基于稀疏分解和混沌理论的微弱信号检测

针对数字锁定放大器中稀疏分解算法检测精度受限的缺点，结合非线性方法进行补偿，采用混沌检测联合稀疏分解的算法设计了数字锁定放大器。数字锁定放大器借助稀疏分解算法估计信号参数，根据估计得到的参数设计对应混沌系统；利用混沌系统检测信号的过程中产生间歇性混沌状态，并通过测量间歇性混沌状态的周期，精确检测信号。最终，在信号的信噪比低至-20 dB时可以成功检测信号，频率精度达到0.05 Hz，提供了一种非线性微弱信号检测方法。

Weak signal detection based on sparse decomposition and chaotic theory

For the disadvantage of high computational complexity in sparse decomposition algorithm,the digital lock-in amplifier based on non-linear method and chaos detection joint sparse decomposition algorithm is designed. With the help of sparse decomposition algorithm,the digital lock-in amplifier estimates the signal parameters and according to the estimated parameters corresponding chaotic systems are designed.The intermittent chaos state in the process of chaotic oscillator and its period are used to detect signals. The precision of frequency is up to 0.05 Hz when the signal-to- noise ratio(SNR) is low to -20 dB,so this paper provides a nonlinear method of weak signal detection.