numerical simulations are conducted to evaluate the accuracy of the LSP modeling methods and the performance of the LFE-ASQC algorithm. In addition, the powerful sound quality of a real vehicle interior noise during acceleration is designed and realized. Experimental results demonstrate that the proposed algorithm achieves satisfactory active sound quality control for stationary and non-stationary multi-tonal noises. [ABSTRACT FROM AUTHOR]