New Linear Estimations from Correlated Uncertain Observations using Covariance Information

S. Nakamori (Japan), R. Caballero, A. Hermoso, and J. Linares (Spain)


Stochastic systems. Least-squares estimator. Uncertain observations. Covariance information.


Least-squares linear filtering and fixed-point smoothing algorithms are derived to estimate a signal from uncertain observations perturbed by an additive white noise. The random variables describing the uncertainty are correlated only at consecutive time instants and this correlation, as well as the probability that the signal exists in each observation, are known. Recursive algorithms are obtained without requiring the state-space model generating the signal, but just the second-order moments of both the signal and the additive noise in the observation equation. The autocovariance function of the signal must be expressed in a semi-degenerate kernel form; this form for expressing autocovariance functions is not very restrictive since it covers many general stochastic processes, including stationary and non-stationary ones.

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