The maximum likelihood least squares based iterative estimation algorithm for bilinear systems with autoregressive moving average noise

Maximum likelihood methods are significant for parameter estimation and system modeling. This paper gives the input-output representation of a bilinear system through eliminating the state variables in it, and derives a maximum likelihood least squares based iterative for identifying the parameters of bilinear systems with colored noises by using the maximum likelihood principle. A least squares based iterative (LSI) algorithm is presented for comparison. It is proved that the maximum of the likelihood function is equivalent to minimize the least squares cost function. The simulation results indicate that the proposed algorithm is effective for identifying bilinear systems and the maximum likelihood LSI algorithm is more accurate than the LSI algorithm.     

An intelligent propagation distance estimation algorithm based on fundamental frequency energy distribution for periodic vibration localization

Earth surface vibrations generated by passing vehicles, excavation equipment, footsteps, etc., attract increasing attentions in the research community due to their wide applications. In this paper, we investigate the periodic vibration source localization problem, which has recently shown significance in excavation device detection and localization for urban underground pipeline network protection. An intelligent propagation distance estimation algorithm based on a novel fundamental frequency energy distribution (FBED) feature is developed for periodic vibration signal localization. Contributions of the paper lie in three aspects: 1) a novel frequency band energy distribution (FBED) feature is developed to characterize the property of vibrations at different propagation distances; 2) an intelligent propagation distance estimation model built on the FBED feature with machine learning algorithms is proposed, where for comparisons, the support vector machine (SVM) for regression and regularized extreme learning machine (RELM) are used; 3) a localization algorithm based on the distance-of-arrival (DisOA) estimation using three piezoelectric transducer sensors is given for source position estimation. To testify the effectiveness of the proposed algorithms, case studies on real collected periodic vibration signals generated by two electric hammers with different fundamental frequencies are presented in the paper. The transmission medium is the cement road and experiments on vibration signals recorded at different propagation distances are conducted.     

Blind estimation of carrier frequency offset for OFDM systems with time-varying DC offset

Orthogonal frequency division multiplexing (OFDM) has been widely adopted in radar and communication systems. High sensitivity to carrier frequency offset (CFO) is one of the major drawbacks of OFDM. CFO estimation for OFDM systems had been extensively studied and various algorithms had been proposed. However, the established algorithms may be compromised by the adoption of direct-conversion architecture and multi-mode low noise amplifier in the OFDM receiver, which introduces time-varying direct current offset (TV-DCO) into the system. In our previous study, we developed an eigen-decomposition based estimation algorithm, which is robust to TV-DCO but suffers from performance degradation under low to medium signal-to-noise ratio and requires high computation efforts. To address those issues, we in this paper propose a novel blind CFO estimation algorithm. By making use of the second order differential filtering and subspace method, the proposed algorithm achieves great performance improvement with reduced complexity. The performance of the proposed algorithm is demonstrated by simulations.     

Event based estimation with correlated noises

For a linear system having event based measurements and correlated noises, a state estimation algorithm is proposed. A general event based sampling is employed to obtain the measurements, where in the case of unavailability of measurements, event based strategy itself is used to obtain approximate state and covariance estimates. To deal with correlated noises, a two-step ahead prediction approach is employed to obtain recursive equations for estimated state and covariance. The obtained results are illustrated using a simulation example.     

Maximum likelihood recursive least squares estimation for multivariate equation-error ARMA systems

This paper focuses on the parameter estimation problems of multivariate equation-error systems. A recursive generalized extended least squares algorithm is presented as a comparison. Based on the maximum likelihood principle and the coupling identification concept, the multivariate equation-error system is decomposed into several regressive identification models, each of which has only a parameter vector, and a coupled subsystem maximum likelihood recursive least squares identification algorithm is developed for estimating the parameter vectors of these submodels. The simulation example shows that the proposed algorithm is effective and has high estimation accuracy.     

Reachable set estimation for discrete-time bilinear systems with time-varying delays

The problem of reachable set estimation is studied for discrete-time bilinear system in this paper. Time-varying delays and bounded input disturbances are both considered in bilinear system. The aim is to find reachable set that converges from all the states of system with initial conditions. By constructing Lyapunov–Krasovskii functional, sufficient delay-dependent less conservative stable conditions of reachable set estimation are obtained for bilinear delay system via the reciprocally convex combination and delay partition approaches. The derived theorem can guarantee that all the states of system with initial conditions from some domain are bounded in an ellipsoid and all the states from other domain are converged exponentially within a ball. One simulation example is presented to illustrate the correctness of the derived result in this paper.     

Moving horizon estimation for multirate systems with time-varying time-delays

This paper presents a moving horizon estimation approach for the multirate sampled-data system with unknown time-delay sequence. To estimate the unknown variables of interest, two main challenging issues need to be addressed: (a) synthesizing the multirate input and output data for state estimation, (b) simultaneously estimating the continuous state and discrete time-delay sequence. In this work a moving horizon estimation based approach is developed to tackle these issues. The proposed approach can simultaneously estimate both the continuous states and discrete time-delay sequence for dynamic systems. The effects of different noise level on the estimation of continuous states and discrete time-delay sequence are analyzed. The effectiveness of this method is illustrated through a simulation study.     

