非线性连续离散随机系统的状态估计
This book addresses the problem of accurate state estimation in nonlinear continuous-time stochastic models with additive noise and discrete measurements. Its main focus is on numerical aspects of computation of the expectation and covariance in Kalman-like filters rather than on statistical properties determining a model of the system state. Nevertheless, it provides the sound theoretical background and covers all contemporary state estimation techniques beginning at the celebrated Kalman filter, including its versions extended to nonlinear stochastic models, and till the most advanced universal Gaussian filters with deterministically sampled mean and covariance. In particular, the authors demonstrate that, when applying such filtering procedures to stochastic models with strong nonlinearities, the use of adaptive ordinary differential equation solvers with automatic local and global error control facilities allows the discretization error―and consequently the state estimation error―to be reduced considerably. For achieving that, the variable-stepsize methods with automatic error regulation and stepsize selection mechanisms are applied to treating moment differential equations arisen. The implemented discretization error reduction makes the self-adaptive nonlinear Gaussian filtering algorithms more suitable for application and leads to the novel notion of accurate state estimation.
英文|2024|ISBN-10:3031613708|819页|Epub PDF（真）|217 MB 本书解决了具有加性噪声和离散测量的非线性连续时间随机模型中的精确状态估计问题。它的主要重点是类卡尔曼滤波器中期望和协方差计算的数值方面，而不是确定系统状态模型的统计特性。然而，它提供了坚实的理论背景，涵盖了从著名的卡尔曼滤波器开始的所有当代状态估计技术，包括其扩展到非线性随机模型的版本，直到具有确定性采样均值和协方差的最先进的通用高斯滤波器。特别是，作者证明，当将这种滤波过程应用于具有强非线性的随机模型时，使用具有自动局部和全局误差控制设施的自适应常微分方程求解器可以大大减少离散化误差，从而大大减少状态估计误差。为了实现这一目标，将具有自动误差调节和步长选择机制的变步长方法应用于处理产生的力矩微分方程。实现的离散化误差减小使自适应非线性高斯滤波算法更适合应用，并带来了精确状态估计的新概念。本站不对文件进行储存，仅提供文件链接，请自行下载，本站不对文件内容负责，请自行判断文件是否安全，如发现文件有侵权行为，请联系管理员删除。
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