Robust Competitive Estimation With Signal and Noise Covariance Uncertainties
Robust Competitive Estimation With Signal and Noise Covariance Uncertainties
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DOI：
10.1109/tit.2006.881749
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发表时间：
2006-10
影响因子：
2.5
通讯作者：
Yonina C. Eldar
中科院分区：
文献类型：
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作者：
Yonina C. Eldar
在最近的一些工作中，研究了存在模型不确定性的线性模型中随机向量的鲁棒估计。虽然以前的方法考虑的情况下，其中的不确定性是在信号协方差，并可能的模型矩阵，但噪声协方差被假定为完全指定的，在这里，我们扩展的结果的情况下，噪声统计也可能受到不确定性。我们提出了几种不同的方法来鲁棒估计，不同的假设在给定的统计量。在第一种方法中，我们假设模型矩阵和信号和噪声的协方差矩阵是不确定的，并开发一个最小化最大均方误差（MSE）估计，最大限度地减少最坏情况下的不确定性区域的MSE。第二种策略假设模型矩阵是给定的，并试图通过最小化最坏情况下的遗憾度量来均匀地接近线性最小MSE估计器的性能，该线性最小MSE估计器知道信号和噪声协方差。遗憾被定义为使用线性估计器可获得的MSE（忽略信号和噪声协方差）与统计量已知时可能的最小MSE之间的差异或比率。正如我们所示，早期的解决方案直接从我们更一般的结果。然而，这里所采用的方法在发展稳健估计是相当简单的比以前的方法
Robust estimation of a random vector in a linear model in the presence of model uncertainties has been studied in several recent works. While previous methods considered the case in which the uncertainty is in the signal covariance, and possibly the model matrix, but the noise covariance is assumed to be completely specified, here we extend the results to the case where the noise statistics may also be subjected to uncertainties. We propose several different approaches to robust estimation, which differ in their assumptions on the given statistics. In the first method, we assume that the model matrix and both the signal and the noise covariance matrices are uncertain, and develop a minimax mean-squared error (MSE) estimator that minimizes the worst case MSE in the region of uncertainty. The second strategy assumes that the model matrix is given and tries to uniformly approach the performance of the linear minimum MSE estimator that knows the signal and noise covariances by minimizing a worst case regret measure. The regret is defined as the difference or ratio between the MSE attainable using a linear estimator, ignorant of the signal and noise covariances, and the minimum MSE possible when the statistics are known. As we show, earlier solutions follow directly from our more general results. However, the approach taken here in developing the robust estimators is considerably simpler than previous methods