Exploring information theory concepts in various filtering applications is not a new idea. It has been done for decades and the number of papers written are beyond the scope of this project. A more specific filter, known as the Kalman filter, has not been extensively explored from an information theoretic perspective. The kalman filter’s most common applications has been for the control of comp...

We develop a physical analogy for the Kalman-Bucy filter, in which the partially observed signal describes a statistical mechanical system interacting with a heat bath. The ‘universe’ comprising this system and the heat bath obeys a non-decrease law of entropy similar to the Second Law of Thermodynamics. However, this law can be violated in the presence of partial observations. Like Maxwell’s d...

A respiratory chamber is used for monitoring VO2, VCO2 and RQ in humans, enabling long term (24h) observation under free living conditions. Computation of VO2 and VCO2 is currently done by inversion of a mass balance equation, with no consideration of measurement errors and other uncertainties. In order to improve the accuracy of the results, a new mathematical model is suggested in the present...

This is a companion paper of Crisan et el [4]. In this article, we study a few classes of solvable models of the stochastic filtering problems with Ornstein-Uhlenbeck noise: Firstly, we study the singular linear filter with OU noise. Secondly, for nonsingular linear filtering with OU noise, we consider the limit to the classical Kalman-Bucy filter as the OU process converges to the Brownian mot...