Weak Harmonic Signal Detecting In Chaotic Noise Based On Empirical Likelihood Ratio

The weak signal is a weak quantity that is difficult to be detected by traditional methods.Compared with noise,it not only refers to the small amplitude of the signal,but also refers to the signal submerged by the noise and the signal with low signal-to-noise ratio.Weak signal detection uses electronics,informatics,probability statistics and other methods to study the characteristics of the detected signal,analyze the composition of noise,and detection methods are used in many fields.In most cases,the weak signal detection problem in engineering can simplify the weak harmonic signal detection problem under strong chaotic noise interference.Chaotic systems have been widely used in the field of weak signal detection due to their many excellent properties.Therefore,the problem of weak signal detection based on chaotic background noise has become a research hots-pot.This paper combines chaos theory and signal detection technology to study the weak harmonic signal detection method under strong chaotic background noise.Since the weak harmonic signal is submerged under the chaotic background noise,the structure of the original chaotic system can be reversely constructed through the one-dimensional chaotic time series(observation signal).First,reconstruct the observed signal using phase space,then use a linear model or a single index model to approximate the mapping function of the phase space,establish a chaotic prediction model and obtain the prediction error,and then use the empirical likelihood ratio method to detect the observation from the prediction error Whether the signal contains weak harmonic signals.Empirical likelihood ratio detection method: construct an estimation equation based on the chaotic prediction model;further construct an empirical likelihood ratio function,use the Lagrange multiplier method to solve the empirical likelihood ratio function,and use the sequence quadratic programming method to optimize the parameters Substitute the R statistic and compare it with the chi-square value to detect weak harmonic signals under chaotic background noise.Finally,chaotic background signals are generated by Lorenz system and Rossler system for simulation.The research results show that:(1)According to the analysis of the prediction results of the chaotic time series,the mean square error MSE of the chaotic linear model and the chaotic single index model for the observation signal prediction is greater than the threshold value 0.1.From the perspective of prediction accuracy,thechaotic single index model is better than the chaotic linear model.Both models predict the mean square error MSE of the chaotic background noise signal generated by the chaotic system is less than the threshold 0.1.By comparing with the threshold value,it is found that both models can detect the existence of weak signals.(2)Based on the Lorenz system,the empirical likelihood ratio method can detect weak harmonic signals with a signal-to-noise ratio as low as-63.237 dB.When the amplitude of the weak harmonic signal is 1,the empirical likelihood ratio method detects the correct rate of 99.8 %.Based on the Rossler system,when the amplitude of the weak harmonic signal is 0.6,the detection accuracy rate is 97.4%,which is superior to other detection methods.