José D. Jiménez-López

Signal estimation with multiple delayed sensors using covariance information

Recursive filtering and smoothing algorithms to estimate a signal from noisy measurements coming from multiple randomly delayed sensors, with different delay characteristics, are proposed. To design these algorithms an innovation approach is used, assuming that the state-space model of the signal is unknown and using only covariance information. To measure the precision of the proposed estimators formulas to calculate the filtering and smoothing error covariance matrices are also derived. The effectiveness of the estimators is illustrated by a numerical simulation example where a signal is estimated using observations from two randomly delayed sensors having different delay properties.

Signal estimation based on covariance information from observations featuring correlated uncertainty and coming from multiple sensors

The linear least-squares estimation problem of signals from observations coming from multiple sensors is addressed when there is a non-zero probability that each observation does not contain the signal to be estimated (uncertain observations). At each sensor, this uncertainty in the observations is modeled by a sequence of Bernoulli random variables correlated at consecutive sampling times. To estimate the signal, recursive filtering and (fixed-point and fixed-interval) smoothing algorithms are derived without requiring the knowledge of the signal state-space model but only the means and covariance functions of the processes involved in the observation equations, the uncertainty probabilities and the correlation between the variables modeling the uncertainty. To measure the estimation accuracy, recursive expressions for the estimation error covariance matrices are also proposed. The theoretical results are illustrated by a numerical simulation example where a signal is estimated from observations featuring correlated uncertainty and coming from two sensors with different uncertainty characteristics.

Least-squares linear filtering using observations coming from multiple sensors with one- or two-step random delay

This paper discusses the least-squares linear filtering problem of discrete-time signals using observations from multiple sensors which can be randomly delayed by one or two sampling times. It is assumed that, at each sensor, the signal is measured in the presence of additive white noise, that the Bernoulli random variables modelling the delays are independent and that the delay probabilities are not necessarily the same for all the sensors. A recursive filtering algorithm is proposed, and derivation of this does not require knowledge of the signal state-space model, but only the covariance functions of the processes involved in the observation equation of each sensor, as well as the delay probabilities. Recursive expressions for the filtering error covariance matrices are also provided, and the performance of the proposed estimator is illustrated by a numerical simulation example in which a scalar signal is estimated from one- or two-step randomly delayed observations from two sensors with different delay characteristics.

Recursive estimation of discrete-time signals from nonlinear randomly delayed observations

In this paper, one-stage prediction, filtering, and fixed-point smoothing problems are addressed for nonlinear discrete-time stochastic systems with randomly delayed measurements perturbed by additive white noise. The observation delay is modelled by a sequence of independent Bernoulli random variables whose values-zero or one-indicate that the real observation arrives on time or it is delayed one sampling time and, hence, the available measurement to estimate the signal is not updated. Assuming that the state-space model generating the signal to be estimated is unknown and only the covariance functions of the processes involved in the observation equation are available, recursive estimation algorithms based on linear approximations of the real observations are proposed.

Signal estimation with nonlinear uncertain observations using covariance information

This paper addresses the signal estimation problem in situations where the observations are nonlinear functions of the signal and the measure mechanism is prone to failure or some observations are accidentally lost (uncertain observations). A recursive filtering and fixed-point smoothing algorithm is proposed assuming that the Bernoulli random variables describing the uncertainty in the observations are independent and the state-space model generating the signal is unknown and only the covariance functions of the processes involved in the observation equation are available. A numerical simulation example concerning the phase modulation problem shows the effectiveness of the proposed algorithm.

Recursive fixed-point smoothing algorithm from covariances based on uncertain observations with correlation in the uncertainty

This paper considers the least-squares linear estimation problem of a discrete-time signal from noisy observations in which the signal can be randomly missing. The uncertainty about the signal being present or missing at the observations is characterized by a set of Bernoulli variables which are correlated when the difference between times is equal to a certain value m. The marginal distribution of each one of these variables, specified by the probability that the signal exists at each observation, as well as their correlation function, are known. A linear recursive filtering and fixed-point smoothing algorithm is obtained using an innovation approach without requiring the state-space model generating the signal, but just the covariance functions of the processes involved in the observation equation.

Chandrasekhar-type filter for a wide-sense stationary signal from uncertain observations using covariance information

In this paper, the least mean-squared error linear filtering problem of a wide-sense stationary signal, from uncertain observations perturbed by a white noise, is approached by means of a Chandrasekhar-type recursive algorithm. In comparison with a Riccati-type algorithm, the proposed algorithm is more advantageous from a computational point of view, since it reduces the number of difference equations contained in it and, consequently, the computation time. The algorithm is derived by using covariance information, without requiring that the state-space model of the signal is completely known.

Polynomial fixed-point smoothing of uncertainly observed signals based on covariances

In this article, the least-squares νth-order polynomial fixed-point smoothing problem of uncertainly observed signals is considered, when only some information about the moments of the processes involved is available. For this purpose, a suitable augmented observation equation is defined such that the optimal polynomial estimator of the original signal is obtained from the optimal linear estimator of the augmented signal based on the augmented observations and, hence, a recursive algorithm for this linear estimator is deduced. The proposed estimator does not require the knowledge of the state-space model of the signal, but only the moments (up to the 2νth one) of the signal and observation noise, as well as the probability that the signal exists in the observations.

Recursive smoothing algorithms for the estimation of signals from uncertain observations via mixture approximations

Considering discrete-time systems with uncertain observations when the signal model is unknown, but only covariance information is available, and the signal and the observation additive noise are correlated and jointly Gaussian, we present recursive algorithms for suboptimal fixed-point and fixed-interval smoothing estimators. To derive the algorithms, we employ a technique consisting in approximating the conditional distributions of the signal given the observations by Gaussian distributions, taking successive approximations of the mixtures of normal distributions. The expectation of these approximations provides us with the suboptimal estimators. In a numerical simulation example, the performance of the proposed estimators is compared with that of linear ones, via the sample mean square values of the corresponding estimation errors.

Recursive Estimation Algorithm Based on Covariances for Uncertainly Observed Signals Correlated with Noise

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.