Fast bias‐constrained optimal FIR filtering for time‐invariant state space models

This paper combines the finite impulse response filtering with the Kalman structure (predictor/corrector) and proposes a fast iterative bias‐constrained optimal finite impulse response filtering algorithm for linear discrete time‐invariant models. In order to provide filtering without any requirement of the initial state, the property of unbiasedness is employed. We first derive the optimal finite impulse response filter constrained by unbiasedness in the batch form and then find its fast iterative form for finite‐horizon and full‐horizon computations. The corresponding mean square error is also given in the batch and iterative forms. Extensive simulations are provided to investigate the trade‐off with the Kalman filter. We show that the proposed algorithm has much higher immunity against errors in the noise covariances and better robustness against temporary model uncertainties. The full‐horizon filter operates almost as fast as the Kalman filter, and its estimate converges with time to the Kalman estimate. Copyright © 2016 John Wiley & Sons, Ltd.     

Beta‐order minimum mean‐square error multichannel spectral amplitude estimation for speech enhancement

In this paper, the minimum mean‐square error (MMSE) β‐order estimator for multichannel speech enhancement is proposed. The estimator is an extension of the single‐channel MMSE β‐order and multichannel MMSE short‐time spectral amplitude estimators using Rayleigh and Gaussian distributions for the statistical models under the assumption of a diffuse noise field where the noise is estimated independently across each of the microphones. Experiments are performed to evaluate the new estimator against the baseline single‐channel and multichannel estimators using various values of the β parameter and number of microphones along with different levels of noises as a function of the input signal‐to‐noise ratio. By the utilization of additional microphones, the multichannel MMSE β‐order estimator achieves performance gains in noise reduction, speech distortion, and speech quality as measured by the segmental signal‐to‐noise ratio, log‐likelihood ratio, and perceptual evaluation of speech quality objective metrics. Copyright © 2015 John Wiley & Sons, Ltd.     

FIR modelling for errors‐in‐variables/closed‐loop systems by exploiting cyclo‐stationarity

Finite impulse response (FIR) modelling of errors‐in‐variables/closed‐loop systems by correlation analysis usually yields biased estimates due to the additive noises on inputs and outputs. A non‐parametric approach, the cyclic correlation analysis (CCRA), provides asymptotically unbiased and consistent estimates. The main feature of the CCRA is to eliminate the adverse effects of stationary noises by exploiting cyclo‐stationarity that may exist naturally or be induced artificially. A complete study of the CCRA is developed, including the statistical performance of the estimated FIR model. Frequency‐domain expressions of the statistical performance provide guidelines in designing a class of cyclo‐stationary signals for modelling. Effectiveness and properties of the CCRA are validated and illustrated by numerical examples. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Optimal control of uncertain quantized linear discrete‐time systems

In this paper, the adaptive optimal regulator design for unknown quantized linear discrete‐time control systems over fixed finite time is introduced. First, to mitigate the quantization error from input and state quantization, dynamic quantizer with time‐varying step‐size is utilized wherein it is shown that the quantization error will decrease overtime thus overcoming the drawback of the traditional uniform quantizer. Next, to relax the knowledge of system dynamics and achieve optimality, the adaptive dynamic programming methodology is adopted under Bellman's principle by using quantized state and input vector. Because of the time‐dependency nature of finite horizon, an adaptive online estimator, which learns a newly defined time‐varying action‐dependent value function, is updated at each time step so that policy and/or value iterations are not needed. Further, an additional error term corresponding to the terminal constraint is defined and minimized along the system trajectory. The proposed design scheme yields a forward‐in‐time and online scheme, which enjoys great practical merits. Lyapunov analysis is used to show the boundedness of the closed‐loop system; whereas when the time horizon is stretched to infinity as in the case of infinite horizon, asymptotic stability of the closed‐loop system is demonstrated. Simulation results on a benchmarking batch reactor system are included to verify the theoretical claims. The net result is the design of the optimal adaptive controller for uncertain quantized linear discrete‐time systems in a forward‐in‐time manner. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Least‐correlation estimates for errors‐in‐variables models

This paper introduces an estimator for errors‐in‐variables models in which all measurements are corrupted by noise. The necessary and sufficient condition minimizing a criterion, defined by squaring the empirical correlation of residuals, yields a new identification procedure that we call least‐correlation estimator. The method of least correlation is a generalization of least‐squares since the least‐correlation specializes to least‐squares when the correlation lag is zero. The least‐correlation estimator has the ability to estimate true parameters consistently from noisy input–output measurements as the number of samples increases. Monte Carlo simulations also support the consistency numerically. We discuss the geometric property of the least‐correlation estimate and, moreover, show that the estimate is not an orthogonal projection but an oblique projection. Finally, recursive realizations of the procedure in continuous‐time as well as in discrete‐time are mentioned with a numerical demonstration. Copyright © 2006 John Wiley & Sons, Ltd.     