Moving horizon estimation for ARMAX processes with additive output noise

Auto-Regressive-Moving-Average with eXogenous input (ARMAX) models play an important role in control engineering for describing practical systems. However, ARMAX models can be non-realistic in many practical contexts because they do not consider the measurement errors on the output of the process. Due to the auto-regressive nature of ARMAX processes, a measurement error may affect multiple data entries, making the estimation problem very challenging. This problem can be solved by enhancing the ARMAX model with additive error terms on the output, and this paper develops a moving horizon estimator for such an extended ARMAX model. In the proposed method, measurement errors are modeled as nuisance variables and estimated simultaneously with the states. Identifiability was achieved by regularizing the least-squares cost with the ?₂-norm of the nuisance variables, which leads to an optimization problem that has an analytical solution. For the proposed estimator, convergence results are established and unbiasedness properties are also proved. Insights on how to select the tuning parameter in the cost function are provided. Because of the explicit modeling of output noise, the impact of a measurement error on multiple data entries can be estimated and reduced. Examples are given to demonstrate the effectiveness of the proposed estimator in dealing with additive output noise as well as outliers.     

Output reachable set estimation for discrete-time switched systems with persistent dwell-time

This paper is concerned with the output reachable set estimation for discrete-time switched systems. The switching signal is considered as persistent dwell-time (PDT), which is more general and flexible compared with the common dwell-time and average dwell-time switching. The estimation of output reachable set is determined by a collection of bounding ellipsoids based on a family of quasi-time-dependent (QTD) Lyapunov functions. Furthermore, a set of non-fragile QTD controllers is designed. Finally, two examples are employed to illustrate the potentials of proposed methods.     

Event-triggered diffusion estimation for asynchronous sensor networks with unreliable measurements

This article aims at investigating the event-triggered (ET) distributed estimation problem for asynchronous sensor networks with randomly occurred unreliable measurements. We propose two ET mechanisms to schedule data transmissions in this paper. One ET mechanism based on dual-criterion is proposed to schedule the transmissions of measurements and avoid the interferences from unreliable measurements. The other ET mechanism is proposed to schedule the transmissions of local estimates. The connotative information in aforementioned ET mechanisms is exploited for taking full use of available information. Then, we provide the corresponding event-triggered asynchronous diffusion estimator based on the diffusion filtering scheme. In the proposed method, a sensor first generates a local estimate by utilizing available information of asynchronous measurements in each estimation period. Then it fuses available information of asynchronous local estimates to generate a fused estimate. Results of simulations in different cases and experiment in an optical-electronic detection network verify the validity and feasibility of the proposed method.     

Distributed estimation and control of multiple nonholonomic mobile agents with external disturbances

This paper investigates the tracking control problem of nonholonomic multiagent systems with external disturbances. For this purpose, distributed finite time controllers (DFCs) based on the terminal sliding mode method are proposed to ensure that states of the agents track the states of the target in a finite time. Furthermore, a distributed estimator (DE) is designed for each agent to estimate the target's states. The stability analysis of DFCs and DE is also considered. Simulation examples demonstrate the promising performance of the proposed algorithms.     

Reachable set estimation for linear systems with time-varying delay and polytopic uncertainties

This study is concerned with the problem of reachable set estimation for linear systems with time-varying delays and polytopic parameter uncertainties. Our target is to find an ellipsoid that contains the state trajectory of linear system as small as possible. Specifically, first, in order to utilize more information about the state variables, the RSE problem for time-delay systems is solved based on an augmented Lyapunov-Krasovskii functional. Second, by dividing the time-varying delay into two non-uniformly subintervals, more general delay-dependent stability criteria for the existence of a desired ellipsoid are derived. Third, the integral interval is decomposed in the same way to estimate the bounds of integral terms more exactly. Fourth, an optimized integral inequality is used to deal with the integral terms, which is based on distinguished Wirtinger integral inequality and Reciprocally convex combination inequality. This can be regard as a new method in the delay systems. Finally, three numerical examples are presented to demonstrate the effectiveness and merits of the theoretical results.     

Fast algorithm for image denoising with different boundary conditions

In recent works several authors have considered the L₁ fidelity term, the L₂ fidelity term and the combined L₁ and L₂ fidelity term for denoising models, and they used the fast Fourier transform (FFT) algorithm which can only use periodic boundary conditions (BCs). In this paper, we combine the augmented Lagrangian method (ALM) and the symmetric Red–Black Gauss–Seidel (SRBGS) method to propose three algorithms that are suitable for different BCs. Experimental results show that the proposed algorithms are effective and the model with the combined L₁ and L₂ fidelity term demonstrates more advantages in efficiency and accuracy than other models with the L₁ fidelity term or the L₂ fidelity term.     

