Different approaches for state filtering in nonlinear systems with uncertain observations

This paper addresses the least squares filtering problem for nonlinear systems with uncertain observations, when random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables. We propose four filtering algorithms which are based on different approximations of the first and second-order statistics of a nonlinear transformation of random vectors perturbed by additive and multiplicative noises. These algorithms generalize the extended and unscented Kalman filters to the case in which there is a positive probability that the observation in each time consists of noise alone and, hence, does not contain the signal to be estimated. The accuracy of the different approximations is also analyzed and the performance of the proposed algorithms is compared in a numerical simulation example.