Multiple characteristic model‐based golden‐section adaptive control: Stability and optimization

The characteristic model‐based golden‐section adaptive control (CM‐GSAC) law has been developed for over 20 years in China with a broad range of applications in various fields. However, quite a few theoretical problems remain open despite its satisfying performance in practice. This paper revisits the stability of the CM‐GSAC from its very beginning and explores the underlying implications of the so‐called golden‐section parameter l₂≈0.618. The closed‐loop system, which consists of the CM and the GSAC, is a discrete time‐varying system, and its stability is discussed from three perspectives. First, attentions have been paid to select the optimal controller coefficients such that the closed‐loop system exhibits the best transient performance in the worst case. Second, efforts are made to improve the robustness in the presence of parameter estimation errors, which provide another choice when designing the adaptive controller. Finally, by measuring the slowly time‐varying nature in an explicit inequality form, a bridge is built between the instantaneous stability and the time‐varying stability. In order to relax the constraints on the parameter bounds of the CM, the GSAC is further extended to multiple CMs, which shows more satisfying tracking performance than that of the traditional multiple model adaptive control method. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Dissipativity and passivity analysis for discrete‐time complex‐valued neural networks with leakage delay and probabilistic time‐varying delays

In this paper, the problem of dissipativity and passivity analysis is investigated for discrete‐time complex‐valued neural networks with time‐varying delays. Both leakage and discrete time‐varying delays have been considered. By constructing a suitable Lyapunov–Krasovskii functional and by using discretized Jensen's inequality approach, sufficient conditions have been established to guarantee the (Q ,S ,R ) ? γ dissipativity and passivity of the addressed discrete‐time complex‐valued neural networks. These conditions are derived in terms of complex‐valued linear matrix inequalities (LMIs), which can be checked numerically using Yet Another LMI Parser toolbox in Matrix Laboratory. Finally, three numerical examples are established to illustrate the effectiveness of the obtained theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

A robust output error identifier for continuous‐time systems

This paper shows that the adaptive output error identifier for linear time‐invariant continuous‐time systems proposed by Bestser and Zeheb is robust vis‐à‐vis finite energy measurement noise. More precisely, it is proven that the map from the noise to the estimation error is –stable—provided a tuning parameter is chosen sufficiently large. A procedure to determine the required minimal value of this parameter is also given. If the noise is exponentially vanishing, asymptotic convergence to zero of the prediction error is achieved. Instrumental for the establishment of the results is a suitable decomposition of the error system equations that allows us to strengthen—to strict—the well‐known passivity property of the identifier. The estimator neither requires fast adaptation, a dead‐zone, nor the knowledge of an upperbound on the noise magnitude, which is an essential requirement to prove stability of standard output error identifiers. To robustify the estimator with respect to non‐square integrable (but bounded) noises, a prediction error‐dependent leakage term is added in the integral adaptation. –stability of the modified scheme is established under a technical assumption. A simulated example, which is unstable for the equation error identifier and the output error identifier of Bestser and Zeheb, is used to illustrate the noise insensitivity property of the new scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Convergence analysis of the RLS identification algorithm with exponential forgetting in stationary ARX‐structures

The recursive least‐squares (RLS) identification algorithm is often extended with exponential forgetting as a tool for parameter estimation in time‐varying stochastic systems. The statistical properties of the parameter estimates obtained from such an extended RLS‐algorithm depend in a non‐linear way on the time‐varying characteristics and on the forgetting factor. In this paper, the RLS‐estimator with exponential forgetting is applied to time‐invariant Gaussian autoregressions with second‐order stationary external inputs, i.e.to Gaussian ARX‐processes. Approximate expressions for the asymptotic bias and covariance of the parameter estimates when the forgetting factor tends to one and time to infinity are given, showing that the bias is non‐zero and that the covariance function decays exponentially with a rate that is given by the forgetting factor. The orders of magnitude of the errors in the asymptotic expressions are also derived. Copyright © 1999 John Wiley & Sons, Ltd.     

Robust time‐varying Kalman estimators for systems with packet dropouts and uncertain‐variance multiplicative and linearly correlated additive white noises

This paper is concerned with robust estimation problem for a class of time‐varying networked systems with uncertain‐variance multiplicative and linearly correlated additive white noises, and packet dropouts. By augmented state method and fictitious noise technique, the original system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with conservative upper bounds of uncertain noise variance, the robust time‐varying Kalman estimators (filter, predictor, and smoother) are presented. A unified approach of designing the robust Kalman estimators is presented based on the robust Kalman predictor. Their robustness is proved by the Lyapunov equation approach in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Their accuracy relations are proved. The corresponding robust steady‐state Kalman estimators are also presented, and the convergence in a realization between the time‐varying and steady‐state robust Kalman estimators is proved. Finally, a simulation example applied to uninterruptible power system shows the correctness and effectiveness of the proposed results.     

Adaptive internal model control: the discrete‐time case

This paper considers the design and analysis of a discrete‐time H₂ optimal robust adaptive controller based on the internal model control structure. The certainty equivalence principle of adaptive control is used to combine a discrete‐time robust adaptive law with a discrete‐time H₂ internal model controller to obtain a discrete‐time adaptive H₂ internal model control scheme with provable guarantees of stability and robustness. The approach used parallels the earlier results obtained for the continuous‐time case. Nevertheless, there are some differences which, together with the widespread use of digital computers for controls applications, justifies a separate exposition. Copyright © 2001 John Wiley & Sons, Ltd.     

