数学代写|matlab代写|Square-Root Methods and All That

如果你也在 怎样代写matlab这个学科遇到相关的难题,请随时右上角联系我们的24/7代写客服。


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。

我们提供的matlab及其相关学科的代写,服务范围广, 其中包括但不限于:

  • 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|Square-Root Methods and All That

数学代写|matlab代写|Numerical Stability Problems

Numerical Stability Problems. The great success of Kalman filtering was not without its problems, not the least of which was marginal stability of the numerical solution of the associated Riccati equation. In some applications, small roundoff errors tended to accumulate and eventually degrade the performance of the filter. In the decades immediately following the introduction of the Kalman filter, there appeared several better numerical implementations of the original formulas. Many of these were adaptations of methods previously derived for the least squares problem.
Early ad hoc Fixes. It was discovered early on ${ }^{13}$ that forcing symmetry on the solution of the matrix Riccati equation improved its apparent numerical stability-a phenomenon that was later given a more theoretical basis by Verhaegen and Van Dooren [232]. It was also found that the influence of roundoff errors could be ameliorated by artificially increasing the covariance of process noise in the Riccati equation. A symmetrized form of the discrete-time Riccati equation was developed by Joseph [15] and used by R. C. K. Lee at Honeywell in 1964. This “structural” reformulation of the Kalman filter equations improved robustness against roundoff errors in some applications, although later methods have performed better on some problems [125].

Square-Root Filtering. These methods can also be considered as “structural” reformulations of the Riccati equation, and they predate the Bucy-Joseph form. The first of these was the “square-root” implementation by Potter and Stern [208], first published in 1963 and successfully implemented for space navigation on the Apollo manned lunar exploration program. Potter and Stern introduced the idea of factoring the covariance matrix into Cholesky factors, ${ }^{14}$ in the format
P=C C^{\mathrm{T}}
and expressing the observational update equations in terms of the Cholesky factor $C$, rather than $P$. The result was better numerical stability of the filter implementation at the expense of added computational complexity. A generalization of the Potter and Stern method to handle vector-valued measurements was published by one of the authors [130] in 1968 , but a more efficient implementation-in terms of triangular Cholesky factors – was published by Bennet in 1967 [138].

数学代写|matlab代写|Beyond Kalman Filtering

Extended Kalman Filtering and the Kalman-Schmidt Filter. Although it was originally derived for a linear problem, the Kalman filter is habitually applied with impunity-and considerable success – to many nonlinear problems. These extensions generally use partial derivatives as linear approximations of nonlinear relations. Schmidt [118] introduced the idea of evaluating these partial derivatives at the estimated value of the state variables. This approach is generally called the extended Kalman filter, but it was called the Kalman-Schmidt filter in some early publications. This and other methods for approximate linear solutions to nonlinear problems are discussed in Chapter 5 , where it is noted that these will not be adequate for all nonlinear problems. Mentioned here are some investigations that have addressed estimation problems from a more general perspective, although they are not covered in the rest of the book.

Nonlinear Filtering Using Higher Order Approximations. Approaches using higher order expansions of the filter equations (i.e., beyond the linear terms) have been derived by Stratonovich [78], Kushner [191], Bucy [147], Bass et al. [134], and others for quadratic nonlinearities and by Wiberg and Campbell [235] for terms through third order.

Nonlinear Stochastic Differential Equations. Problems involving nonlinear and random dynamic systems have been studied for some time in statistical mechanics. The propagation over time of the probability distribution of the state of a nonlinear dynamic system is described by a nonlinear partial differential equation called the Fokker-Planck equation. It has been studied by Einstein [157], Fokker [160], Planck [207], Kolmogorov [187], Stratonovich [78], Baras and Mirelli [52], and others. Stratonovich modeled the effect on the probability distribution of information obtained through noisy measurements of the dynamic system, an effect called conditioning. The partial differential equation that includes these effects is called the conditioned Fokker-Planck equation. It has also been studied by Kushner [191], Bucy [147], and others using the stochastic calculus of Kiyosi Itô-also called the “Itô calculus.” It is a non-Riemannian calculus developed specifically for stochastic differential systems with noise of infinite bandwidth. This general approach results in a stochastic partial differential equation describing the evolution over time of the probability distribution over a “state space” of the dynamic system under study. The resulting model does not enjoy the finite representational characteristics of the Kalman filter, however. The computational complexity of obtaining a solution far exceeds the already considerable burden of the conventional Kalman filter. These methods are of significant interest and utility but are beyond the scope of this book.

