A new approach to distributed fusion filtering for networked systems with random parameter matrices and correlated noises

This paper is concerned with the distributed filtering problem for a class of discrete-time stochastic systems over a sensor network with a given topology. The system presents the following main features: (i) random parameter matrices in both the state and observation equations are considered; and (ii) the process and measurement noises are one-step autocorrelated and two-step cross-correlated. The state estimation is performed in two stages. At the first stage, through an innovation approach, intermediate distributed least-squares linear filtering estimators are obtained at each sensor node by processing available output measurements not only from the sensor itself but also from its neighboring sensors according to the network topology. At the second stage, noting that at each sampling time not only the measurement but also an intermediate estimator is available at each sensor, attention is focused on the design of distributed filtering estimators as the least-squares matrix-weighted linear combination of the intermediate estimators within its neighborhood. The accuracy of both intermediate and distributed estimators, which is measured by the error covariance matrices, is examined by a numerical simulation example where a four-sensor network is considered. The example illustrates the applicability of the proposed results to a linear networked system with state-dependent multiplicative noise and different network-induced stochastic uncertainties in the measurements; more specifically, sensor gain degradation, missing measurements and multiplicative observation noises are considered as particular cases of the proposed observation model.This research is supported by Ministerio de Economía y Competitividad and Fondo Europeo de Desarrollo Regional FEDER (grant no. MTM2014- 52291-P, MTM2017-84199-P)

Two Compensation Strategies for Optimal Estimation in Sensor Networks with Random Matrices, Time-Correlated Noises, Deception Attacks and Packet Losses

Due to its great importance in several applied and theoretical fields, the signal estimation problem in multisensor systems has grown into a significant research area. Networked systems are known to suffer random flaws, which, if not appropriately addressed, can deteriorate the performance of the estimators substantially. Thus, the development of estimation algorithms accounting for these random phenomena has received a lot of research attention. In this paper, the centralized fusion linear estimation problem is discussed under the assumption that the sensor measurements are affected by random parameter matrices, perturbed by time-correlated additive noises, exposed to random deception attacks and subject to random packet dropouts during transmission. A covariance-based methodology and two compensation strategies based on measurement prediction are used to design recursive filtering and fixed-point smoothing algorithms. The measurement differencing method— typically used to deal with the measurement noise time-correlation—is unsuccessful for these kinds of systems with packet losses because some sensor measurements are randomly lost and, consequently, cannot be processed. Therefore, we adopt an alternative approach based on the direct estimation of the measurement noises and the innovation technique. The two proposed compensation scenarios are contrasted through a simulation example, in which the effect of the different uncertainties on the estimation accuracy is also evaluated.Ministerio de Ciencia e Innovacion, Agencia Estatal de InvestigacionEuropean Commission PID2021-124486NB-I0

Networked fusion estimation with multiple uncertainties and time-correlated channel noise

This paper is concerned with the fusion filtering and fixed-point smoothing problems for a class of networked systems with multiple random uncertainties in both the sensor outputs and the transmission connections. To deal with this kind of systems, random parameter matrices are considered in the mathematical models of both the sensor measurements and the data available after transmission. The additive noise in the transmission channel from each sensor is assumed to be sequentially time-correlated. By using the time-differencing approach, the available measurements are transformed into an equivalent set of observations that do not depend on the timecorrelated noise. The innovation approach is then applied to obtain recursive distributed and centralized fusion estimation algorithms for the filtering and fixed-point smoothing estimators of the signal based on the transformed measurements, which are equal to the estimators based on the original ones. The derivation of the algorithms does not require the knowledge of the signal evolution model, but only the mean and covariance functions of the processes involved (covariance information). A simulation example illustrates the utility and effectiveness of the proposed fusion estimation algorithms, as well as the applicability of the current model to deal with different network-induced random phenomena.This research is supported by Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación and Fondo Europeo de Desarrollo Regional FEDER (grant no. MTM2017-84199-P)

Networked distributed fusion estimation under uncertain outputs with random transmission delays, packet losses and multi-packet processing

This paper investigates the distributed fusion estimation problem for networked systems whose mul- tisensor measured outputs involve uncertainties modelled by random parameter matrices. Each sensor transmits its measured outputs to a local processor over different communication channels and random failures –one-step delays and packet dropouts–are assumed to occur during the transmission. White sequences of Bernoulli random variables with different probabilities are introduced to describe the ob- servations that are used to update the estimators at each sampling time. Due to the transmission failures, each local processor may receive either one or two data packets, or even nothing and, when the current measurement does not arrive on time, its predictor is used in the design of the estimators to compensate the lack of updated information. By using an innovation approach, local least-squares linear estimators (filter and fixed-point smoother) are obtained at the individual local processors, without requiring the signal evolution model. From these local estimators, distributed fusion filtering and smoothing estimators weighted by matrices are obtained in a unified way, by applying the least-squares criterion. A simula- tion study is presented to examine the performance of the estimators and the influence that both sensor uncertainties and transmission failures have on the estimation accuracy.This research is supported by Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación and Fondo Europeo de Desarrollo Regional FEDER (grant no. MTM2017-84199-P)

