基于状态空间实现的EDS频率与时延联合估计

Joint time delay and frequency estimation of exponentially damped sinusoid via state-space realization

针对指数衰减正弦信号(EDS)模型提出了状态空间实现的频率、衰减因子及时延联合估计方法.在此方法中,得到了一个状态过渡矩阵和观测矩阵,频率和衰减因子估计由状态过渡矩阵的特征值获得,时延由观测矩阵和估计的频率和衰减因子得到,结果具有闭式解,不需要搜索计算.由于状态空间方法具有对模型误差不敏感的优点,因而具有更好的数值稳定性.仿真实验表明在一定信噪比的情况下,该方法性能接近相应的CRLB下界.

In this paper, we present a subspace-based method for joint estimation of the time delay and frequency parameter of a exponentially damped sinusoidal signal. Using state-space realization, the frequency and damped factor estimates are obtained from the eigenvalues of the state transition matrix while the time delay is determined using the observation matrix and the estimated frequencies and damped factors. The searching computation is not required in the proposed method. Moreover, the proposed approach has better numerical value stability because of being insensitive to the model error. Computer simulations show that the performance of the frequency, damped factor and time delay estimation can attain the CRLB at a wide range of SNR.