Sequential fusion estimation for state-saturated nonlinear complex networks: a centre difference set-membership approach by zonotopes

ABSTRACTThis 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 covariance-based 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.

Sequential fusion estimation for clustered sensor networks

This paper focuses on the linear optimal recursive sequential fusion filter design for multisensor systems subject to stochastic parameter perturbations, fading measurements, and correlated noises. The stochastic parameter perturbations existing in the state model are described by white multiplicative noises. The fading measurement phenomena for different sensors are described by independent random variables with known statistical properties. Moreover, the measurement noises of different sensors are correlated with each other and also correlated with the system noise at the same time step. First, a model equivalent to the original system is established by transferring the multiplicative noises into the additive noises. Then, based on the equivalent model and an innovation analysis method, a sequential fusion filter in the linear minimum variance sense is proposed to solve the linear optimal state estimation problem in real time according to the arriving order of measurements from different sensors. Finally, the equivalence on estimation accuracy of the proposed sequential fusion filter and the centralized fusion filter is strictly proven, which shows the optimality of the proposed sequential fusion algorithm. Moreover, the proposed sequential fusion filter has a reduced computational burden. Compared with the distributed matrix-weighted fusion filter, the computation of cross-covariance matrices is avoided and the estimation accuracy is improved. Finally, a simulation example verifies the effectiveness of the proposed sequential fusion filtering algorithm.

In this article, the sequential fusion estimation problem is investigated for multirate complex networks (MRCNs) with uniformly quantized measurements. The process and measurement noises, which are unknown-yet-bounded (UYB), are restrained into a family of zonotopes, and the multiple sensors are allowed to have different sampling periods. To facilitate digital transmissions, the sensor measurements are uniformly quantized before being sent to the remote estimator. The purpose of this article is to design a sequential set-membership estimator such that, in the simultaneous presence of UYB noises, multirate samplings, and uniform quantization effects, the estimation error (after each measurement update) is confined to a zonotope with minimum F -radius at each time instant. By introducing certain virtual measurements, the MRCNs are first transformed into single-rate ones exhibiting a switching phenomenon. Then, by utilizing the properties of zonotopes, the desired zonotopes are derived, which contain the estimation error dynamics after each measurement update. Subsequently, the gain matrices of the sequential estimator are derived by minimizing the F -radii of these zonotopes, and the uniform boundedness is analyzed for the F -radius of the zonotope containing the estimation error after all measurement updates. Furthermore, sufficient conditions are derived to ensure the existence of the desired uniform upper/lower bounds. Finally, an illustrated example is proposed to show the effectiveness of the proposed sequential fusion estimation method.

Watermarking-based remote secure sequential fusion estimation under the event-triggered mechanism

This paper investigates the suboptimal sequential fusion estimation problem for multisensor multirate networked systems with colored measurement noises under the interference of measurement outliers. The saturation function is used to constrain the innovation polluted by measurement outliers. Due to diverse physical restrictions, the sampling period of the sensor is assumed to be different from the update period of the system state, thereby better reflecting the engineering practice. The lifting technique is used to convert the multirate sampling system into a single‐rate form. By solving the matrix difference equation, an upper bound of the filtering error covariance is obtained, and the filter gain is then derived, which can minimize the upper bound of the error covariance. Finally, a simulation example is given to demonstrate the effectiveness of the proposed sequential fusion method for multirate sampling systems under outlier interference.

This paper concentrates on a globally sequential fusion state estimation problem for clustered wireless sensor networks (WSNs). Therein, frequent data communications in WSN will significantly increase energy consumption and communication burden, and it needs to be taken into account. To reduce unnecessary data transmissions and save energy, an event-triggered mechanism that decides whether the current measurement should be transmitted or not, therefore, is introduced. Then a novel variational Bayesian based event-triggered sequential measurement fusion (VB-ESMF) estimator is proposed to produce the local fused results of the clustered WSNs, where the variational Bayesian approach is used to infer the measurement noise covariance matrices of pseudo measurement noises. Therein, the local fused measurements of the clusters in the clustered WSNs are used sequentially by the remote fusion center, and thus a global fusion state estimation, which is globally optimal when all measurements are transmitted successfully, is computed. Additionally, certain boundedness and convergence conditions of the proposed estimator are derived, and an expected compromise between communication rate and estimation accuracy can be obtained by properly turning the trigger threshold. Finally, the effectiveness of both the VB-ESMF estimation and the globally sequential fusion state estimation is illustrated by simulation results.

In this paper, the problem of interactive multi-model (IMM) based sequential fusion estimation with heavy-tailed noise in an unreliable transmission environment is considered. The measurement values are affected by random packet loss during transmission. For non-Gaussian noise, the Student’s t-distribution is used to model the heavy-tailed noise that appears in some practical scenarios. An IMM estimation method is effectively combined with the Student’s t-distribution to investigate a multi-model filtering algorithm. On this basis, a corresponding sequential fusion algorithm is proposed. Finally, the effectiveness of the algorithm is verified by a target tracking example simulation.

