## 数学代写|组合学代写Combinatorics代考|CS586

2022年9月27日

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## 数学代写|组合学代写Combinatorics代考|Tracking with Unresolved Objects

Three simulated scenarios illustrating the problem of unresolved objects/merged measurements for $N=2$ objects are presented. The setup here is similar to the IPDA numerical example presented in Sect. 2.8, with necessary changes to accommodate two separate objects and resolution issues.

Each of the scenarios comprises two cases. In one case, the tracking filter runs standard JPDA and is “ignorant” of resolution issues. In the other case, the tracker runs the JPDA/Res filter and, thus, the resolution issue is handled by the tracker. This tracker is said to be “smart.” In all three scenarios, the tracker parameters are matched to the simulation parameters, with the exception of the handling of unresolved measurements.

Object motion and measurement models. All spatial units are in meters, and all time units are in seconds. For the remainder of this section, the variable $n$ is an object index and is restricted to the set ${1,2}$. The individual object state spaces are denoted $X^1$ and $X^2$, where $X^1=X^2 \equiv X$. Each state space is a subset of $\mathbb{R}^4$ and comprises position and velocity components. Elements of $\mathcal{X}^1$ and $\mathcal{X}^2$, as well as the common measurement space $Y$, are represented using boldface text so that they will not be confused with the components of the 2D position vector $(x y)^T$. An element $\mathbf{x}^n \in X^n$ is represented in coordinate form as $\mathbf{x}^n=\left(x^n \dot{x}^n y^n \dot{y}^n\right)^T$.

A sensor provides spatial $x-y$ measurements of the form $\mathbf{y}=(x y)^T \in y \subset \mathbb{R}^2$ at one second intervals starting at time $t_1=1$ and ending at time $t_K \equiv t_{120}=120$, that is, $\Delta t=1$. Simulated clutter measurements are realizations of a homogeneous PPP with uniform clutter intensity over a finite spatial region of interest $\mathcal{R} \subseteq \mathscr{Y}$. Specifically, the mean number of clutter measurements $\lambda_k^c \equiv \lambda^c$ is constant over all scans, and the clutter PDF $p_k^c(\mathbf{y}) \equiv \frac{1}{\operatorname{Vol}(\mathcal{R})}$ for $\mathbf{y} \in \mathcal{R}$ and $k=1, \ldots, K$.

At each scan $k$, object $n$ is in state $\mathbf{x}k^n \in \mathcal{X}$. Linear-Gaussian assumptions are adopted for object motion. The PDFs for the initial state, process noise, and measurement noise are given by (2.51)-(2.53). The prior object state $\mu_0^n(\cdot)$ for object $n$ at time $t_0$ is assumed to be normally distributed with mean $\hat{x}{0 \mid 0}^n=\mathbf{x}0^n$ and diagonal covariance matrix $P{000}^n=\operatorname{diag}\left(50^2, 3^2, 50^2, 3^2\right)$.

## 数学代写|组合学代写Combinatorics代考|JPDA/Res Filter with Weak and Strong Crossing Tracks

In this scenario, two objects move through $\mathcal{R}$ with constant velocities, eventually crossing paths at the origin as shown in Fig. 3.2. Object one (red) begins in state $\mathbf{x}_0^1 \approx(-2000 \quad 31.5-352.75 .6)^T$ at time $t_0=0$, and it moves at this constant velocity for $120 \mathrm{~s}$. Object two (blue) mirrors object one. It begins in state $\mathbf{x}_0^2 \approx$

$\left(\begin{array}{llll}-2000 & 31.5 & 352.7 & -5.6\end{array}\right)^T$, and it moves at this constant velocity for $120 \mathrm{~s}$. The objects cross at the origin at a $20^{\circ}$ angle.

The region of interest is $\mathcal{R}=[-2000,2000] \times[-1000,1000]$. The mean number of clutter measurements $\lambda_k^c \equiv \lambda^c=250$ is constant over all scans. Thus, in each scan, there is an average of approximately $2.2$ clutter measurements in a $3 \sigma_M$ measurement window.

The unresolved weighting factor is chosen to be $w_r=10 / 11 \approx 0.91$. 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. The tracker process noise standard deviation is set to $\sigma_p=0.5$. The resolution parameter is chosen to be $\sigma{\text {res }}=$ 235.7. This value for $\sigma_{\text {res }}$ gives a resolution probability of approximately $0.5$ when the objects are around $275 \mathrm{~m}$ apart, and the resolution probability drops to 0 when the objects eventually cross.

The filter outputs are depicted in Fig. 3.2. Ground truth object position in $x-y$ space is given by the black dashed line, the gray dots are the superposed clutter realizations over the last five scans (clutter realizations are independent from scan to scan), and red/blue ellipses are the $99 \%$ error ellipses centered at the tracker spatial estimate (” $x$ “) for each object at scans $1,10,20,30,40,50,60,70,80,90,100,110$, and 120 . The tracker spatial estimates over all 120 scans are given by the red/blue lines. Red/blue asterisks represent individual object measurements. Green asterisks are unresolved/merged measurements. For reference, the dark gray circle in the lower right-hand corner of each plot depicts a $3 \sigma_M$ measurement window.

# 组合学代考

## 数学代写|组合学代写Combinatorics代考|带有弱和强交叉轨迹的JPDA/Res滤波器

$\left(\begin{array}{llll}-2000 & 31.5 & 352.7 & -5.6\end{array}\right)^T$，它以这个恒定的速度移动$120 \mathrm{~s}$。这些物体在原点处以$20^{\circ}$的角度相交。

## 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。