statistics-lab™ 为您的留学生涯保驾护航 在代写SLAM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SLAM代写方面经验极为丰富，各种代写SLAM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

Adding a new landmark to FastSLAM can be difficult decision to make, just as with EKF-based algorithms. This is especially true when an individual measurement is insufficient to constrain the new landmark in all dimensions [13]. If the measurement function $g\left(\theta_{n_{t}}, s_{t}\right)$ is invertible, however, a single measurement is sufficient to initialize a new landmark. Each observation defines a Gaussian:
$$\mathcal{N}\left(z_{t} ; \hat{z}{t}+G{\theta_{n_{t}}}\left(\theta_{n_{t}}-\mu_{n_{t}, t}^{[m]}\right), R_{t}\right)$$
This Gaussian can be written explicitly as:
\begin{aligned} \frac{1}{\sqrt{\left|2 \pi R_{t}\right|}} \exp {&-\frac{1}{2}\left(z_{t}-\hat{z}{t}-G{\theta_{n_{t}}}\left(\theta_{n_{t}}-\mu_{n_{t}, t-1}^{[m]}\right)\right)^{T} \ &\left.R_{t}^{-1}\left(z_{t}-\hat{z}{t}-G{\theta_{n_{t}}}\left(\theta_{n_{t}}-\mu_{n_{t}, t-1}^{[m]}\right)\right)\right} \end{aligned}
We define a function J to be equal to the negative of the exponent of this Gaussian:
$$J=\frac{1}{2}\left(z_{t}-\hat{z}{t}-G{\theta_{n_{t}}}\left(\theta_{n_{t}}-\mu_{n_{t}, t-1}^{[m]}\right)\right)^{T} R_{t}^{-1}\left(z_{t}-\hat{z}{t}-G{\theta_{n_{t}}}\left(\theta_{n_{t}}-\mu_{n_{t}, t-1}^{[m]}\right)\right)$$

The second derivative of $J$ with respect to $\theta_{n_{t}}$ will be the inverse of the covariance matrix of the Gaussian in landmark coordinates.
\begin{aligned} \frac{\partial J}{\partial \theta_{n_{t}}} &=-\left(z_{t}-\hat{z}{t}-G{\theta_{n_{t}}}\left(\theta_{n_{t}}-\mu_{n_{t}, t-1}^{[m]}\right)\right)^{T} R_{t}^{-1} G_{\theta_{n_{t}}} \ \frac{\partial^{2} J}{\partial \theta_{n_{t}}^{2}} &=G_{\theta_{n_{t}}}^{T} R_{t}^{-1} G_{\theta_{n_{t}}} \end{aligned}
Consequently, an invertible observation can be used to create a new landmark as follows.
\begin{aligned} \mu_{n_{t}, t}^{[m]} &=g^{-1}\left(s_{t}^{[m]}, z_{t}\right) \ \Sigma_{n_{t}, t}^{[m]} &=\left(G_{\theta_{n_{t}}, t}^{T} R^{-1} G_{\theta_{n_{t}}, t}\right)^{-1} \ w_{t}^{[m]} &=p_{0} \end{aligned}
In practice, a simpler initialization procedure also works well. Instead of computing the correct initial covariance, the covariance can be computed by setting the variance of each landmark parameter to a large initial value $K$ and incorporating the first observation. Higher values of $K$ lead to closer approximations of the true covariance, but can also lead to numerical instability.
\begin{aligned} \mu_{n_{t}, t}^{[m]} &=g^{-1}\left(s_{t}^{[m]}, z_{t}\right) \ \Sigma_{n_{t}, t}^{[m]} &=K \cdot I \end{aligned}
Initialization techniques for situations in which $g$ is not invertible (e.g. bearings-only SLAM) are discussed in $[12,13]$. These situations require the accumulation of multiple observations in order to estimate the location of a landmark. FastSLAM is currently being applied to the problem of bearingsonly SLAM [83].

## 机器人代写|SLAM代写机器人导航代考|Summary of the FastSLAM Algorithm

Table $3.2$ summarizes the FastSLAM algorithm with unknown data association. Particles in the complete FastSLAM algorithm have the form:
$$S_{t}^{[m]}=\left\langle s_{t}^{[m]} \mid N_{t}^{[m]}, \mu_{1, t}^{[m]}, \Sigma_{1, t}^{[m]}, \ldots, \mu_{N_{t}^{[m]}, t}^{[m]}, \Sigma_{N_{t}^{[m]}, t}^{[m]}\right\rangle$$
In addition to the latest robot pose $s_{t}^{[m]}$ and the feature estimates $\mu_{n, t}^{[m]}$ and $\Sigma_{n, t}^{[m]}$, each particle maintains the number of features $N_{t}^{[m]}$ in its local map. It is interesting to note that each particle may have a different number of landmarks. This is an expressive representation, but it can lead to difficulties in determining the most probable map.