We study a sequential fusion estimation problem for Markov jump multi-sensor systems with heavy-tailed noises. By modelling the noises as Student's t distributions, a sequential fusion estimation algorithm is designed by utilising the interacting multiple model method and Bayes' rule. To improve the robustness against measurement outliers caused by measurement heavy-tailed noise, an F-distribution detection strategy is designed to detect and reject the measurement outliers. Simulation results demonstrate that the designed sequential fusion estimation algorithm can effectively fuse the measurements from multiple sensors, and the accuracy of the designed algorithm is superior to the existing interacting multiple model Student's t batch fusion algorithm and single model adaptive Student's t batch fusion algorithm when there exist model switching and disturbances with heavy-tailed property.

A sequential fusion and state estimation algorithm for an asynchronous multirate multisensor dynamic system is presented in this paper. The dynamic system at the finest scale is known. There are multiple sensors observing a single target independently with different sampling rates, and the observations are obtained asynchronously. The present algorithm is shown to be more effective and efficient than the existed methods. Simulations on a radar tracking system with three sensors are done and show the effectiveness of the present algorithm.

The accuracy of interval estimation systems is usually measured using interval lengths for given covering probabilities. The confidence intervals are the intervals of a fixed width if the length of the interval is determined, i.e., not random, and tends to zero for a given covering probability. We consider two important directions of statistical analysis -sequential interval estimation with confidence intervals of fixed width and sequential point estimation with asymptotically minimum risk. Two statistical models are used to describe the basis problems of sequential interval estimation by confidence intervals of a fixed width and point estimation. A review of data on nonparametric sequential estimation is carried out and new original results obtained by the authors are presented. Sequential analysis is characterized by the fact that the moment of termination of observations (stopping time) is random and is determined depending on the values of the observed data and on the adopted measure of optimality of the constructed statistical estimate. Therefore, to solve the asymptotic problems of sequential estimation, the methods of summation of random variables are used. To prove the asymptotic consistency of the confidence intervals of a fixed width, we used a method based on application of limit theorems for randomly stopped random processes. General conditions of the consistency and efficiency of sequential interval estimation of a wide class of functionals of an unknown distribution function are obtained and verified by sequential interval estimation of an unknown probability density of asymptotically uncorrelated and linear processes. Conditions of the regularity are specified that provide the property of being an estimate with an asymptotically minimum risk for a wide class of estimates and loss functions. Those conditions are verified by sequential point estimation of an unknown distribution function.

This paper presents a hybrid sequential fusion estimation method for target tracking in asynchronous wireless sensor networks (WSNs). The model mismatching caused by asynchronous sampling, as well as model uncertainties, is compensated by introducing a time-varying fading factor into the unscented Kalman filter (UKF) and the square root unscented strong tracking filter (SR-USTF) is proposed to improve the stability of the USTF. Moreover, a hybrid sequential measurement fusion estimation method, combining the merits of the UKF and the USTF, is presented and it is able to deal with communication uncertainties such as delays and packet losses in a uniform framework. Simulations of mobile robot tracking are provided to show the effectiveness and superiorities of the proposed hybrid sequential fusion estimation method.

Global state estimation under sequential measurement fusion for clustered sensor networks with cross-correlated measurement noises

In this paper, the impact of the fusion framework on the fault diagnosis process is discussed. The centralized fusion framework makes it difficult to locate and estimate the sensor fault. Based on the fault detection method, the sequential fusion framework could locate and estimate the sensor fault and realize the fault-tolerant estimation of system states. In the sense of minimum mean square error (MMSE), based on the sequential detection of bias fault of sensors, a sequential fault-tolerant fusion estimation approach is presented to estimate the sensor fault and the system state, simultaneously, optimally, in real time. Further, a novel alternate fault-tolerant fusion estimation method is proposed to alternately estimate the sensor fault and the system state, in the frame of sequential fusion. What is more, the equivalency of the two proposed methods is proved. And the feasibility and equivalency of them are also verified by the computer simulation.

This paper is concerned with the state estimation problem for non-uniform sampling systems subject to fading measurements. The concerned non-uniform sampling scheme is that the state is updated uniformly and the measurements are sampled randomly. Moreover, the fading measurement phenomena may occur in different sensor measurement channels where the independent random variables obeying different certain probability distributions over different known intervals are employed to describe this phenomena. Firstly, a new state space model is established to depict the dynamics at the measurement sampling points within a state update period. Then, based on single sensor measurements, the non-augmented state estimator is proposed by applying an innovation analysis approach. Finally, the sequential inverse covariance intersection fusion estimation algorithm is proposed for the multi-sensor case. The simulation research verifies the effectiveness of the proposed estimation algorithms.