Centralized Fusion White Noise Estimator for Multi-sensor Systems with Missing Measurements

White noise deconvolution or input white noise estimation problem has important application backgrounds in oil seismic exploration, communication and signal processing. By the modern time series analysis method, based on the autoregressive moving average (ARMA) innovation model, under the linear minimum variance optimal fusion rules, three optimal weighted fusion white noise deconvolution estimators are presented for the multisensor systems with different local dynamic models and correlated noises, respectively. They can handle the input white noise fused filtering, prediction and smoothing problems, and are applicable for the multisensor systems with colored measurement noises. They are locally optimal and globally suboptimal. The accuracy of the fusers is higher than that of each local white noise estimator, and is lower than that of the centralized fuser. In order to compute the optimal weights, the formula of computing the local estimation error cross-covariances is given. A Monte Carlo simulation example for the system with 3 sensors and the Bernoulli-Gaussian input white noise shows their effectiveness and performances.

This paper is concerned with the design of networked multi-sensor fusion estimation system (NMFES). The Kalman filtering problem is considered for the NMFES with random observation delays, packet dropouts and missing measurements caused by sensor failures. For each observation subsystem, the sensor failure phenomenon is described by a Bernoulli distributed white sequence with a known conditional probability, and the packet dropout phenomenon and randomly delayed measurements are described by multiple binary random variables. Without resorting to the augmentation technique, an optimal recursive fusion filter for NMFES is obtained in the linear minimum variance sense by using the innovation analysis method. The dimension of the designed filter is the same to the original system, which can help reduce computation costs as compared with the augmentation method. Moreover, the performance of the designed Kalman filter is dependent on the missing rates of the measurements, the upper bounds of random delays and the occurrence probabilities of delays. Finally, the effectiveness of the proposed results is demonstrated by an illustrative example.

Using the innovation analysis method in the time domain, based on the autoregressive moving average (ARMA) innovation model and white noise estimators, a pole-assignment fixed-interval steady-state Kalman smoother is presented for discrete-time linear stochastic systems. It avoids the computation of the optimal initial smoothing estimate, and can rapidly eliminate the effect of arbitrary initial smoothing estimate by assigning the poles of the smoother, with an exponentially decaying rate. Several simulation examples show its effectiveness.

This article is concerned with the centralized fusion (CF) robust steady‐state Kalman filtering problem for a class of multisensor networked systems with mixed uncertainties including state‐dependent and noise‐dependent multiplicative noises, missing measurements, packet dropouts, and uncertain noise variances. By using a model transformation approach, the initial multisensor system under study is transformed into a multi‐model multisensor system only with uncertain noise variances. By introducing an augmented state vector, the CF system is obtained. In the light of the minimax robust estimation method, and based on the worst‐case fusion system with conservative upper bounds of uncertain noise variances, the CF robust steady‐state Kalman estimators (predictor, filter, and smoother) are proposed in a unified form. By means of the permutation matrices and Lyapunov equation method, the robustness of CF estimators is proved. The accuracy relations among the robust local and fusion steady‐state estimators are proved. An example applied to autoregressive moving average signal estimation is put forward, and the robust CF steady‐state signal estimators are proposed. Simulation experiment shows the correctness of the proposed approach.

In this paper, an H ∞ filter design problem is studied for networked stochastic linear discrete-time systems with mixed uncertainties of random measurement delays, packet dropouts and missing measurements. We model the packet delivery characteristics of the network as a four-state Markov process and note that the results for discrete-time linear systems with Markovian jumping parameters can be applied. We focus on the design problem of a full-order H ∞ filter such that for all possible uncertain measurements the filtering error dynamics is exponentially mean square stable and a prescribed H ∞ performance bound is guaranteed. Necessary and sufficient bilinear matrix inequality (BMI) condition for the synthesis of the aforementioned filter for a discrete-time jump system is presented. Some simulation examples are presented to show the applicability and effectiveness of the proposed approach.

A Unified Approach to Optimal State Estimation for Stochastic Singular Systems

Fusion identification and estimation of multisensor multichannel AR signals with missing measurements and sensor biases

Multisensor distributed information fusion state estimator is presented in this paper. The algorithm deals with descriptor and non descriptor discrete time time-invariant stochastic linear system which is described by state space model. Under the assumption of the observability of the system, the state of the system is a linear combination of input white noise, observation white noise and observation signal. Further non-recursive state estimators algorithm is presented, which can be computed by the white noise estimators and measurement predictor. In order to improve the accuracy of the state estimator, this paper presents information fusion algorithm including matrix weighted, diagonal matrices weighted, scalar weighted and covariance intersection fusion, in the sense of linear minimum variance. The formula of optimal weighting coefficients is given. The algorithm analyzes the relationship between the accuracy and the computation of the four fusion algorithm. A simulation example for non descriptor system with 3 sensors shows its correctness and effectiveness.

