Robust centralized and weighted measurement fusion white noise deconvolution estimators for multisensor systems with mixed uncertainties

Estimating the input signal of a system is called deconvolution or input estimation. The white noise deconvolution has important applications in oil seismic exploration, communications, and signal processing. This paper addresses the design of robust centralized fusion (CF) and weighted measurement fusion (WMF) white noise deconvolution estimators for a class of uncertain multisensor systems with mixed uncertainties, including uncertain‐variance multiplicative noises in measurement matrix, missing measurements, and uncertain‐variance linearly correlated measurement and process white noises. By introducing the fictitious noise, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with the conservative upper bounds of uncertain noise variances, the robust CF and WMF time‐varying white noise deconvolution estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities are analyzed and compared. Compared with the CF algorithm, the WMF algorithms can significantly reduce the computational burden when the number of sensors is larger. The corresponding robust fused steady‐state white noise deconvolution estimators are also presented. A simulation example with respect to the multisensor IS‐136 communication systems shows the effectiveness and correctness of the proposed results.     

Hierarchical fusion robust Kalman filter for clustering sensor network time‐varying systems with uncertain noise variances

For the clustering time‐varying sensor network systems with uncertain noise variances, according to the minimax robust estimation principle, based on the worst‐case conservative system with conservative upper bounds of noise variances, applying the optimal Kalman filtering, the two‐level hierarchical fusion time‐varying robust Kalman filter is presented, where the first‐level fusers consist of the local decentralized robust fusers for the clusters, and the second‐level fuser is a global decentralized robust fuser for the cluster heads. It can reduce the communication load and save energy resources of sensors. Its robustness is proved by the proposed Lyapunov equation method. The concept of robust accuracy is presented, and the robust accuracy relations of the local, decentralized, and centralized fused robust Kalman filters are proved. Specially, the corresponding steady‐state robust local and fused Kalman filters are also presented, and the convergence in a realization between the time‐varying and steady‐state robust Kalman filters is proved by the dynamic error system analysis method. A simulation example shows correctness and effectiveness. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust integrated covariance intersection fusion Kalman estimators for networked systems with random measurement delays,multiplicative noises,and uncertain noise variances

In this article, the robust distributed fusion Kalman filtering problems are addressed for the networked mixed uncertain multisensor systems with random one-step measurement delays, multiplicative noises, and uncertain noise variances. A new augmented state approach with fictitious measurement noises modeled by the first-order moving average models is presented, by which the original system is transformed into a standard uncertain system only with uncertain-variance fictitious white noises. Based on the minimax robust estimation principle and Kalman filtering theory, a universal integrated covariance intersection (ICI) fusion approach is presented in the sense that first of all the robust local estimators and their conservative error variances and crosscovariances are presented, and then integrating the local estimation information yields ICI fusers. An extended Lyapunov equation approach with two kinds of Lyapunov equations is presented in order to prove the robustness and to compute fictitious noise statistics. Applying these approaches, the minimax robust local, ICI, and fast ICI fused Kalman estimators (predictor, filter, and smoother) are presented, such that for all admissible uncertainties, their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. Their robustness, accuracy relations, and convergence are also proved. The proposed ICI fusers improve the robust accuracies and overcome the drawbacks of the original covariance intersection fusers, such that the robust local estimators and their conservative variances are assumed to be known, and their conservative crosscovariances are ignored. Two simulation examples applied to the offshore platform system verify their correctness, effectiveness, and applicability.     

Weighted fusion robust steady-state estimators for multisensor networked systems with one-step random delay and inconsecutive packet dropouts

