Filtering With Uncertain Noise
Robert James Elliott · IEEE Transactions on Automatic Control · 2016
Filtering is concerned with estimating signals observed in noise. In this technical note, we consider a signal which is a Markov chain. In turn, this is observed in Gaussian noise whose parameters are not known. Peng has considered nonlinear expectations which can be represented as the supremum of a family of expectations. This approach is followed below, providing one of the first studies of filtering in this framework by extending methods of Elliott et al.. Modified recursive filters are derived where expected values are replaced by maximum likelihoods.