Using cloudy kernels for imprecise linear filtering

Abstract

Selecting a particular summative (i.e., formally equivalent to a probability distribution) kernel when filtering a digital signal can be a difficult task. To circumvent this difficulty, one can work with maxitive (i.e., formally equivalent to a possibility distribution) kernels. These kernels allow to consider at once sets of summative kernels with upper bounded bandwith. They also allow to perform a robustness analysis without additional computational cost. However, one of the drawbacks of filtering with maxitive kernels is sometimes an overly imprecise output, due to the limited expressiveness of summative kernels. We propose to use a new uncertainty representation, namely cloud, to achieve a compromise between summative and maxitive kernels, avoiding some of their respective shortcomings. The proposal is then experimented on a simulated signal. © 2010 Springer-Verlag Berlin Heidelberg.