Weak Harmonic Signal Detecting in Chaotic Noise Based on Empirical Likelihood Ratio

Aiming at the problem of insufficient detection ability of weak harmonic signals under the background of chaotic noise, a method for detecting weak harmonic signals using empirical likelihood ratio (ELR) is proposed. First, the problem of detecting weak harmonic signals in a chaotic background is transformed into a test of heteroscedasticity hypothesis in a chaotic background. Then, based on the sensitivity of chaotic signal to initial value and short-term predictability, the phase space of observation signal is reconstructed, and the chaotic linear prediction model (CLP model) is established. The mean square error, mean absolute error, and root mean square error are used as the evaluation criteria for the chaotic linear prediction model. Then, an estimation equation is established according to the CLP model, and the existence of harmonic signals is tested by the ELR method. The method of sequential quadratic programming is used to optimize the model parameters, and the chi-square distribution is used to judge whether there are harmonic signals, so as to detect the weak harmonic signals submerged in the background of chaotic noise. Finally, Lorenz system was used as the background of chaotic noise for simulation experiments. The experimental results showed that the weak harmonic signals in the chaotic background could still be detected when the SNR was − 72.801 dB, which was more effective than the traditional method.