随机共振噪声修改决策解决方案用于在最小值标准下对二元假设进行测试
Ting Yang1, Lin Liu1, You Xiang1
1School of Computer Science and Information Engineering, Chongqing Technology and Business University, Chongqing, 400067, China.
Heliyon
|December 13, 2024
概括
本研究介绍了在Minimx标准下对未知的先前概率进行噪声增强二进制假设测试. 开发了一个最佳的恒定噪声策略,以最大限度地降低非线性系统中的决策风险.
科学领域:
- 信号处理 信号处理
- 统计决策理论 统计决策理论
- 控制系统 控制系统
背景情况:
- 二元假设测试在信号处理中至关重要,但性能随着未知的先前概率而降低.
- 最低限度标准为不确定性下决策提供了一个强有力的方法.
- 一般的非线性系统对传统的假设测试方法提出了挑战.
研究的目的:
- 在未知先验概率的情况下,研究对一般非线性系统的噪声增强二元假设测试.
- 开发一个最小决策规则,通过故意添加噪音来最大限度地降低决策风险.
- 为了简化优化问题并确定最佳决策规则和贝叶斯风险.
主要方法:
- 添加噪音是故意注入到输入信号.
- 对于决策的噪声修改输出,应用一个Minimx标准.
- 一个优化问题是为了最大限度地降低贝叶斯条件风险而制定的.
- 参数和定理被用来证明一个恒定的噪声向量的最佳性.
- 开发了一个算法,以找到最佳的噪声常数和探测器参数.
主要成果:
- 已经证明,最佳的添加噪声是一个常量向量,大大简化了这个问题.
- 一个算法有效地确定了最佳决策规则和相关的贝叶斯风险.
- 与原始系统相比,模拟结果证明了噪声修改方法的有效性.
结论:
- 噪声增强为在具有未知先验的非线性系统中进行可靠的二进制假设测试提供了可行的策略.
- 建议采用最佳恒定噪声的Minimx方法,可以降低决策风险.
- 开发的算法和理论发现为现实世界的应用提供了实际的解决方案.
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