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Recently, the subspace-least mean square (S-LMS) method has been proposed for power system measurement. The high accuracy and high resolution of the S-LMS method are achieved at the cost of being computationally expensive. In this paper, the S-LMS method is enhanced in two aspects: 1) speed and 2) accuracy. The computation burden of S-LMS is significantly reduced in three ways: 1) exploring the sparsity of power system signals; 2) using an iterative multisectional search scheme; and 3) the combination of these two techniques. Further, detection of the harmonic components based on the fact that they are multiples of the fundamental frequency has been effectively employed, resulting in a more accurate and robust algorithm for fundamental and harmonic estimation in the presence of noise. The enhanced S-LMS algorithm, which detects harmonics more accurately, is more than 150 times faster than the original S-LMS if the interharmonic level is negligibly low. The dynamic behavior of the method is discussed and the method is compared with Prony and DFT. Simulations show the methods are highly resilient to off-nominal conditions and noise.