Information and Entropy Flow in the Kalman–Bucy Filter
Information and Entropy Flow in the Kalman–Bucy Filter
复制标题
卡尔曼-布西滤波器中的信息和熵流
DOI：
10.1007/s10955-004-8781-9
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发表时间：
2005
影响因子：
1.6
通讯作者：
Nigel J. Newton
中科院分区：
文献类型：
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作者：
S. Mitter;Nigel J. Newton
我们研究了卡尔曼-布西滤波器在连续时间中的信息论性质，发展了信息供应、存储和耗散的概念。引入能量的概念，我们开发了一个物理类比，其中未观察到的信号描述了与热浴相互作用的统计力学系统。由信号和热浴组成的抽象“宇宙”遵守熵不增加定律;然而，随着部分观测的引入，这一定律可能被违反。在这个类比中，卡尔曼-布西滤波器的行为就像麦克斯韦恶魔，将信号能量返回到热浴而不引起熵增加。这是由于不断提供新的信息。在第二个类比中，信号和滤波器相互作用，建立一个稳定的非平衡状态，其中能量在热浴、信号和滤波器之间流动，而不会引起任何整体熵增加。我们引入了一个互动的熵流率，隔离统计力学的边际效应，这个流量。这两个类比都提供了兰道尔原理的定量例子。
We investigate the information theoretic properties of Kalman–Bucy filters in continuous time, developing notions of information supply, storage and dissipation. Introducing a concept of energy, we develop a physical analogy in which the unobserved signal describes a statistical mechanical system interacting with a heat bath. The abstract ‘universe’ comprising the signal and the heat bath obeys a non-increase law of entropy; however, with the introduction of partial observations, this law can be violated. The Kalman–Bucy filter behaves like a Maxwellian demon in this analogy, returning signal energy to the heat bath without causing entropy increase. This is made possible by the steady supply of new information. In a second analogy the signal and filter interact, setting up a stationary non-equilibrium state, in which energy flows between the heat bath, the signal and the filter without causing any overall entropy increase. We introduce a rate of interactive entropy flow that isolates the statistical mechanics of this flow from marginal effects. Both analogies provide quantitative examples of Landauer’s Principle.