Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation
Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation
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MLE 统计和近似上下界 - 第一部分：TOA 估计的应用
DOI：
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发表时间：
2014
影响因子：
5.4
通讯作者：
L. Vandendorpe
中科院分区：
文献类型：
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作者：
A. Mallat;S. Gezici;D. Dardari;C. Craeye;L. Vandendorpe
在非线性确定性参数估计中，由于阈值和模糊现象的存在，极大似然估计器在低信噪比和中信噪比时不能达到Cramér-Rao下界。为了估计在这些信噪比水平下的均方误差，我们利用区间估计的方法提出了新的均方误差近似(MSEA)和一个近似的上界。对最大似然估计的均值和分布也进行了近似。MIE包括将未知参数的先验域分割成区间，并计算每个区间中估计器的统计量。基于噪声的泰勒级数展开式和基于二进制检测原理的ALB族，我们得到了一个近似的下界。以到达时间估计为例，验证了所提出的最小二乘估计的精度和所得近似界的紧密性。
In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramér-Rao lower bound at low and medium signal-to-noise ratios (SNRs) due the threshold and ambiguity phenomena. In order to evaluate the achieved mean-squared error (MSE) at those SNR levels, we propose new MSE approximations (MSEA) and an approximate upper bound by using the method of interval estimation (MIE). The mean and the distribution of the MLE are approximated as well. The MIE consists in splitting the a priori domain of the unknown parameter into intervals and computing the statistics of the estimator in each interval. Also, we derive an approximate lower bound (ALB) based on the Taylor series expansion of noise and an ALB family by employing the binary detection principle. The accuracy of the proposed MSEAs and the tightness of the derived approximate bounds are validated by considering the example of time-of-arrival estimation.