In this paper, the weighted fusion robust steady-state Kalman filtering problem is studied for a class of multisensor networked systems with mixed uncertainties. The uncertainties include same multiplicative noises in system parameter matrices, uncertain noise variances, as well as the one-step random delay and inconsecutive packet dropouts, which modeled by sequences of Bernoulli variables with different probabilities. By defining a new observation vector and applying the augmented method, the system under study is converted into one with only uncertain noise variances. The sufficient conditions for the existence of steady-state estimators are given. According to the minimax robust estimation principle, based on the worst-case subsystems with conservative upper bounds of uncertain noise variances, the robust local steady-state Kalman estimators (predictor, filter, and smoother) are proposed. Applying the optimal fusion algorithm weighted by matrices and the covariance intersection fusion algorithm, the two kinds of robust fusion steady-state Kalman estimators are derived in a unified framework. The robustness of the proposed fusion estimators is proved by applying the permutation matrices and the global Lyapunov equations method, such that, for all admissible uncertainties, the actual steady-state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fusion steady-state Kalman estimators are proved. An example with application to autoregressive moving average signal processing is proposed, which shows that the robust local and fusion signal estimation problems can be solved by the state estimation problems. Simulation example verifies the effectiveness and correctness of the proposed results.     

Optimal and self‐tuning weighted measurement fusion Kalman filters and their asymptotic global optimality

For the multisensor linear discrete time‐invariant stochastic systems with unknown noise variances, using the correlation method, the information fusion noise variance estimators with consistency are given by taking the average of the local noise variance estimators. Substituting them into two optimal weighted measurement fusion steady‐state Kalman filters, two new self‐tuning weighted measurement fusion Kalman filters with a self‐tuning Riccati equation are presented. By the dynamic variance error system analysis (DVESA) method, it is rigorously proved that the self‐tuning Riccati equation converges to the steady‐state optimal Riccati equation. Further, by the dynamic error system analysis (DESA) method, it is proved that the steady‐state optimal and self‐tuning Kalman fusers converge to the global optimal centralized Kalman fuser, so that they have the asymptotic global optimality. Compared with the centralized Kalman fuser, they can significantly reduce the computational burden. A simulation example for the target tracking systems shows their effectiveness. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust CAWOF Kalman predictors for uncertain multi-sensor generalized system

Robust centralized and weighted observation fusion (CAWOF) prediction algorithm is addressed in this article for an uncertain multi-sensor generalized system with linear correlation between observation noises and an input white noise. This uncertainty in the generalized system primarily means that the variances of the aforementioned types of noise, as well as the multiplicative noise variances, are uncertain. Through singular value decomposition and virtual noise compensation, the original generalized system is changed to non-generalized reduced-order subsystems in which only noise variances are uncertain. Utilizing the minimax robustness estimation criterion, robust CAWOF Kalman predictors are put forward on account of the first subsystem with conservative upper bounds of noise variances. Eventually, robust observation fusion Kalman predictors of the original generalized system are proposed. The Lyapunov equation method is applied to verify two fusion predictors' robustness. With regard to all permissible uncertain practical noise variances, CAWOF predictors are robust, namely, the practical prediction error variances of two robust predictors will have minimum upper bounds. This equivalence between CAWOF Kalman predictors is proved by an information filter. In this article, the precision relationship of fusion predictors is given. Meanwhile, robust Kalman predictors for steady-state case are proposed, and the astringency of robust time-variant Kalman predictors is analyzed through the analysis of dynamic error system. The validity and correctness of proposed algorithm are proved by the simulation example of random dynamic input and output system in an economic system.     

Self‐tuning fusion Kalman filter weighted by scalars and its convergence analysis for multi‐channel autoregressive moving average signals

For the multi‐sensor multi‐channel autoregressive (AR) moving average signals with white measurement noises and an AR‐colored measurement noise, a multi‐stage information fusion identification method is presented when model parameters and noise variances are partially unknown. The local estimators of model parameters and noise variances are obtained by the multidimensional recursive instrumental variable algorithm and correlation method, and the fused estimators are obtained by taking the average of the local estimators. They have the strong consistency. Substituting them into the optimal information fusion Kalman filter weighted by scalars, a self‐tuning fusion Kalman filter for multi‐channel AR moving average signals is presented. Applying the dynamic error system analysis method, it is proved that the proposed self‐tuning fusion Kalman filter converges to the optimal fusion Kalman filter in a realization, so that it has asymptotic optimality. A simulation example for a target tracking system with three sensors shows its effectiveness. Copyright © 2014 John Wiley & Sons, Ltd.     

