To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’...To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.展开更多
针对室内环境影响定位精度的非视距传播(non-line-of-sight,NLOS)问题,在对基于到达时间差(time differ-ence of arrival,TDOA)的超宽带(ultra wideband,UWB)室内定位模型和算法进行分析研究的基础上,提出了质心-Taylor混合定位算法。...针对室内环境影响定位精度的非视距传播(non-line-of-sight,NLOS)问题,在对基于到达时间差(time differ-ence of arrival,TDOA)的超宽带(ultra wideband,UWB)室内定位模型和算法进行分析研究的基础上,提出了质心-Taylor混合定位算法。该算法利用对测距误差不敏感的质心算法对目标进行初始粗定位,然后将其作为Taylor级数展开法的迭代初值进行二次精细定位,并动态地将前期定位完毕的节点转化为后续定位过程的参考节点,最大限度地利用不断增加的已知信息,在提高Taylor初值质量的前提下减少预设参考节点数目,降低系统硬件成本。采用MATLAB软件进行了模拟仿真。仿真结果表明,该算法定位性能优越,尤其在NLOS测距误差较大的环境下能有效地提高系统的定位精度。展开更多
文摘To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.
文摘针对室内环境影响定位精度的非视距传播(non-line-of-sight,NLOS)问题,在对基于到达时间差(time differ-ence of arrival,TDOA)的超宽带(ultra wideband,UWB)室内定位模型和算法进行分析研究的基础上,提出了质心-Taylor混合定位算法。该算法利用对测距误差不敏感的质心算法对目标进行初始粗定位,然后将其作为Taylor级数展开法的迭代初值进行二次精细定位,并动态地将前期定位完毕的节点转化为后续定位过程的参考节点,最大限度地利用不断增加的已知信息,在提高Taylor初值质量的前提下减少预设参考节点数目,降低系统硬件成本。采用MATLAB软件进行了模拟仿真。仿真结果表明,该算法定位性能优越,尤其在NLOS测距误差较大的环境下能有效地提高系统的定位精度。
