### 数学代写|组合学代写Combinatorics代考|CS519

statistics-lab™ 为您的留学生涯保驾护航 在代写组合学Combinatorics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写组合学Combinatorics代写方面经验极为丰富，各种代写组合学Combinatorics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|组合学代写Combinatorics代考|The Benefits of Analytic Combinatorics to Tracking

The $\mathrm{AC}$ approach makes it easy to understand what distinguishes the different filters by comparing the individual algebraic factors of the GFs of the likelihood functions. Each factor has a specific combinatorial interpretation, and their product uniquely determines the fundamental structure of the filter. Using a chemistry analogy, factors are “elements” and their product is the “molecular formula” of the filter.
$\mathrm{AC}$ also gives a simple explanation of why it is that two seemingly similar filters may have very different computational complexities. As shown in Appendix A, the mathematical form of a filter is found by taking derivatives of the filter’s GF. The complexity of a filter is determined by the number of distinct terms in the derivative. As calculus students discover, the derivatives of similar looking functions can have very different numbers of terms. Simply by counting the number of terms in a derivative, practicing engineers can see in detail how a proposed change in the model alters the likelihood function and how that, in turn, affects the filter complexity.
AC enables approximations to be computed for very high computational complexity tracking filters using established classical applied mathematics. Further discussion is given in Sect. $6.3$ of Chap. 6, but it suffices here to say that the derivatives of the GF are written as Cauchy integrals (this is an exact equivalence), and then the saddle point method is applied to compute numerical approximations to the integrals. The saddle point method is a standard tool used in applied mathematics and physics for asymptotic analysis. The topic is the subject of ongoing work.

## 数学代写|组合学代写Combinatorics代考|Sensor and Object Models in Tracking

Single-object tracking filters estimate an object’s state using sensor data collected over a sequence of (non-overlapping) time intervals called scans. What constitutes the state of an object depends on the application, but it often comprises kinematic properties such as position and velocity. Object states are modeled as points, that is, objects appear as point sources in the sensor output. This modeling assumption has practical implications, e.g., in some surveillance applications, it requires that objects be neither too close nor too far from the sensor. ${ }^{2}$ Multiple object tracking filters estimate the multiobject state, which comprises the state of every object. The number of objects is stipulated in some filters and estimated in others, in which case the number of objects is part of the multiobject state.

Object motion is only partially predictable when some agent (e.g., a human pilot) is controlling them. This well-known and thorny modeling problem arises in other fields, too (e.g., control theory). It is treated here by assuming that object motion is governed by a random process whose probability distribution models the many sources of uncertainty in the object motion. Satisfying the assumption in practice is often a nontrivial exercise in model development – the model must incorporate not only the statistical nature of the inherent and unavoidable variability in object motion due to “system noise,” but it must also incorporate plausible models of the various unknown deterministic inputs from a controller (e.g., the pilot mentioned above).

## 数学代写|组合学代写Combinatorics代考|The Benefits of Analytic Combinatorics to Tracking

AC 能够使用已建立的经典应用数学计算非常高计算复杂度的跟踪滤波器的近似值。进一步的讨论在第 3 节中给出。6.3章。6，但这里只要说 GF 的导数写成柯西积分（这是精确等价的），然后应用鞍点法计算积分的数值近似就足够了。鞍点法是应用数学和物理学中用于渐近分析的标准工具。该主题是正在进行的工作的主题。

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。