## 机器人代写|SLAM代写机器人导航代考|Greedy Mutual Exclusion

If multiple observations are incorporated simultaneously, the simplest approach to data association is to consider the identity of each observation independently. However, the data associations of each observation are clearly correlated, as was shown in Section 3.4. The data associations are correlated

through error in the robot pose, and they also must all obey a mutual exclusion constraint; more than one observation cannot be associated with the same landmark at the same time. Considering the data associations jointly does address these problems $[1,14,68]$, but these techniques are computationally expensive for large numbers of simultaneous observations.

FastSLAM addresses the first problem, motion ambiguity, by sampling over robot poses and data associations. Each set of data association decisions is conditioned on a particular robot path. Thus, the data associations can be chosen independently without fear that pose error will corrupt all of the decisions. Some of the particles will chose the correct data associations, while others draw inconsistent robot poses, pick incorrect data associations, and receive low weights. Picking associations independently per particle still ignores the issue of mutual exclusion, however. Mutual exclusion is particularly useful for deciding when to add new landmarks in noisy environments. Instead of assigning an observation of an unseen landmark to an existing landmark, mutual exclusion will force the creation of a new landmark if both features are observed.

Proper handling of mutual exclusion requires that the data associations of all observations be considered simultaneously. However, mutual exclusion can also be enforced in a greedy fashion. Each observation is processed sequentially and ignores the landmarks associated with previously assigned observations. With a single data association hypothesis, applying mutual exclusion greedily can lead to failures in noisy environments. It can work well in FastSLAM, though, because the motion ambiguity that commonly causes greedy mutual exclusion failures is largely factored out by sampling over the the robot’s path. Furthermore, errors due to the greedy nature of the algorithm can also be minimized by processing the observations in different orders for each particle.

## SLAM代写

ñ(和吨;和^吨+Gθn吨(θn吨−μn吨,吨[米]),R吨)

\begin{aligned} \frac{1}{\sqrt{\left|2 \pi R_{t}\right|}} \exp {&-\frac{1}{2}\left(z_{t}- \hat{z}{t}-G{\theta_{n_{t}}}\left(\theta_{n_{t}}-\mu_{n_{t}, t-1}^{[m]} \right)\right)^{T} \ &\left.R_{t}^{-1}\left(z_{t}-\hat{z}{t}-G{\theta_{n_{t} }}\left(\theta_{n_{t}}-\mu_{n_{t}, t-1}^{[m]}\right)\right)\right} \end{aligned}\begin{aligned} \frac{1}{\sqrt{\left|2 \pi R_{t}\right|}} \exp {&-\frac{1}{2}\left(z_{t}- \hat{z}{t}-G{\theta_{n_{t}}}\left(\theta_{n_{t}}-\mu_{n_{t}, t-1}^{[m]} \right)\right)^{T} \ &\left.R_{t}^{-1}\left(z_{t}-\hat{z}{t}-G{\theta_{n_{t} }}\left(\theta_{n_{t}}-\mu_{n_{t}, t-1}^{[m]}\right)\right)\right} \end{aligned}

Ĵ=12(和吨−和^吨−Gθn吨(θn吨−μn吨,吨−1[米]))吨R吨−1(和吨−和^吨−Gθn吨(θn吨−μn吨,吨−1[米]))

∂Ĵ∂θn吨=−(和吨−和^吨−Gθn吨(θn吨−μn吨,吨−1[米]))吨R吨−1Gθn吨 ∂2Ĵ∂θn吨2=Gθn吨吨R吨−1Gθn吨

μn吨,吨[米]=G−1(s吨[米],和吨) Σn吨,吨[米]=(Gθn吨,吨吨R−1Gθn吨,吨)−1 在吨[米]=p0

μn吨,吨[米]=G−1(s吨[米],和吨) Σn吨,吨[米]=ķ⋅一世

## 机器人代写|SLAM代写机器人导航代考|Greedy Mutual Exclusion

FastSLAM 通过对机器人姿势和数据关联进行采样来解决第一个问题，即运动模糊性。每组数据关联决策都以特定的机器人路径为条件。因此，可以独立选择数据关联，而不必担心姿势错误会破坏所有决策。一些粒子会选择正确的数据关联，而其他粒子会绘制不一致的机器人姿势，选择不正确的数据关联，并获得低权重。然而，每个粒子独立地选择关联仍然忽略了互斥问题。互斥对于决定何时在嘈杂环境中添加新地标特别有用。如果两个特征都被观察到，互斥将强制创建新的地标，而不是将未见地标的观察分配给现有地标。

## 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。