改进高阶Vanderpol振子在微弱信号检测中的应用

在高精度的微弱光电信号检测系统中，存在信号被强噪声湮没的情况。针对这一问题，提出了一种基于改进高阶Vanderpol振子的微弱正弦信号定量检测方法。该方法利用改进高阶广义Vanderpol系统的高灵敏度与强抗噪性的特点提高了微弱信号检测的可靠性，再结合Lyapunov指数定量检测和90°移相补偿来实现混沌系统状态的量化判断和待测信号参数的高精度提取。仿真结果表明改进的Vanderpol振子比传统Vanderpol振子运算速度更快。与传统Duffing振子相比，在5%幅值检测误差范围内，改进的高阶广义Vanderpol系统可多获得37 dB的信噪比增益和60 dB的检测门限增益；与基于相轨迹突变定性检测待测信号幅相法相比，90°移相补偿幅相定量检测法在信噪比降低时其检测相对误差仍可控制在2%以内。改进算法实现了微弱正弦信号的高灵敏度和高精度的幅相检测。

Application of improved higher order Vanderpol oscillator in weak signal detection

The signal will be submerged by strong noise in the high precision weak photoelectric signal detection system. A novel approach for quantitative detection of weak sine signal based on Vanderpol oscillator is proposed to solve this problem. The new method improves the reliability of weak signal detection by refining the high order generalized Vanderpol oscillator with higher sensitivity and stronger noise immunity. At the same time,quantitative judgment of the state of chaotic system is achieved with Lyapunov index and higher precision extraction of the signal parameters is realized by combining Lyapunov index with 90 degrees phase shift compensation. Simulation result shows that the improved Vanderpol oscillator has faster computing speed than the traditional one. The improved Vanderpol oscillator can obtain 37 dB signal-to-noise ratio(SNR) gain and 60 dB detection threshold gain compared with the traditional Duffing oscillator in the range of 5% amplitude detection error. The detection based on 90° phase shift compensation can control the relative error within 2% compared with the amplitude and phase detection based on phase trajectory mutation when the SNR is reduced. Therefore the high sensitive and precise detection of weak signal''s amplitude and phase is realized.