基于贝叶斯准则的随机共振算法研究

发布时间：2019-03-01 12:07

【摘要】：该文针对二元假设检验问题,首先在贝叶斯准则的基础上,分析了最小化贝叶斯代价所对应的最优噪声,将贝叶斯代价的最小化问题等价为虚警概率和/或检测概率的最优化。其次,在保证一定虚警概率和检测概率的前提下,建立起能同时改善检测概率和虚警概率的模型。然后分别给出当检测概率一定时虚警概率最小和虚警概率一定时检测概率最大这两种极限情况下对应的最优加性噪声,并对其进行线性凸组合以获得模型所需的最优加性噪声,进一步分析并证明了该模型能够成立的充分条件。再次,获得先验概率已知和未知两种情况下最小化贝叶斯代价时所对应的加性噪声,且当先验知识发生改变时,该算法只需调整加性噪声中一个可变参数即可获得相应的最优贝叶斯代价。最后,结合具体的检测问题,通过仿真验证了所提算法的有效性。
[Abstract]:In this paper, on the basis of Bayesian criterion, the optimal noise corresponding to minimizing Bayesian cost is analyzed, and the equivalence of Bayesian cost minimization problem is considered as the optimization of false alarm probability and / or detection probability. Secondly, on the premise of ensuring certain false alarm probability and detection probability, a model which can improve both detection probability and false alarm probability is established. Then the optimal additive noise corresponding to the minimum false alarm probability and the maximum detection probability are given when the detection probability is fixed, and the optimal additive noise required by the model is obtained by linear convex combination. The sufficient conditions under which the model can be established are further analyzed and proved. Thirdly, the additive noise corresponding to the minimization of Bayesian cost is obtained when the prior probability is known and unknown, and when the prior knowledge is changed, The optimal Bayesian cost can be obtained by adjusting only one variable parameter in the additive noise. Finally, the validity of the proposed algorithm is verified by simulation combined with specific detection problems.
【作者单位】：重庆大学通信工程学院;
【基金】：重庆市基础与前沿研究(cstc2016jcyj A0134,cstc2016 jcyj A0043) 国家自然科学基金(61501072,61301224,41404027,61108086,61471072) 重庆市社会事业与民生保障专项(cstc2016 shmszx40002) 中央高校重点基金(CDJZR155507)~~
【分类号】：TB53

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