# An Enhanced Genetic Algorithm for Parameter Estimation of Sinusoidal Signals
## 1 Introduction  
Many practical signals, such as voice and audio signals, power system transient signals, and response signals of sensors, are recognized as signals of the sum of sinusoidal signals. The parameter estimation of sinusoidal signals from the periodic time series data is a classical problem of ongoing interest in signal processing. In recent years, it has drawn considerable attention of scientists and researchers from various fields including speech analysis [1], electrical power and energy system [2], and sensor signal analysis [3], among others. There are some methods addressing this problem; in general, these can be classified into two categories, classical techniques [3; 4; 5; 6; 7; 8; 9; 10], and intelligent algorithms [11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. The classical techniques, when compared with intelligent ones, are easier to implement and are computationally more efficient. However, they do have limitations, including frequency resolution, low accuracy, mathematical demands, and so on. On the other hand, the intelligent algorithms and hybrids are favorably employed due to their fewer requirements about the problems and excellent resolution. A few recent applications include atomic physics [21], electrical machines [22], big data [23], traveling salesman problem [24], and fuel cell [25]. Thus, intelligent techniques have extended significantly to provide effective and reliable solutions for parameter estimations of sinusoidal signals [11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 26; 27; 28; 29] accordingly. In a literature [11], [PERSON] et al., used a particle swarm optimization (PSO)-based approach for the parameterization of a power capacitor model fed by harmonic voltages in power distribution systems. For parameter estimation of exponentially damped sinusoidal signals, [PERSON] et al. [15] presented a specific artificial neural network (ANN) based estimator, by which the parameters of each exponentially damped sinusoidal signal component could be directly calculated with a high precision. However, the performance strongly relies on the converged weights of the ANN, and hence, an absence of optimal weights or insufficient training will result in a poor performance. Based on a genetic algorithm (GA), [PERSON] et al. [18; 20] presented an efficient estimator to evaluate the frequency and phase for a phasor management unit. In comparison to the phase-locked loop (PLL) and the discrete Fourier transform (DFT) based methods, the GA revealed the fastest response to a sufficient precision. In order to minimize bias and improve estimation performance, researchers generally combine different methods to overcome the individual drawbacks. In another article, [PERSON] et al. [17] presented a hybrid genetic algorithm (HGA) fused with a maximum likelihood approach to estimate the phase parameters of frequency modulated signals. [PERSON] et al. [30] proposed a cloud model-based genetic algorithm (CMGA) for optimization problems. Benefiting from the cloud model, the CMGA continuously produces new individuals, and hence, the exploration and randomness can be significantly improved, showing a better optimization when compared to other methods. In the literatures [31; 32; 33], [PERSON] et al., introduced some hybrid techniques with ANN, GA, and other algorithms for the dynamics of nonlinear singular heat conduction model of the human head, nonlinear Painleve II systems, and nonlinear singular Thomas-Fermi systems. Comparisons between the proposed schemes and the standard numerical solutions as well as analytical methods revealed the feasibility and effectiveness of the proposed schemes. Similarly, a hybrid approach using a differential evolution (DE) and GA was proposed by [PERSON] et al. [34], where a DE-based multi-parent crossover operation was introduced to enhance the search ability and to avoid premature convergence by exploring more solutions in the problem search space. In combination with a local search optimization algorithms, [PERSON] et al.