Self‐tuning weighted fusion Kalman filter for ARMA signal with colored measurement noise and its convergence analysis

For the multisensor single‐channel autoregressive moving average (ARMA) signal with colored measurement noise, when the partial model parameters and the noise variance are unknown, a self‐tuning fusion Kalman filter weighted by scalar is presented based on the ARMA innovation model by the modern time series analysis method. With the application of the recursive instrumental variable algorithm and the Gevers–Wouters iterative algorithm with dead band, the information fusion estimators for the unknown model parameters and noise variance are obtained, and their consistence is proved by the existence and continuity theorem of implicit function. Then, substituting them into the optimal weighted fusion Kalman filter, one can obtain the corresponding self‐tuning weighted fusion Kalman filter. Further, with the application of the dynamic variance error system analysis method, the convergence of the self‐tuning Lyapunov equations for filtering error cross‐covariances is proved. With the application of the dynamic error system analysis method, it is rigorously proved that the self‐tuning weighted fusion Kalman filter converges to the optimal weighted fusion Kalman filter in a realization; that is, it has asymptotic optimality. A simulation example shows its effectiveness.Copyright © 2012 John Wiley & Sons, Ltd.     

Distributed fusion white noise deconvolution estimators

The white noise deconvolution or input white noise estimation problem has important applications in oil seismic exploration, communication and signal processing. By combining the Kalman filtering method with the modern time series analysis method, based on the autoregressive moving average (ARMA) innovation model, new distributed fusion white noise deconvolution estimators are presented by weighting local input white noise estimators for general multisensor systems with different local dynamic models and correlated noises. The new estimators can handle input white noise fused filtering, prediction and smoothing problems, and are applicable to systems with colored measurement noise. Their accuracy is higher than that of local white noise deconvolution estimators. To compute the optimal weights, the new formula for local estimation error cross-covariances is given. A Monte Carlo simulation for the system with Bernoulli-Gaussian input white noise shows their effectiveness and performance.     

Optimal and self‐tuning fusion Kalman filters for discrete‐time stochastic singular systems

Based on the optimal fusion estimation algorithm weighted by scalars in the linear minimum variance sense, a distributed optimal fusion Kalman filter weighted by scalars is presented for discrete‐time stochastic singular systems with multiple sensors and correlated noises. A cross‐covariance matrix of filtering errors between any two sensors is derived. When the noise statistical information is unknown, a distributed identification approach is presented based on correlation functions and the weighted average method. Further, a distributed self‐tuning fusion filter is given, which includes two stage fusions where the first‐stage fusion is used to identify the noise covariance and the second‐stage fusion is used to obtain the fusion state filter. A simulation verifies the effectiveness of the proposed algorithm. Copyright © 2008 John Wiley & Sons, Ltd.     

Noise covariance estimation for Kalman filter tuning using Bayesian approach and Monte Carlo

Linear time‐invariant systems play significant role in the control field. A number of methods have been published for identification of the deterministic part of a process. However, identification of the stochastic part has had much less attention. This paper deals with estimation of covariance matrices of the noise entering a linear system. The process and measurement noise covariance matrices are tuning parameters of the Kalman filter, and they affect the quality of the state estimation. The noise covariance matrices are generally not known, and their estimation from the measured data is a challenging task. This paper introduces a method for estimation of the noise covariance matrices using Bayesian approach along with Monte Carlo numerical methods. Performance of the approach is tested on various systems and noise properties. The second part of the paper compares Monte Carlo approach with the recently published methods. The speed of convergence is compared with the Cramér–Rao bounds. Copyright © 2012 John Wiley & Sons, Ltd.     

An adaptive regulation method for a class of uncertain time‐delay systems

In this paper, a new adaptive robust stabilization scheme is proposed for uncertain neutral time‐delay systems. No upper bounds on the uncertainties are assumed to be available. An update law is first used to find estimates of these upper bounds. A state‐feedback controller is then designed, which is shown to stabilize the underlying system under some mild conditions. The asymptotic stability of the state trajectories is proved using the Lyapunov–Krasovskii approach. An example is provided, which demonstrates the efficacy of the proposed adaptive control scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Windowing and random weighting‐based adaptive unscented Kalman filter