Constructive approximation of non‐linear discrete‐time systems

It is known that large classes of approximately‐finite‐memory maps can be uniformly approximated arbitrarily well by the maps of certain non‐linear structures. As an application, it was proved that time‐delay networks can be used to uniformly approximate arbitrarily well the members of a large class of causal nonlinear dynamic discrete‐time input–output maps. However, the proof is non‐constructive and provides no information concerning the determination of a structure that corresponds to a prescribed bound on the approximation error. Here we give some general results concerning the problem of finding the structure. Our setting is as follows. There is a large family 𝒢 of causal time‐invariant approximately‐finite‐memory input‐output maps G from a set S of real d‐vector‐valued discrete‐time inputs (with d⩾1) to the set of ℝ‐valued discrete‐time outputs, with both the inputs and outputs defined on the non‐negative integers 𝒵₊. We show that for each ϵ>0, any Gϵ𝒢 can be uniformly approximated by a structure map H(G, ·) to within tolerance ϵ, and we give analytical results and an example to illustrate how such a H(G, ·) can be determined in principle. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

Frequency domain subspace identification with the aid of the w‐operator

Frequency domain subspace identification algorithms have been studied recently by several researchers in the literature, motivated by the significant development of the more popular time domain counterparts. Usually, this class of methods are focused on discrete‐time models, since in the case of continuous‐time models, the data matrices often become ill‐conditioned if we simply rewrite the Laplace operator s as s = jω, where ω denotes the frequency. This paper proposes an efficient and convenient approach to frequency domain subspace identification for continuous‐time systems. The operator w = (s−α)/(s+α) is introduced to avoid the ill‐conditioned problem. Hence, the system can be identified based on a state‐space model in the w‐operator. Then the estimated w‐operator state‐space model can be transformed back to the common continuous‐time state‐space model. An instrumental variable matrix in the frequency domain is also proposed to obtain consistent estimates of the equivalent system matrices in the presence of measurement noise. Simulation results are included to verify the efficiency of the proposed algorithms. © 2000 Scripta Technica, Electr Eng Jpn, 132(1): 46–56, 2000     

An indirect adaptive pole‐placement control for MIMO discrete‐time stochastic systems

In this paper, an indirect adaptive pole‐placement control scheme for multi‐input multi‐output (MIMO) discrete‐time stochastic systems is developed. This control scheme combines a recursive least squares (RLS) estimation algorithm with pole‐placement control design to produce a control law with self‐tuning capability. A parametric model with a priori prediction outputs is adopted for modelling the controlled system. Then, a RLS estimation algorithm which applies the a posteriori prediction errors is employed to identify the parameters of the model. It is shown that the implementation of the estimation algorithm including a time‐varying inverse logarithm step size mechanism has an almost sure convergence. Further, an equivalent stochastic closed‐loop system is used here for constructing near supermartingales, allowing that the proposed control scheme facilitates the establishment of the adaptive pole‐placement control and prevents the closed‐loop control system from occurring unstable pole‐zero cancellation. An analysis is provided that this control scheme guarantees parameter estimation convergence and system stability in the mean squares sense almost surely. Simulation studies are also presented to validate the theoretical findings. Copyright © 2005 John Wiley & Sons, Ltd.     

Neural‐network‐based finite‐time H∞ control for extended Markov jump nonlinear systems

This paper presents a neural‐network‐based finite‐time H_∞ control design technique for a class of extended Markov jump nonlinear systems. The considered stochastic character is described by a Markov process, but with only partially known transition jump rates. The sufficient conditions for the existence of the desired controller are derived in terms of linear matrix inequalities such that the closed‐loop system trajectory stays within a prescribed bound in a fixed time interval and has a guaranteed H_∞ noise attenuation performance for all admissible uncertainties and approximation errors of the neural networks. A numerical example is used to illustrate the effectiveness of the developed theoretic results. Copyright © 2009 John Wiley & Sons, Ltd.     

Reliable H∞ filtering for discrete time‐delay Markovian jump systems with partly unknown transition probabilities

In this paper, the reliable H_∞ filtering problem is studied for a class of discrete nonlinear Markovian jump systems with sensor failures and time delays. The transition probabilities of the jumping process are assumed to be partly unknown. The failures of sensors are quantified by a variable taking values in a given interval. The time‐varying delay is unknown with given lower and upper bounds. The purpose of the addressed reliable H_∞ filtering problem is to design a mode‐dependent filter such that the filtering error dynamics is asymptotically mean‐square stable and also achieves a prescribed H_∞ performance level. By using a new Lyapunov–Krasovskii functional and delay‐partitioning technique, sufficient delay‐dependent conditions for the existence of such a filter are obtained. The filter gains are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi‐definite programme method. A numerical example is provided to demonstrate the effectiveness of the proposed design approach. Copyright © 2011 John Wiley & Sons, Ltd.