# 数学代写|组合学代写Combinatorics代考|CS519

#### Doug I. Jones

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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
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## 数学代写|组合学代写Combinatorics代考|JPDA/Res with Parallel Object Tracks

In this section, the two objects move in close proximity to one another for an extended period of time. The object motion is quite similar to that in the IPDA numerical example in Sect. 2.8, and tracking results are shown in Figs. $3.3$ and 3.4.

Both objects move through $\mathcal{R}$ at a constant speed of $50 \mathrm{~m} / \mathrm{s}$. Object one begins in state $\mathbf{x}0^1=\left(\begin{array}{llll}-1700 & 0 & 1830 & -50\end{array}\right)^T$ at time $t_0=0$. It moves at this constant velocity for $15 \mathrm{~s}$, turns at $3^{\circ}$ per second counterclockwise for the next $30 \mathrm{~s}$, and then moves in the positive $x$-direction for $75 \mathrm{~s}$. Object two mirrors this process. For $k=0,1, \ldots, K$, if $\mathbf{x}_k^1=\left(\begin{array}{llll}x_k^1 & \dot{x}_k^1 & y_k^1 & \dot{y}_k^1\end{array}\right)^T$ is the state of ohject one at scan $k$, then $\mathbf{x}_k^2=\left(x_k^1 \quad \dot{x}_k^1-y_k^1-\dot{y}_k^1\right)^T$ is the state of object two at scan $k$. Thus, the two objects remain at a constant distance of $6 \sigma_M=300$ from one another for the final $75 \mathrm{~s}$. The region of interest spans $\mathcal{R}=[-2000,3000] \times[-3000,3000]$. The mean number of clutter measurements $\lambda_k^c \equiv \lambda^c=100$ is constant over all scans. Thus, in each scan, there is an average of approximately $0.24$ clutter measurements in a $3 \sigma_M$ measurement window. The tracker process noise standard deviation is set to $\sigma_p=4$, and the resolution parameter is chosen to be $\sigma{\mathrm{res}}=182.6$. This value for $\sigma_{\mathrm{res}}$ gives a resolution probability of approximately $0.75$ when the objects are moving in parallel (i.e., $300 \mathrm{~m}$ apart).

Figures $3.3$ and $3.4$ represent two different scenarios. The annotations in the figures are the same as in Fig. 3.2. In the first scenario, the unresolved weighting factor is $w_r=10 / 11 \approx 0.91$. Under the relative signal return strength interpretation, the signal return strength of object one is $10 \log _{10}\left(\frac{w_r}{1-w_r}\right)=10 \mathrm{~dB}$ higher than that of object two and, thus, most of the green unresolved measurements are close to object two, as seen in Fig. 3.3.

In the second scenario, the unresolved weighting factor is $w_r=0.5$, i.e., the signal return strengths of both objects are equal-neither of the objects is favored. Tracking results for both the standard JPDA and JPDA/Res trackers are displayed in Fig. 3.4.

## 数学代写|组合学代写Combinatorics代考|Discussion of Results

The standard JPDA filter inherently assumes that a given measurement is either clutter, or it originates from exactly one of the objects of interest. Thus, in the unresolved measurement case where an object’s return is buried under the return of another object or where objects are close enough so that they fall into a single resolution cell, the standard JPDA filter model is hopelessly mismatched to the reality of the data-it lacks model fidelity.

The mismatch is clearly seen in the upper subplots of Figs. $3.2$ and 3.3. In both the crossing and parallel scenarios, since the red object produces stronger returns than the blue, the unresolved measurement more often “favors” the red object than the blue; thus, the blue object is left without a measurement. Therefore, the existing unresolved measurement is, for all practical purposes, assigned to the red object when performing the measurement update, whereas the blue object’s estimate is extrapolated based on its motion model and the previous measurement update.

In contrast, the JPDA/Res filter allows for the possibility that only one signal return (measurement) could mean that the two objects are unresolved. The various ways this can happen are accounted for by the six terms (3.60)-(3.65). Thus, despite increased estimation error due to inflated covariance, both objects are successfully tracked as shown in the bottom subplots of Figs. $3.2$ and 3.3. It is also seen in the bottom subplot of Fig. $3.2$ that the blue object is extrapolated without being drawn off, or seduced, by clutter, as it was in the upper plot. This is rather remarkable, and somewhat unexpected. The explanation is the improved fidelity of the model.

JPDA/Res also improves tracking performance when both objects produce equal strength returns and, hence, neither object is favored. As illustrated in the top subplot of Fig. 3.4, although standard JPDA maintains two tracks in the presence of unresolved measurements, the tracks switch at the start of the parallel motion and then switch back later. This is an undesirable situation in, e.g., radar tracking where maintaining track IDs is of utmost importance. Such an outcome is not observed with JPDA/Res, however, as can be seen in the lower subplot of Fig. 3.4. The reason, again, is that the likelihood function has six terms (3.60)-(3.65) to account for the way point measurements can be generated by the sensor.

# 组合学代考

## 数学代写|组合学代写Combinatorics代考|结果讨论

JPDA/Res也提高了跟踪性能，当两个对象产生相同的强度回报，因此，两个对象都不受青睐。如图3.4的顶部子图所示，尽管标准JPDA在存在未解测量时保持两条轨迹，但在平行运动开始时轨迹切换，随后又切换回来。这是一个不希望出现的情况，例如，在雷达跟踪中，保持航迹标识是极其重要的。然而，在JPDA/Res中没有观察到这样的结果，从图3.4的下副图中可以看到。同样，原因是似然函数有6项(3.60)-(3.65)来解释传感器产生的点测量的方式

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

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