María J. García-Ligero

Distributed fusion estimation in networked systems with uncertain observations and Markovian random delays

This paper addresses the least-squares linear estimation problem in networked systems with uncertain observations and one-step random delays in the measurements. The uncertainties in the observations and the delays are modeled by sequences of Bernoulli random variables with different characteristics for each sensor; the uncertainties are described by independent random variables whereas the delays are modeled by homogeneous Markov chains. The estimators are obtained by a distributed fusion method; specifically, for each sensor, local estimation algorithms are derived by using the information provided by the covariance functions of the processes involved in the observation model, as well as the probability distributions of the variables modeling the uncertainties and delays. The distributed fusion filter and fixed-point smoother are then obtained as the linear combination of the corresponding local linear estimators verifying that the mean squared error is minimum. HighlightsEstimation problem in a multi-sensor environment is considered.Uncertain observations and random delays are considered.Distributed filtering and fixed-point smoothing algorithms are proposed.The algorithms, based on covariances, are derived using an innovation approach.

Distributed and centralized fusion estimation from multiple sensors with Markovian delays

Abstract Least-squares linear estimation of signals from randomly delayed measurements acquired from multiple sensors with random delays modeled by homogeneous Markov chains is addressed. Assuming that the state-space model is unknown and using the information provided by the covariance functions of the processes involved in the observation equations, the signal estimation problem is studied by distributed and centralized methods to fuse the information provided by different sensors. Distributed and centralized filtering and fixed-point smoothing algorithms are derived using an innovation approach. The goodness of the proposed distributed and centralized filters and smoothers is compared by examining their respective error covariance matrices.

Filtering of images corrupted by multiplicative and white plus coloured additive noises using covariance information

This paper considers the restoration problem of images which are affected by multiple degradations. Under the assumption that the state-space model of the signal to be estimated is unknown, we propose an algorithm for the filtering problem of images which are corrupted by white plus coloured additive noises and multiplicative noise. Using the fact that the autocovariance functions of the signal and coloured noise are known and expressed in semi-degenerated kernel form, and the fact that the first and second-order moments of the multiplicative and white additive noises are also known, the least mean-squared error linear estimator is obtained. The proposed algorithm is applied to an image which has been corrupted by multiplicative and additive noises.

Estimation for discrete-time systems with multiple packet dropouts using covariance information

Abstract The problem is considered of estimating a signal based on measurements with multiple packet dropouts when the probability of data arrival at a processing unit is known. Assuming that the equation which describes the signal is unknown, we derive recursive algorithms for the prediction, filtering and smoothing problems using the information provided by the covariance functions of the processes involved in the measurement equation.

Derivation of linear estimation algorithms from measurements affected by multiplicative and additive noises

This paper addresses the problem of estimating signals from observation models with multiplicative and additive noises. Assuming that the state-space model is unknown, the multiplicative noise is non-white and the signal and additive noise are correlated, recursive algorithms are derived for the least-squares linear filter and fixed-point smoother. The proposed algorithms are obtained using an innovation approach and taking into account the information provided by the covariance functions of the process involved.

Derivation of fixed-interval smoothing algorithm using covariance information in distributed parameter systems

This paper proposes a recursive least mean squared error fixed-interval smoothing algorithm in distributed parameter systems. It is assumed that the state-space model of the signal to be estimated is unknown, and the algorithm only requires the second-order moments of the signal and the white noise perturbing its observations. Practical application of the proposed algorithm is illustrated with a restoration image problem.

Filtering in Generalized Signal-Dependent Noise Model Using Covariance Information

In this paper, we propose a recursive filtering algorithm to restore monochromatic images which are corrupted by general dependent additive noise. It is assumed that the equation which describes the image field is not available and a filtering algorithm is obtained using the information provided by the covariance functions of the signal, noise that affects the measurement equation, and the fourth-order moments of the signal. The proposed algorithm is obtained by an innovation approach which provides a simple derivation of the least mean-squared error linear estimators. The estimation of the grey level in each spatial coordinate is made taking into account the information provided by the grey levels located on the row of the pixel to be estimated. The proposed filtering algorithm is applied to restore images which are affected by general signal-dependent additive noise.

Derivation of centralized and distributed filters using covariance information

The problem of estimating a degraded image using observations acquired from multiple sensors is addressed when the image degradation is modelled by white multiplicative and additive noise. Assuming the state-space model is unknown, the centralized and distributed filtering algorithms are derived using the information provided by the covariance functions of the processes involved in the measurement equation. The filters obtained are applied to an image affected by multiplicative and additive noise, and the goodness of the centralized and distributed filters is compared by examining the respective filtering error variances.

Covariance-based least-squares filtering algorithm under Markovian measurement delays

ABSTRACT This paper addresses the least-squares linear filtering problem of signals from measurements which may be randomly delayed by one or two sampling times. The delays are modelled by a homogeneous discrete-time Markov chain to capture the dependence between them. Assuming that the evolution equation generating the signal is not available and that only the first- and second-order moments of the processes involved in the observation model are known, a recursive filtering algorithm is derived using an innovation approach. Recursive formulas for the filtering error variances are also obtained to measure the precision of the proposed estimators.