离散实正弦信号参数估计的Cramer Rao方差下限

Cramer Rao Bounds of Real Sinusoid Parameter Estimation from Discrete-Time Observations

研究了高斯白噪声背景下根据离散观测值估计实正弦信号的参数问题。分析了实正弦信号幅度、频率和相位估计的方差下限 ,并讨论了实正弦信号参数的最大似然 (ML)估计。给出了观测数据长度 N较大时实正弦信号参数估计的 Cramer Rao方差下限的计算公式。指出了实正弦信号参数估计方差下限与观测数据长度 N、信号频率及初相有关 ,当 N较大时实信号参数估计的方差下限约为对应的复信号的参数估计的方差下限的 2倍。在不同的信噪比下进行了计算机模拟 ,模拟结果与本文分析结果吻合。

The parameter estimation of real sinusoid under white Gaussian noise is investigated. The Cramer Rao bounds (CRBs) of the frequency, phase and amplitude estimation of the real sinusoid are analyzed and formulas for computing the CRBs are derived when the length of the observation data N is large. The maximum likelihood (ML) estimators are discussed. It is concluded that the CRBs of the real sinusoid parameter estimation are affected by the length of observation data, the frequency and the initial phase of the signal. When N is large, the CRBs of the real signal are approximately twice of the corresponding complex signal. Computer simulations are conducted under different signal to noise ratio conditions and simulational results fit well with the computational results achieved by the formulas.