### 数学代写|matlab代写|General Information

matlab是一个编程和数值计算平台，被数百万工程师和科学家用来分析数据、开发算法和创建模型。

statistics-lab™ 为您的留学生涯保驾护航 在代写matlab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matlab代写方面经验极为丰富，各种代写matlab相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• 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

## 数学代写|matlab代写|ON KALMAN FILTERING

Theoretically the Kalman Filter is an estimator for what is called the linear-quadratic problem, which is the problem of estimating the instantaneous “state” (a concept that will be made more precise in the next chapter) of a linear dynamic system perturbed by white noise-by using measurements linearly related to the state but corrupted by white noise. The resulting estimator is statistically optimal with respect to any quadratic function of estimation error.

Practically, it is certainly one of the greater discoveries in the history of statistical estimation theory and possibly the greatest discovery in the twentieth century. It has enabled humankind to do many things that could not have been done without it, and it has become as indispensable as silicon in the makeup of many electronic systems. Its most immediate applications have been for the control of complex dynamic systems such as continuous manufacturing processes, aircraft, ships, or spacecraft. To control a dynamic system, you must first know what it is doing. For these applications, it is not always possible or desirable to measure every variable that you want to control, and the Kalman filter provides a means for inferring the missing information from indirect (and noisy) measurements. The Kalman filter is also used for predicting the likely future courses of dynamic systems that people are not likely to control, such as the flow of rivers during flood, the trajectories of celestial bodies, or the prices of traded commodities.

## 数学代写|matlab代写|How It Came to Be Called a Filter

It might seem strange that the term “filter” would apply to an estimator. More commonly, a filter is a physical device for removing unwanted fractions of mixtures. (The word felt comes from the same medieval Latin stem, for the material was used as a filter for liquids.) Originally, a filter solved the problem of separating unwanted components of gas-liquid-solid mixtures. In the era of crystal radios and vacuum tubes, the term was applied to analog circuits that “filter” electronic signals. These

signals are mixtures of different frequency components, and these physical devices preferentially attenuate unwanted frequencies.

This concept was extended in the 1930 s and $1940 \mathrm{~s}$ to the separation of “signals” from “noise,” both of which were characterized by their power spectral densities. Kolmogorov and Wiener used this statistical characterization of their probability distributions in forming an optimal estimate of the signal, given the sum of the signal and noise.

With Kalman filtering the term assumed a meaning that is well beyond the original idea of separation of the components of a mixture. It has also come to include the solution of an imversion problem, in which one knows how to represent the measurable variables as functions of the variables of principal interest. In essence, it inverts this functional relationship and estimates the independent variables as inverted functions of the dependent (measurable) variables. These variables of interest are also allowed to be dynamic, with dynamics that are only partially predictable.

## 数学代写|matlab代写|What It Is Used For

The applications of Kalman filtering encompass many fields, but its use as a tool is almost exclusively for two purposes: estimation and performance analysis of estimators.

Role 1: Estimating the State of Dynamic Systems What is a dynamic system? Almost everything, if you are picky about it. Except for a few fundamental physical constants, there is hardly anything in the universe that is truly constant. The orbital parameters of the asteroid Ceres are not constant, and even the “fixed” stars and continents are moving. Nearly all physical systems are dynamic to some degree. If one wants very precise estimates of their characteristics over time, then one has to take their dynamics into consideration.

The problem is that one does not always know their dynamics very precisely either. Given this state of partial ignorance, the best one can do is express our ignorance more precisely – using probabilities. The Kalman filter allows us to estimate the state of dynamic systems with certain types of random behavior by using such statistical information. A few examples of such systems are listed in the second column of Table 1.1.
Role 2: The Analysis of Estimation Systems. The third column of Table $1.1$ lists some possible sensor types that might be used in estimating the state of the corresponding dynamic systems. The objective of design analysis is to determine how best to use these sensor types for a given set of design criteria. These criteria are typically related to estimation accuracy and system cost.
The Kalman filter uses a complete description of the probability distribution of its estimation errors in determining the optimal filtering gains, and this probability distribution may be used in assessing its performance as a function of the “design parameters” of an estimation system, such as

• the types of sensors to be used,
• the locations and orientations of the various sensor types with respect to the system to be estimated.

## 数学代写|matlab代写|What It Is Used For

• 要使用的传感器类型，
• 各种传感器类型相对于要估计的系统的位置和方向。

## 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。