Widely linear estimation for multisensor quaternion systems with mixed uncertainties in the observations

The optimal widely linear state estimation problem for quaternion systems with multiple sensors and mixed uncertainties in the observations is solved in a unified framework. For that, we devise a unified model to describe the mixed uncertainties of sensor delays, packet dropouts and uncertain observations by using three Bernoulli distributed quaternion random processes. The proposed model is valid for linear discrete-time quaternion stochastic systems measured by multiple sensors and it allows us to provide filtering, prediction and smoothing algorithms for estimating the quaternion state through a widely linear processing. Simulation results are employed to show the superior performance of such algorithms in comparison to standard widely linear methods when mixed uncertainties are present in the observations.     

Robust state estimation for discrete time systems with colored noises and communication constraints

This paper investigates the state estimation problem for networked systems with colored noises and communication constraints. The colored noises are considered to be correlated to itself at other time steps, and communication constraints include two parts: (1) the information is quantized by a logarithmic quantizer before transmission, (2) only one node can access the network channel at each instant based on a specified media access protocol. A robust recursive estimator is designed under the condition of colored noises, quantization error and partially available measurements. The upper bound of the covariance of the estimation error is then derived and minimized by properly designing estimator gains. An illustrative example is finally given to demonstrate the effectiveness of the developed estimator.     

State estimation for networked systems with Markovian communication constraints and multiple packet dropouts

In this paper, the state estimation problem for discrete-time networked systems with communication constraints and random packet dropouts is considered. The communication constraint is that, at each sampling instant, there is at most one of the various transmission nodes in the networked systems is allowed to access a shared communication channel, and then the received data are transmitted to a remote estimator to perform the estimation task. The channel accessing process of those transmission nodes is determined by a finite-state discrete-time Markov chain, and random packet dropouts in remote data transmission are modeled by a Bernoulli distributed white sequence. Using Bayes’ rule and some results developed in this study, two state estimation algorithms are proposed in the sense of minimum mean-square error. The first algorithm is optimal, which can exactly compute the minimum mean-square error estimate of system state. The second algorithm is a suboptimal algorithm obtained under a lot of Gaussian hypotheses. The proposed suboptimal algorithm is recursive and has time-independent complexity. Computer simulations are carried out to illustrate the performance of the proposed algorithms.     

Finite-horizon state estimation for time-varying complex networks with random coupling strengths under Round-Robin protocol

In this paper, the problem of finite-horizon H_∞ state estimation is investigated for a class of discrete time-varying complex networks with multiplicative noises and random coupling strengths. The network nodes and estimators are connected via a constrained communication network which allows only one node to send measurement data at each transmission instant. The Round-Robin protocol is introduced to determine which node obtains the access to the network at certain transmission instant. The aim of the addressed problem is to design a set of time-varying estimator parameters such that the prescribed H_∞ performance is guaranteed over a finite horizon. By using the stochastic analysis approach and completing-the-square method, sufficient conditions are derived for the existence of the desired estimators in terms of the solution to backward recursive Riccati difference equations. Finally, a numerical example is provided to validate the feasibility and effectiveness of the proposed results.     

Experimental validation of a continuous-time MCSI algorithm with bounded adaptive gains

Model reference adaptive control algorithms with minimal controller synthesis have proven to be an effective solution to tame the behaviour of linear systems subject to unknown or time-varying parameters, unmodelled dynamics and disturbances. However, a major drawback of the technique is that the adaptive control gains might exhibit an unbounded behaviour when facing bounded disturbances. Recently, a minimal controller synthesis algorithm with an integral part and either parameter projection or σ-modification strategies was proposed to guarantee boundedness of the adaptive gains. In this article, these controllers are experimentally validated for the first time by using an electro-mechanical system subject to significant rapidly varying disturbances and parametric uncertainty. Experimental results confirm the effectiveness of the modified minimal controller synthesis methods to keep the adaptive control gains bounded while providing, at the same time, tracking performances similar to that of the original algorithm.     

Finite frequency range robust iterative learning control of linear discrete system with multiple time-delays

This paper uses repetitive process stability theory to design robust iterative learning control law for linear discrete systems with multiple time-delays and polytopic uncertainty. Both dynamic and static forms of the control law are considered and used when designing robust iterative learning control schemes. Also, based on the generalized Kalman-Yakubovich-Popov Lemma, the proposed design procedures a required frequency attenuation over a finite frequency range and the monotonic trial-to-trial error convergence. Moreover, linear matrix inequality techniques are applied to formulate the convergence conditions and to obtain formulas for the control law designs. Finally, an illustrative numerical simulation example is given and concludes the paper.     

Consensus control for multi-agent systems with distributed parameter models via iterative learning algorithm

This paper deals with the problem of iterative learning control algorithm for a class of multi-agent systems with distributed parameter models. And the considered distributed parameter models are governed by the parabolic or hyperbolic partial differential equations. Based on the framework of network topologies, a consensus-based iterative learning control protocol is proposed by using the nearest neighbor knowledge. When the iterative learning control law is applied to the systems, the consensus errors between any two agents on L² space are bounded, and furthermore, the consensus errors on L² space can converge to zero as the iteration index tends to infinity in the absence of initial errors. Simulation examples illustrate the effectiveness of the proposed method.