This paper develops a framework for the mean-square analysis of adaptive lters with general data and error nonlinearities. The approach relies on energy conservation arguments and is carried out without restrictions on the probability distribution of the input sequence. In particular, for adaptive lters with diagonal matrix nonlinearities, we provide closed form expressions for the steady-state...

Uncertain parameters of state-space models have always been a considerable problem. Consider Kalman filter (CKF) and desensitized Kalman filter (DKF) are two methods to solve this problem. Based on the sensitivity matrix respected to the uncertain parameter vector, a special DKF with an analytical gain is given and a new form of the CKF is derived. The mathematical equivalence between the speci...

The notion of a fantastic filter in a lattice implication algebra is introduced, and the relations among filter, positive implicative filter, and fantastic filter are given. We investigate an equivalent condition for a filter to be fantastic, and state an extension property for fantastic filter.

Estimation of a dynamical system’s latent state subject to sensor noise and model inaccuracies remains critical yet difficult problem in robotics. While Kalman filters provide the optimal solution least squared sense for linear Gaussian problems, general nonlinear non-Gaussian case is significantly more complicated, typically relying on sampling strategies that are limited low-dimensional space...