数学代写|matlab代写|Point Processes and the Detection Problem

Point Processes and the Detection Problem. A point process is a type of random process for modeling events or objects that are distributed over time or space, such as the arrivals of messages at a communications switching center or the locations of stars in the sky. It is also a model for the initial states of systems in many estimation problems, such as the locations of aircraft or spacecraft under surveillance by a radar installation or the locations of submarines in the ocean. The dection problem for these surveillance applications must usually be solved before the estimation problem (i.e., tracking of the objects with a Kalman filter) can begin. The Kalman filter requires an initial state for each object, and that initial state estimate must be obtained by detecting it. Those initial states are distributed according to some point process, but there are no technically mature methods (comparable to the Kalman filter) for estimating the state of a point process. A unified approach combining detection and tracking into one optimal estimation method was derived by Richardson [214] and specialized to several applications. The detection and tracking problem for a single object is represented by the conditioned Fokker-Planck equation. Richardson derived from this one-object model an infinite hierarchy of partial differential equations representing object densities and truncated this hierarchy with a simple closure assumption about the relationships between orders of densities. The result is a single partial differential equation approximating the evolution of the density of objects. It can be solved numerically. It provides a solution to the difficult problem of detecting dynamic objects whose initial states are represented by a point process.

数学代写|matlab代写|Square-Root Methods and All That


数学代写|matlab代写|Numerical Stability Problems

数值稳定性问题。卡尔曼滤波的巨大成功并非没有问题,其中最重要的是相关的 Riccati 方程的数值解的边际稳定性。在某些应用中,小的舍入误差往往会累积并最终降低滤波器的性能。在引入卡尔曼滤波器之后的几十年里,出现了几个更好的原始公式的数值实现。其中许多是先前为最小二乘问题导出的方法的改编。
早期的临时修复。很早就被发现了13对矩阵 Riccati 方程的解强制对称性提高了其明显的数值稳定性——这一现象后来被 Verhaegen 和 Van Dooren [232] 提供了更多的理论基础。还发现,可以通过人为地增加 Riccati 方程中过程噪声的协方差来改善舍入误差的影响。Joseph [15] 开发了离散时间 Riccati 方程的对称形式,并于 1964 年由霍尼韦尔的 RCK Lee 使用。卡尔曼滤波器方程的这种“结构”重构提高了在某些应用中对舍入误差的鲁棒性,尽管后来的方法已经在一些问题上表现更好[125]。

平方根滤波。这些方法也可以被认为是 Riccati 方程的“结构”重新表述,它们早于 Bucy-Joseph 形式。其中第一个是 Potter 和 Stern [208] 的“平方根”实现,于 1963 年首次发表,并成功实现了阿波罗载人探月计划的太空导航。Potter 和 Stern 引入了将协方差矩阵分解为 Cholesky 因子的想法,14在格式
并根据 Cholesky 因子表达观测更新方程C, 而不是磷. 结果是滤波器实现的数值稳定性更好,但代价是增加了计算复杂性。其中一位作者 [130] 于 1968 年发表了对处理向量值测量的 Potter 和 Stern 方法的推广,但 Bennet 于 1967 年发表了一种更有效的实现——就三角 Cholesky 因子而言——发表了[138]。

数学代写|matlab代写|Beyond Kalman Filtering

扩展卡尔曼滤波和卡尔曼-施密特滤波器。尽管卡尔曼滤波器最初是针对线性问题推导出来的,但习惯性地将卡尔曼滤波器应用于许多非线性问题而不受惩罚且相当成功。这些扩展通常使用偏导数作为非线性关系的线性近似。Schmidt [118] 引入了在状态变量的估计值处评估这些偏导数的想法。这种方法通常被称为扩展卡尔曼滤波器,但在一些早期出版物中被称为卡尔曼-施密特滤波器。第 5 章讨论了非线性问题的近似线性解的这种方法和其他方法,其中指出这些方法不适用于所有非线性问题。

