Least squares error (LSE) method adopted recursively can be used to track the frequency and amplitude of signals in steady states and kinds of non-steady ones in power system. Taylor expansion is used to give another version of this recursive LSE method. Aided by variable-windowed short-time discrete Fourier transform, recursive LSEs with and without Taylor expansion converge faster than the original ones in the circumstance of off-nominal input singles. Different versions of recursive LSE were analyzed under various states, such as signals of off-nominal frequency with harmonics, signals with step changes, signals modulated by a sine signal, signals with decaying DC offset and additive Gaussian white noise. Sampling rate and data window size are two main factors influencing the performance of method recursive LSE in transient states. Recursive LSE is sensitive to step changes of signals, but it is in-sensitive to signals' modulation and singles with decaying DC offset and noise.