Optimal Joint Detection and Estimation Based on Decision-Dependent Bayesian Cost
Optimal Joint Detection and Estimation Based on Decision-Dependent Bayesian Cost
复制标题
DOI：
10.1109/tsp.2016.2529585
复制
发表时间：
2016-05
影响因子：
5.4
通讯作者：
Shang Li;Xiaodong Wang
中科院分区：
文献类型：
--
作者：
Shang Li;Xiaodong Wang
本文考虑假设检验和参数估计都是主要关注的统计推断问题。在每个假设中存在未知参数的情况下，目标是在检测真实假设的同时估计未知参数。针对这两个子问题的耦合特性，我们采用了同时依赖于检测结果和估计方案的贝叶斯估计代价函数。在满足检测性能约束的前提下，通过最小化贝叶斯估计代价得到最优的联合检测器和估计器。与单独处理检测和估计的方法相比，提出的联合解决方案不仅获得了更低的估计代价，而且允许在这两个子问题的性能之间进行灵活的折衷。此外，我们还将我们的框架扩展到多假设情形，其中存在K假设及其相关的未知参数。最后，我们将所提出的联合检测与估计框架应用于认知无线电的频谱感知，旨在检测主用户的存在，同时估计噪声/干扰水平。
This paper considers the statistical inference problem where both the hypothesis testing and the parameter estimation are of primary interest. With unknown parameters present in each hypothesis, the goal is to detect the true hypothesis and to estimate the unknown parameters simultaneously. In light of the coupling nature of these two subproblems, we adopt the Bayesian estimation cost function that depends on both the detection result and the estimation scheme. We then obtain the optimal joint detector and estimator by minimizing the Bayesian estimation cost subject to the constraint on detection performance. The proposed joint solution not only yields lower estimation cost compared with the method that treats the detection and estimation separately, but also allows for flexible tradeoff between the performances of these two subproblems. In addition, we also extend our framework to the multi-hypothesis scenario, where K hypotheses and their associated unknown parameters are present. Finally, we apply the proposed joint detection and estimation framework to the spectrum sensing for cognitive radio, which aims to detect the presence of the primary user and to estimate the noise/interference level at the same time.