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Seiichi NAKAMORI Raquel CABALLERO-AGUILA Aurora HERMOSO-CARAZO Jose D. JIMENEZ-LOPEZ Josefa LINARES-PEREZ
The least-squares linear filtering and fixed-point smoothing problems of uncertainly observed signals are considered when the signal and the observation additive noise are correlated at any sampling time. Recursive algorithms, based on an innovation approach, are proposed without requiring the knowledge of the state-space model generating the signal, but only the autocovariance and crosscovariance functions of the signal and the observation white noise, as well as the probability that the signal exists in the observations.
Seiichi NAKAMORI Aurora HERMOSO-CARAZO Josefa LINARES-PEREZ
This paper discusses the least-squares linear filtering and fixed-lag smoothing problems of discrete-time signals from uncertain observations when the random interruptions in the observation process are modelled by a sequence of not necessarily independent Bernoulli variables. It is assumed that the observations are perturbed by white noise and the autocovariance function of the signal is factorizable. Using an innovation approach we obtain the filtering and fixed-lag smoothing recursive algorithms, which do not require the knowledge of the state-space model generating the signal. Besides the observed values, they use only the matrix functions defining the factorizable autocovariance function of the signal, the noise autocovariance function, the marginal probabilities and the (2,2)-element of the conditional probability matrices of the Bernoulli variables. The algorithms are applied to estimate a scalar signal which may be transmitted through one of two channels.
Seiichi NAKAMORI Raquel CABALLERO-AGUILA Aurora HERMOSO-CARAZO Josefa LINARES-PEREZ
This paper treats the least-squares linear filtering and smoothing problems of discrete-time signals from uncertain observations when the random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables. Using an innovation approach we obtain the filtering algorithm and a general expression for the smoother which leads to fixed-point, fixed-interval and fixed-lag smoothing recursive algorithms. The proposed algorithms do not require the knowledge of the state-space model generating the signal, but only the covariance information of the signal and the observation noise, as well as the probability that the signal exists in the observed values.
Seiichi NAKAMORI Raquel CABALLERO-AGUILA Aurora HERMOSO-CARAZO Josefa LINARES-PEREZ
This paper presents recursive algorithms for the least mean-squared error linear filtering and fixed-interval smoothing estimators, from uncertain observations for the case of white and white plus coloured observation noises. The estimators are obtained by an innovation approach and do not use the state-space model, but only covariance information about the signal and the observation noises, as well as the probability that the signal exists in the observed values. Therefore the algorithms are applicable not only to signal processes that can be estimated by the conventional formulation using the state-space model but also to those for which a realization of the state-space model is not available. It is assumed that both the signal and the coloured noise autocovariance functions are expressed in a semi-degenerate kernel form. Since the semi-degenerate kernel is suitable for expressing autocovariance functions of non-stationary or stationary signal processes, the proposed estimators provide estimates of general signal processes.
Seiichi NAKAMORI Raquel CABALLERO-AGUILA Aurora HERMOSO-CARAZO Josefa LINARES-PEREZ
Least-squares second-order polynomial filter and fixed-point smoother are derived in systems with uncertain observations, when the variables describing the uncertainty are non-independent. The proposed estimators do not require the knowledge of the state-space model of the signal. The available information is only the moments, up to the fourth one, of the involved processes, the probability that the signal exists in the observations and the (2,2) element of the conditional probability matrices of the sequence describing the uncertainty.