The Generalised Moment-based approach to Filtering and Control

Can we solve the filtering problem from the only knowledge of few moments of the noise terms? By exploiting set of distributions based filtering, I show how to solve this problem without introducing additional assumptions on the distributions of the noises (e.g., Gaussianity) or on the final form of the estimator (e.g., linear estimator). Given the moments (e.g., mean and variance) of random variable X, it is in fact possible to define the set of all distributions that are compatible with the moments information. The filtering problem can then be solved by propagating in time this set of distributions. In this talk, I present his approach, show the connection with set-membership estimation, discuss extensions to control. Finally, I will briefly discuss the theory of desirable gambles that could provide a new foundation of filtering and control theory based on a gambling interpretation of probability.