Unreliable networks with random parameter matrices and time-correlated noises: distributed estimation under deception attacks

This paper examines the distributed filtering and fixed-point smoothing problems for networked systems, considering random parameter matrices, time-correlated additive noises and random deception attacks. The proposed distributed estimation algorithms consist of two stages: the first stage creates intermediate estimators based on local and adjacent node measurements, while the second stage combines the intermediate estimators from neighboring sensors using least-squares matrix-weighted linear combinations. The major contributions and challenges lie in simultaneously considering various network-induced phenomena and providing a unified framework for systems with incomplete information. The algorithms are designed without specific structure assumptions and use a covariance-based estimation technique, which does not require knowledge of the evolution model of the signal being estimated. A numerical experiment demonstrates the applicability and effectiveness of the proposed algorithms, highlighting the impact of observation uncertainties and deception attacks on estimation accuracy

Uncertainty-Aware Principal Component Analysis

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to non-linear methods, linear dimensionality reduction techniques have the advantage that the characteristics of such probability distributions remain intact after projection. We derive a representation of the PCA sample covariance matrix that respects potential uncertainty in each of the inputs, building the mathematical foundation of our new method: uncertainty-aware PCA. In addition to the accuracy and performance gained by our approach over sampling-based strategies, our formulation allows us to perform sensitivity analysis with regard to the uncertainty in the data. For this, we propose factor traces as a novel visualization that enables to better understand the influence of uncertainty on the chosen principal components. We provide multiple examples of our technique using real-world datasets. As a special case, we show how to propagate multivariate normal distributions through PCA in closed form. Furthermore, we discuss extensions and limitations of our approach

Linear Estimation in Interconnected Sensor Systems with Information Constraints

A ubiquitous challenge in many technical applications is to estimate an unknown state by means of data that stems from several, often heterogeneous sensor sources. In this book, information is interpreted stochastically, and techniques for the distributed processing of data are derived that minimize the error of estimates about the unknown state. Methods for the reconstruction of dependencies are proposed and novel approaches for the distributed processing of noisy data are developed

Linear Estimation in Interconnected Sensor Systems with Information Constraints

A ubiquitous challenge in many technical applications is to estimate an unknown state by means of data that stems from several, often heterogeneous sensor sources. In this book, information is interpreted stochastically, and techniques for the distributed processing of data are derived that minimize the error of estimates about the unknown state. Methods for the reconstruction of dependencies are proposed and novel approaches for the distributed processing of noisy data are developed

Fusion Estimation from Multisensor Observations with Multiplicative Noises and Correlated Random Delays in Transmission

In this paper, the information fusion estimation problem is investigated for a class of multisensor linear systems affected by different kinds of stochastic uncertainties, using both the distributed and the centralized fusion methodologies. It is assumed that the measured outputs are perturbed by one-step autocorrelated and cross-correlated additive noises, and also stochastic uncertainties caused by multiplicative noises and randomly missing measurements in the sensor outputs are considered. At each sampling time, every sensor output is sent to a local processor and, due to some kind of transmission failures, one-step correlated random delays may occur. Using only covariance information, without requiring the evolution model of the signal process, a local least-squares (LS) filter based on the measurements received from each sensor is designed by an innovation approach. All these local filters are then fused to generate an optimal distributed fusion filter by a matrix-weighted linear combination, using the LS optimality criterion. Moreover, a recursive algorithm for the centralized fusion filter is also proposed and the accuracy of the proposed estimators, which is measured by the estimation error covariances, is analyzed by a simulation example.This research is supported by Ministerio de Economía y Competitividad and Fondo Europeo de Desarrollo Regional FEDER (grant No. MTM2014-52291-P)

Quadratic estimation for stochastic systems in the presence of random parameter matrices, time-correlated additive noise and deception attacks

This research was suported by the ``Ministerio de Ciencia e Innovación, Agencia Estatal de Investigación'' of Spain and the European Regional Development Fund [grant number PID2021-124486NB-I00].Networked systems usually face different random uncertainties that make the performance of the least-squares (LS) linear filter decline significantly. For this reason, great attention has been paid to the search for other kinds of suboptimal estimators. Among them, the LS quadratic estimation approach has attracted considerable interest in the scientific community for its balance between computational complexity and estimation accuracy. When it comes to stochastic systems subject to different random uncertainties and deception attacks, the quadratic estimator design has not been deeply studied. In this paper, using covariance information, the LS quadratic filtering and fixed-point smoothing problems are addressed under the assumption that the measurements are perturbed by a time-correlated additive noise, as well as affected by random parameter matrices and exposed to random deception attacks. The use of random parameter matrices covers a wide range of common uncertainties and random failures, thus better reflecting the engineering reality. The signal and observation vectors are augmented by stacking the original vectors with their second-order Kronecker powers; then, the linear estimator of the original signal based on the augmented observations provides the required quadratic estimator. A simulation example illustrates the superiority of the proposed quadratic estimators over the conventional linear ones and the effect of the deception attacks on the estimation performance.Ministerio de Ciencia e Innovación MICINNEuropean Regional Development Fund PID2021-124486NB-I00 ERDFAgencia Estatal de Investigación AE