正弦调制相位信号参数估计的Cramer-Rao下限

The Cramer-Rao Lower Bound for Parameters Estimation of Signals with Sinusoid Modulated Phase

正弦调制相位信号是微动目标雷达回波微多谱勒信号的一般形式,微动特征提取最终可以转化为这类信号的参数估计问题。本文首先给出了目标微动背景下正弦调制相位信号的一般形式以及各参数对应的物理意义,重点推导了高斯白噪声条件下,正弦调制相位信号参数估计的Cramer-Rao下限,得到了估计相位幅度和频率的Cramer-Rao下限与信噪比及数据长度之间的近似关系,并给出了近似所需满足的条件。最后通过理论推导和仿真计算得到了近似处理的误差曲线,证明了近似的合理性。

Signals with sinusoid modulated phase is the general form of micro-doppler signals in radar echoes from targets with micro-motions. Micro-motion features extraction can be transformed to parameter estimation of these signals finally. At the beginning, the paper presents the general form of signals with sinusoid modulated phase on the background of targets with micro-motion and the physical meanings of the parameters respectively. And then, it mainly derivers the Cramer-Rao lower bound for the variances of the estimated parameters of signals with sinusoid modulated phase, measured in additive Gaussian noise. The approximate relationship between the CRLB of phase amplitude/frequency estimation and SNR, or the data length is studied. And the qualification of the approximate process is mentioned. At last, theoretic deduction and the error curves by simulations prove the validity of the approximate process.