For the multisensor linear discrete time-invariant systems with unknown constant input and unknown noise statistics, the on-line estimators of unknown input and unknown noise statistics are obtained based on CARMA innovation model. For the multisensor stochastic control systems with known input and noise statistics, the optimal information fusion steady-state white noise estimator is presented based on Fadeeva formula. Furthermore, a self-tuning information fusion white noise estimator with input estimation is presented. Based on the dynamic error system analysis method, its asymptotic optimality is proved, i.e. it converges to the optimal fusion steady-state white noise estimator in a realization. A simulation example for a 3-sensor system with Bernoulli-Gaussian input white noise shows its effectiveness.

For the practical multisensor systems, the communication channels are often unreliable, especially in large, wireless, multi hop sensor networks. Thus, the communication delays often appear and produce random and unknown influence upon the performance of fusion estimators. Recently, data fusion for "Out-of-sequence" measurements (OOSM) attracts a mass of attentions gradually and some filters based on single sensor and multiple sensors have been reported. However, the existing methods for OOSM problem have several shortcomings, such as limited application for single sensor, bad real-time performance for the smooth property, low fusion estimate for neglecting the delayed information, and so forth. To tackle these problems, a novel batch fusion estimator based on the relative measurements for multisensor tracking systems with OOSM is proposed. The estimator is optimal in linear minimum mean square error (LMMSE). The paper also presents the suboptimal recursive form of the proposed estimator. Its principle is to establish the relative measurement equations of delayed observations to the next latest systemic state. Compared with some existingfusion methods for OOSM, the proposed method with arbitrary time delays has the best total performance. At the same time, algorithm analysis and computer simulation validate the advantages of the proposed fusion estimator.

Using the modern time-series analysis method in the time domain, based on the autoregressive moving average (ARMA) innovation model and white noise estimator, non-regular descriptor discrete-time stochastic linear systems are researched. Under assumption 1~3, an asymptotically stable reduced-order Wiener state estimator for descriptor systems is given by using projection and block matrix theories. Non-regular descriptor systems include general descriptor systems in them. And the algorithm is reduced-order. It avoids the solution of the Riccati equations and Diophantine equations. So that it reduces the computational burden, and is suitable for real time applications.

The prediction and smoothing fusion problems in multisensor systems with mixed uncertainties and correlated noises are addressed in the tessarine domain, under Tk-properness conditions. Bernoulli distributed random tessarine processes are introduced to describe one-step randomly delayed and missing measurements. Centralized and distributed fusion methods are applied in a Tk-proper setting, k=1,2, which considerably reduce the dimension of the processes involved. As a consequence, efficient centralized and distributed fusion prediction and smoothing algorithms are devised with a lower computational cost than that derived from a real formalism. The performance of these algorithms is analyzed by using numerical simulations where different uncertainty situations are considered: updated/delayed and missing measurements.

In this paper, we are concerned with the robust filtering problem for a class of nonlinear discrete time-delay stochastic systems. The system under consideration involves parameter uncertainties, stochastic disturbances, time-varying delays and sector nonlinearities. Both missing measurements and randomly occurring nonlinearities are described via the binary switching sequences satisfying a conditional probability distribution, and the nonlinearities are assumed to be sector bounded. The problem addressed is the design of a full-order filter such that, for all admissible uncertainties, nonlinearities and time-delays, the dynamics of the filtering error is constrained to be robustly exponentially stable in the mean square, and a prescribed disturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and some new techniques, sufficient conditions are first established to ensure the existence of the desired filtering parameters. Then, the explicit expression of the desired filter gains is described in terms of the solution to a linear matrix inequality. Finally, a numerical example is exploited to show the usefulness of the results derived.

The optimal least-squares linear estimation problem is addressed for a class of discrete-time multisensor linear stochastic systems with missing measurements and autocorrelated and cross-correlated noises. The stochastic uncertainties in the measurements coming from each sensor (missing measurements) are described by scalar random variables with arbitrary discrete probability distribution over the interval[0,1]; hence, at each single sensor the information might be partially missed and the different sensors may have different missing probabilities. The noise correlation assumptions considered are (i) the process noise and all the sensor noises are one-step autocorrelated; (ii) different sensor noises are one-step cross-correlated; and (iii) the process noise and each sensor noise are two-step cross-correlated. Under these assumptions and by an innovation approach, recursive algorithms for the optimal linear filter are derived by using the two basic estimation fusion structures; more specifically, both centralized and distributed fusion estimation algorithms are proposed. The accuracy of these estimators is measured by their error covariance matrices, which allow us to compare their performance in a numerical simulation example that illustrates the feasibility of the proposed filtering algorithms and shows a comparison with other existing filters.

This paper presents the stabilization problem of a class of discrete-time stochastic linear systems with time delay using an event-triggered control(ETC) strategy. For the general linear systems, we propose a new event triggering mechanism and deduce sufficient conditions for mean square exponentially stabilizability(MSES) and almost sure exponentially stabilizability(ASES) via ETC. The results show that the stability of the system depends on the system parameters (time delay, noise, event trigger threshold parameter, and unstable characteristic value of the original system). When the feedback control is disturbed by low-intensity noise, the unstable system can be stable in the mean square. Finally, the validity of the theoretical results is illustrated through a simulation example.