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)

Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

Recent advances on recursive filtering and sliding mode design for networked nonlinear stochastic systems: A survey

Copyright © 2013 Jun Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Some recent advances on the recursive filtering and sliding mode design problems for nonlinear stochastic systems with network-induced phenomena are surveyed. The network-induced phenomena under consideration mainly include missing measurements, fading measurements, signal quantization, probabilistic sensor delays, sensor saturations, randomly occurring nonlinearities, and randomly occurring uncertainties. With respect to these network-induced phenomena, the developments on filtering and sliding mode design problems are systematically reviewed. In particular, concerning the network-induced phenomena, some recent results on the recursive filtering for time-varying nonlinear stochastic systems and sliding mode design for time-invariant nonlinear stochastic systems are given, respectively. Finally, conclusions are proposed and some potential future research works are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61329301, 61333012, 61374127 and 11301118, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant no. GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

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)

Optimal Fusion Estimation with Multi-Step Random Delays and Losses in Transmission

This paper is concerned with the optimal fusion estimation problem in networked stochastic systems with bounded random delays and packet dropouts, which unavoidably occur during the data transmission in the network. The measured outputs from each sensor are perturbed by random parameter matrices and white additive noises, which are cross-correlated between the different sensors. Least-squares fusion linear estimators including filter, predictor and fixed-point smoother, as well as the corresponding estimation error covariance matrices are designed via the innovation analysis approach. The proposed recursive algorithms depend on the delay probabilities at each sampling time, but do not to need to know if a particular measurement is delayed or not. Moreover, the knowledge of the signal evolution model is not required, as the algorithms need only the first and second order moments of the processes involved. Some of the practical situations covered by the proposed system model with random parameter matrices are analyzed and the influence of the delays in the estimation accuracy are examined in a numerical example.This research is supported by the “Ministerio de Economía y Competitividad” and “Fondo Europeo de Desarrollo Regional” FEDER (Grant No. MTM2014-52291-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)

Centralized, distributed and sequential fusion estimation from uncertain outputs with correlation between sensor noises and signal

This paper focuses on the least-squares linear fusion filter design for discrete-time stochastic signals from multisensor measurements perturbed not only by additive noise, but also by different uncertainties that can be comprehensively modeled by random parameter matrices. The additive noises from the different sensors are assumed to be cross-correlated at the same time step and correlated with the signal at the same and subsequent time steps. A covariancebased approach is used to derive easily implementable recursive filtering algorithms under the centralized, distributed and sequential fusion architectures. Although centralized and sequential estimators both have the same accuracy, the evaluation of their computational complexity reveals that the sequential filter can provide a significant reduction of computational cost over the centralized one. The accuracy of the proposed fusion filters is explored by a simulation example, where observation matrices with random parameters are used to describe different kinds of sensor uncertainties.This research is supported by Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación and Fondo Europeo de Desarrollo Regional FEDER [grant number MTM2017- 84199-P]

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)

Centralized filtering and smoothing algorithms from outputs with random parameter matrices transmitted through uncertain communication channels

The least-squares linear centralized estimation problem is addressed for discrete-time signals from measured outputs whose disturbances are modeled by random parameter matrices and correlated noises. These measurements, coming from different sensors, are sent to a processing center to obtain the estimators and, due to random transmission failures, some of the data packet processed for the estimation may either contain only noise (uncertain observations), be delayed (sensor delays) or even be definitely lost (packet dropouts). Different sequences of Bernoulli random variables with known probabilities are employed to describe the multiple random transmission uncertainties of the different sensors. Using the last observation that successfully arrived when a packet is lost, the optimal linear centralized fusion estimators, including filter, multi-step predictors and fixed-point smoothers, are obtained via an innovation approach; this approach is a general and useful tool to find easily implementable recursive algorithms for the optimal linear estimators under the least-squares optimality criterion. The proposed algorithms are obtained without requiring the evolution model of the signal process, but using only the first and second-order moments of the processes involved in the measurement model.This research is supported by Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigaciónand Fondo Europeo de Desarrollo Regional FEDER (grant no. MTM2017-84199-P)