使用高阶近似的非线性滤波。Stratonovich [78]、Kushner [191]、Bucy [147]、Bass 等人已经推导出了使用滤波器方程的高阶展开(即超出线性项)的方法。[134],以及其他关于二次非线性的以及 Wiberg 和 Campbell [235] 的通过三阶项。

非线性随机微分方程。涉及非线性和随机动态系统的问题已经在统计力学中研究了一段时间。非线性动态系统状态的概率分布随时间的传播由称为 Fokker-Planck 方程的非线性偏微分方程描述。Einstein [157]、Fokker [160]、Planck [207]、Kolmogorov [187]、Stratonovich [78]、Baras 和 Mirelli [52] 等对其进行了研究。Stratonovich 模拟了对通过动态系统的噪声测量获得的信息概率分布的影响,这种影响称为调节。包含这些效应的偏微分方程称为条件 Fokker-Planck 方程。Kushner [191]、Bucy [147] 也对它进行了研究,和其他人使用 Kiyosi Itô 的随机演算——也称为“伊藤演算”。它是专门为具有无限带宽噪声的随机微分系统开发的非黎曼微积分。这种通用方法产生了一个随机偏微分方程,该方程描述了概率分布在所研究的动态系统的“状态空间”上随时间的演变。然而,所得模型不具有卡尔曼滤波器的有限表示特性。获得解的计算复杂度远远超过了传统卡尔曼滤波器已经相当大的负担。这些方法具有重要意义和实用性,但超出了本书的范围。” 它是专门为具有无限带宽噪声的随机微分系统开发的非黎曼微积分。这种通用方法产生了一个随机偏微分方程,该方程描述了概率分布在所研究的动态系统的“状态空间”上随时间的演变。然而,所得模型不具有卡尔曼滤波器的有限表示特性。获得解的计算复杂度远远超过了传统卡尔曼滤波器已经相当大的负担。这些方法具有重要意义和实用性,但超出了本书的范围。” 它是专门为具有无限带宽噪声的随机微分系统开发的非黎曼微积分。这种通用方法产生了一个随机偏微分方程,该方程描述了概率分布在所研究的动态系统的“状态空间”上随时间的演变。然而,所得模型不具有卡尔曼滤波器的有限表示特性。获得解的计算复杂度远远超过了传统卡尔曼滤波器已经相当大的负担。这些方法具有重要意义和实用性,但超出了本书的范围。这种通用方法产生了一个随机偏微分方程,该方程描述了概率分布在所研究的动态系统的“状态空间”上随时间的演变。然而,所得模型不具有卡尔曼滤波器的有限表示特性。获得解的计算复杂度远远超过了传统卡尔曼滤波器已经相当大的负担。这些方法具有重要意义和实用性,但超出了本书的范围。这种通用方法产生了一个随机偏微分方程,该方程描述了概率分布在所研究的动态系统的“状态空间”上随时间的演变。然而,所得模型不具有卡尔曼滤波器的有限表示特性。获得解的计算复杂度远远超过了传统卡尔曼滤波器已经相当大的负担。这些方法具有重要意义和实用性,但超出了本书的范围。

数学代写|matlab代写|Point Processes and the Detection Problem

点过程和检测问题。点过程是一种随机过程,用于建模随时间或空间分布的事件或对象,例如消息到达通信交换中心或天空中星星的位置。它也是许多估计问题中系统初始状态的模型,例如雷达装置监视下的飞机或航天器的位置或海洋中潜艇的位置。这些监视应用的检测问题通常必须在估计问题(即,使用卡尔曼滤波器跟踪对象)开始之前解决。卡尔曼滤波器需要每个对象的初始状态,并且必须通过检测来获得初始状态估计。那些初始状态是根据一些点过程分布的,但是没有技术上成熟的方法(类似于卡尔曼滤波器)来估计点过程的状态。Richardson [214] 推导出了一种将检测和跟踪结合为一种最佳估计方法的统一方法,并专门用于多种应用。单个对象的检测和跟踪问题由条件 Fokker-Planck 方程表示。理查森从这个单对象模型中推导出代表对象密度的无限层次的偏微分方程,并用关于密度阶数之间关系的简单闭包假设截断了这个层次。结果是一个近似于物体密度演变的偏微分方程。可以用数值求解。

数学代写|matlab代写 请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。







术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。



有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。





随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。


多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。


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。



您的电子邮箱地址不会被公开。 必填项已用*标注