Optimal recursive estimation with uncertain observation
IEEE Transactions on Information Theory
Discrete optimal linear smoothing for systems with uncertain observations
IEEE Transactions on Information Theory
Optimal linear estimation with uncertain observations (Corresp.)
IEEE Transactions on Information Theory
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Journal of Computational and Applied Mathematics
Hi-index | 0.00 |
A least-squares linear fixed-interval smoothing algorithm is derived to estimate signals from uncertain observations perturbed by additive white noise. It is assumed that the Bernoulli variables describing the uncertainty are only correlated at consecutive time instants. The marginal distribution of each of these variables, specified by the probability that the signal exists at each observation, as well as their correlation function, are known. The algorithm is obtained without requiring the state-space model generating the signal, but just the covariances of the signal and the additive noise in the observation equation. The covariance function of the signal must be expressed in a semi-degenerate kernel form, assumption which covers many general situations, including stationary and non-stationary signals.