等价无穷小是极限理论的一个重要组成部分,选取合适的等价无穷小代换,可以极大地简化极限问题的处理。使用等价无穷小需要满足一定的条件,很多学习者对等价无穷小代换的使用条件认识不深,经常错用等价无穷小代换。针对这个问题,本文通...等价无穷小是极限理论的一个重要组成部分,选取合适的等价无穷小代换,可以极大地简化极限问题的处理。使用等价无穷小需要满足一定的条件,很多学习者对等价无穷小代换的使用条件认识不深,经常错用等价无穷小代换。针对这个问题,本文通过等价无穷小的本质对等价无穷小代换的使用条件进行解析,使学习者能够充分认识并理解等价无穷小的使用条件,理解和掌握等价无穷小的应用,对于深入学习和应用微积分知识具有重要的作用。Equivalent infinitesimal is an important component of limit theory, and selecting appropriate equivalent infinitesimal substitutions can greatly simplify the handling of limit problems. The use of equivalent infinitesimal substitution requires certain conditions to be met, and many learners have a limited understanding of the conditions for using equivalent infinitesimal substitution and often misuse it. In response to this issue, this article analyzes the usage conditions of equivalent infinitesimal substitution through the essence of equivalent infinitesimal, enabling learners to fully understand and comprehend the usage conditions of equivalent infinitesimal, understand and master the applications of equivalent infinitesimal, which plays an important role in in-depth learning and application of micro integration knowledge.展开更多
基于接收信号强度差(Difference of Received Signal Strength, DRSS)的定位模型具有节省能量、带宽和时间的优点,并且在定位过程中隐藏了发射机的传输方式,非常有益于机密监视或军事应用。然而DRSS模型具有较高的非凸性,在定位求解时...基于接收信号强度差(Difference of Received Signal Strength, DRSS)的定位模型具有节省能量、带宽和时间的优点,并且在定位过程中隐藏了发射机的传输方式,非常有益于机密监视或军事应用。然而DRSS模型具有较高的非凸性,在定位求解时比较困难,本文提出了一种改进的定位方法——相对误差及凸优化混合定位方法。首先借助相对误差方法构建最小化问题,然后借助半正定规划和二阶锥规划对模型进行近似求解。为了验证所提方法的有效性,引入均方根误差(Root Mean Square Error, RMSE)作为估计方法精度的评判标准,通过对比本文所提方法以及现有四种方法(A-BLUE、U-BLUE、LARE-SDP、SOCP)的RMSE,研究结果发现本文提出方法的RMSE值最低,并且更加贴近理论误差的CRLB下界。The positioning model based on Difference of Received Signal Strength (DRSS) has the advantages of saving energy, bandwidth, and time, and hides the transmission mode of the transmitter during the positioning process, which is very beneficial for confidential monitoring or military applications. However, the DRSS model has high nonconvexity and is difficult to solve in localization. This paper proposes an improved localization method—a hybrid localization method of relative error and convex optimization. Firstly, the minimization problem is constructed using the relative error method, and then the model is approximately solved using semi positive definite programming and second-order cone programming. In order to verify the effectiveness of the proposed method, Root Mean Square Error (RMSE) was introduced as the evaluation criterion for the accuracy of the estimation method. By comparing the RMSE of the proposed method with four existing methods (A-BLUE, U-BLUE, LARE-SDP, SOCP), the research results showed that the RMSE value of the proposed method was the lowest and closer to the CRLB lower bound of the theoretical error.展开更多
文摘等价无穷小是极限理论的一个重要组成部分,选取合适的等价无穷小代换,可以极大地简化极限问题的处理。使用等价无穷小需要满足一定的条件,很多学习者对等价无穷小代换的使用条件认识不深,经常错用等价无穷小代换。针对这个问题,本文通过等价无穷小的本质对等价无穷小代换的使用条件进行解析,使学习者能够充分认识并理解等价无穷小的使用条件,理解和掌握等价无穷小的应用,对于深入学习和应用微积分知识具有重要的作用。Equivalent infinitesimal is an important component of limit theory, and selecting appropriate equivalent infinitesimal substitutions can greatly simplify the handling of limit problems. The use of equivalent infinitesimal substitution requires certain conditions to be met, and many learners have a limited understanding of the conditions for using equivalent infinitesimal substitution and often misuse it. In response to this issue, this article analyzes the usage conditions of equivalent infinitesimal substitution through the essence of equivalent infinitesimal, enabling learners to fully understand and comprehend the usage conditions of equivalent infinitesimal, understand and master the applications of equivalent infinitesimal, which plays an important role in in-depth learning and application of micro integration knowledge.
文摘基于接收信号强度差(Difference of Received Signal Strength, DRSS)的定位模型具有节省能量、带宽和时间的优点,并且在定位过程中隐藏了发射机的传输方式,非常有益于机密监视或军事应用。然而DRSS模型具有较高的非凸性,在定位求解时比较困难,本文提出了一种改进的定位方法——相对误差及凸优化混合定位方法。首先借助相对误差方法构建最小化问题,然后借助半正定规划和二阶锥规划对模型进行近似求解。为了验证所提方法的有效性,引入均方根误差(Root Mean Square Error, RMSE)作为估计方法精度的评判标准,通过对比本文所提方法以及现有四种方法(A-BLUE、U-BLUE、LARE-SDP、SOCP)的RMSE,研究结果发现本文提出方法的RMSE值最低,并且更加贴近理论误差的CRLB下界。The positioning model based on Difference of Received Signal Strength (DRSS) has the advantages of saving energy, bandwidth, and time, and hides the transmission mode of the transmitter during the positioning process, which is very beneficial for confidential monitoring or military applications. However, the DRSS model has high nonconvexity and is difficult to solve in localization. This paper proposes an improved localization method—a hybrid localization method of relative error and convex optimization. Firstly, the minimization problem is constructed using the relative error method, and then the model is approximately solved using semi positive definite programming and second-order cone programming. In order to verify the effectiveness of the proposed method, Root Mean Square Error (RMSE) was introduced as the evaluation criterion for the accuracy of the estimation method. By comparing the RMSE of the proposed method with four existing methods (A-BLUE, U-BLUE, LARE-SDP, SOCP), the research results showed that the RMSE value of the proposed method was the lowest and closer to the CRLB lower bound of the theoretical error.