The conventional unscented Kalman filter (UKF) requires prior knowledge on system noise statistics. If the statistical characteristics of system noise are not known exactly, the filtering solution will be biased or even divergent. This paper presents an adaptive UKF by combining the windowing and random weighting concepts to address this problem. It extends the windowing concept from the linear Kalman filter to the nonlinear UKF for estimation of system noise statistics. Subsequently, the random weighting concept is adopted to refine the obtained windowing estimation by adjusting random weights of each window. The proposed adaptive UKF overcomes the limitation of the conventional UKF by online estimating and adjusting system noise statistics. Experimental results and comparison analysis demonstrate that the proposed adaptive UKF outperforms the conventional UKF and adaptive robust UKF under the condition without precise knowledge on system noise statistics.Copyright © 2014 John Wiley & Sons, Ltd.     

Use of prior bounds on time constants and steady‐state gain in recursive parameter bounding

Computation of parameter bounds of a linear dynamical system, given input–output observations and bounds on model‐output error, has been developed as an alternative to classical parameter estimation using least squares, maximum likelihood or the prediction error method. When bounds on time‐domain plant behaviour are known in advance, they can be used to develop prior parameter bounds for discrete‐time rational transfer‐function parameters. These bounds can be used to initialize standard parameter‐bounding algorithms which process input–output observations to update the exact polytope feasible set or one of its outer bounding approximations such as an ellipsoid, orthotope or parallelotope. This paper presents a method to compute such prior bounds from bounds on time constants and steady‐state (dc) gain, often available from the physics of the system or from previous experience. The method finds subsets making up the prior feasible parameter set, recursively in model order, for any configuration of the pole ranges. An analysis leading to measures of the value of prior bounds, in terms of their chances of remaining active when new bounds derived from observations are imposed, is presented. A simulation study compares polytope updating with and without such initial bounds. The simulations investigate the influence of the tightness of time‐constant and steady‐state‐gain bounds in reducing the volume of the feasible sets obtained as observations are processed. The effects of initial bound tightness and signal‐to‐noise ratio on survival time of the prior bounds are also examined. Copyright © 2002 John Wiley & Sons, Ltd.     

Prescribed performance adaptive fuzzy dynamic surface control of nonaffine time‐varying delayed systems with unknown control directions and dead‐zone input

In this paper, an adaptive prescribed performance control method is presented for a class of uncertain strict feedback nonaffine nonlinear systems with the coupling effect of time‐varying delays, dead‐zone input, and unknown control directions. Owing to the universal approximation property, fuzzy logic systems are used to approximate the uncertain terms in the system. Since there is no systematic approach to determine the required upper bounds of errors in control systems, the prior selection of control parameters to have a satisfactory performance is somehow impossible. Therefore, the prescribed performance technique as a solution is applied in this study to bring satisfactory performance indices to the system such as overshoot and steady state performance within a predetermined bound. Dynamic surface control strategy is also introduced to the proposed control scheme to address the “explosion of complexity” behavior existing in conventional backstepping methods. To ease the control design, the mean‐value theorem is utilized to transform the nonaffine system into the affine one. Moreover, with the help of this theorem, the unknown dead‐zone nonlinearity is separated into the linear and nonlinear disturbance‐like bounded term. The proposed method relaxes a prior knowledge of control direction by employing Nussbaum‐type functions, and the effect of time‐varying delays are compensated by constructing the proper Lyapunov‐Krasovskii functions. The proposed controller guarantees that all the closed‐loop signals are semiglobally uniformly ultimately bounded and the error evolves within the decaying prescribed bounds. In the end, in order to demonstrate the superiority of this method, simulation examples are given.     

Distributed Kalman filters with adaptive strategy for linear time‐varying interconnected systems

