A Nonlinear Stochastic Filter for Continuous-Time State Estimation.
A Nonlinear Stochastic Filter for Continuous-Time State Estimation.
复制标题
DOI：
10.1109/tac.2015.2409910
复制
发表时间：
2015-08
影响因子：
6.8
通讯作者：
Sanger TD
中科院分区：
文献类型：
--
作者：
Ghoreyshi A;Sanger TD
非线性滤波器在每个时间点产生状态概率密度的非参数估计。目前已知的非线性滤波器包括粒子滤波器和库什纳方程（以及它的非标准化版本：扎凯方程）。然而，这些滤波器具有有限的测量模型：粒子滤波器需要在离散时间进行测量，并且Kushner和Zakai方程仅在测量可以表示为状态的函数时才适用。我们提出了一种新的非线性滤波器，用于更一般的随机测量模型的连续时间测量。它集成到贝叶斯规则在短时间间隔，并提供贝叶斯最优估计从量化，间歇，或模糊的传感器测量。该滤波器与信息论有密切的联系，我们证明了密度估计的熵的变化率等于测量和状态之间的互信息，因此是可实现的最大值。这是一类全新的滤波器，广泛应用于连续时间控制的非线性估计。
Nonlinear filters produce a nonparametric estimate of the probability density of state at each point in time. Currently-known nonlinear filters include Particle Filters and the Kushner equation (and its un-normalized version: the Zakai equation). However, these filters have limited measurement models: Particle Filters require measurement at discrete times, and the Kushner and Zakai equations only apply when the measurement can be represented as a function of the state. We present a new nonlinear filter for continuous-time measurements with a much more general stochastic measurement model. It integrates to Bayes’ rule over short time intervals and provides Bayes-optimal estimates from quantized, intermittent, or ambiguous sensor measurements. The filter has a close link to Information Theory, and we show that the rate of change of entropy of the density estimate is equal to the mutual information between the measurement and the state and thus the maximum achievable. This is a fundamentally new class of filter that is widely applicable to nonlinear estimation for continuous-time control.