Cramer Rao Bounds of Real Sinusoid Parameter Estimation from Discrete-Time Observations
Guoqing Qi · Shuju caiji yu chuli · 2003
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.