We consider the problem of distributed state estimation over a sensor network in which a set of nodes collaboratively estimates the state of a continuous‐time linear time‐varying system. In particular, our work focuses on the benefits of weight adaptation of the interconnection gains in distributed Kalman filters. To this end, an adaptation strategy is proposed with the adaptive laws derived via a Lyapunov‐redesign approach. The justification for the gain adaptation stems from a desire to adapt the pairwise difference of state estimates as a function of their agreement, thereby enforcing an interconnection‐dependent gain. In the proposed scheme, an adaptive gain for each pairwise difference of the interconnection terms is used in order to address edge‐dependent differences in the state estimates. Accounting for node‐specific differences, a special case of the scheme is also presented, where it uses a single adaptive gain in each node estimate and which uniformly penalizes all pairwise differences of state estimates in the interconnection term. The filter gains can be designed either by standard Kalman filter or Luenberger observer to construct the adaptive distributed Kalman filter or adaptive distributed Luenberger observer. Stability of the schemes has been shown, and it is not restricted by the graph topology and therefore the schemes are applicable to both directed and undirected graphs. The proposed algorithms offer a significant reduction in communication costs associated with information flow by the nodes. Finally, numerical studies are presented to illustrate the performance and effectiveness of the proposed adaptive distributed Kalman filters. Copyright © 2015 John Wiley & Sons, Ltd.     

Asynchronous distributed state estimation based on a continuous‐time stochastic model

In this paper, the problem of state estimation in an asynchronous distributed multi‐sensor estimation (ADE) system is considered. In such an ADE system, the state of a plant of interest is estimated by a group of local estimators. Each local estimator based, for example, on a Kalman filter, performs fusion of data from its local sensor and other (remote) processors to compute possibly best state estimates. In performing data fusion, however, two important issues need to be addressed, namely, the problem of asynchronism of local processors and the one of unknown correlation between asynchronous data in local processors. Consequently, there are two main contributions proposed in this paper. The first is a method to deal with asynchronous discrete‐time data based on a continuous‐time stochastic plant model. The second contribution is an asynchronous distributed data‐fusion algorithm. Simulated experiments illustrate the effectiveness of the proposed ADE approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Variance analysis of robust state estimation in power system using influence function

An analytical equation is derived using influence function approximation to calculate the variance of the state estimate for traditional robust state estimators such as the Quadratic-Constant, Quadratic-Linear, Square-Root, Schweppe-Huber Generalized-M and Multiple-Segment estimator. The equation gives insights into the precision of the estimation. Using the equation, the variance of a state estimate can be expressed as a function of measurement noise variances enabling the selection of sensors for a specified estimator precision. It can also be used to search for the optimum estimator parameters to give the minimum sum of variances. The well-known Weighted-Least-Squares variance formula is a special case of the equation and simulations on the IEEE 14-bus system are given to show the usefulness of the equation.     

Self-tuning decoupled fusion Kalman filter based on the Riccati equation

An online noise variance estimator for multisensor systems with unknown noise variances is proposed by using the correlationmethod. Based on the Riccati equation and optimal fusion rule weighted by scalars for state components, a self-tuning component decoupled information fusion Kalman filter is presented. It is proved that the filter converges to the optimal fusion Kalman filter in a realization by dynamic error system analysis method, so that it has asymptotic optimality. Its effectiveness is demonstrated by simulation for a tracking system with 3 sensors. __________ Translated from Control and Decision, 2008, 23(2): 195–199 [译自: 控制与决策]     

An improved adaptive unscented Kalman filter for estimating the states of in‐wheel‐motored electric vehicle

Vehicle state is essential for active safety stability control. However, the accurate measurement of some vehicle states is difficult to achieve without the use of expensive equipment. To improve estimation accuracy in real time, this paper proposes an estimator of vehicle velocity based on the adaptive unscented Kalman filter (AUKF) for an in‐wheel‐motored electric vehicle (IWMEV). Given the merits of an independent drive structure, the tire forces of the IWMEV can be directly calculated through a vehicle dynamic model. Additionally, by means of the normalized innovation square, the validity of vehicle velocity estimation can be detected, and the sliding window length can be adjusted adaptively; thus, the steady‐state error and the dynamic performance of the IWMEV are demonstrated to be simultaneously improved over an alternative approach in comparisons. Then, an adaptive adjustment strategy for the noise covariance matrices is introduced to overcome the impact of parameter uncertainties. The numerically simulated and experimental results prove that the proposed vehicle velocity estimator based on AUKF not only improves estimation accuracy but also possesses strong robustness against parameter uncertainties. The deployment of the estimation algorithm by using a single‐chip microcomputer verifies the strong real‐time performance and easy‐to‐implement characteristics of the proposed algorithm.