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ABSTRACT This study tackles the problem of fault‐tolerant attitude estimation for small satellites. A probabilistic adaptive technique is presented for the multiplicative extended Kalman filter (MEKF) algorithm that is used in attitude estimation. The presented method is based on tracking the normalized measurement innovations in the filter and calculating the probability of the normal operation of the estimation system. Using this probability, the filter gain is corrected to maintain the tracking performance of the filter despite faulty measurements. In order to evaluate the performance of this method, several simulations are performed where different types of faults are introduced to the synthetic attitude sensor measurements (magnetometer and sun sensor) at different times. Simulation results are compared not only with a conventional EKF but also with another popular adaptive Kalman filter, an adaptive Kalman filter with multiple scaling factors (MSFs). [ABSTRACT FROM AUTHOR]

Aiming at the problem of sub‐synchronous oscillations induced by direct‐drive wind farms with series‐compensated lines, this paper proposes an unknown system dynamics estimation‐based PI controller to achieve sub‐synchronous oscillation suppression. According to the mathematical model of the direct‐drive wind farm grid‐connected system, the relationship between the direct‐drive wind turbine grid‐side converter current inner‐loop PI controller and the sub‐synchronous components is first established. Secondly, the uncertain sub‐synchronous current components and voltage components in the series‐compensated lines of the direct‐drive wind farm are taken as the total disturbance, and an unknown system dynamic estimator‐based PI controller is designed by introducing the first‐order low‐pass filter operation. Then, the stability and convergence of the closed‐loop system are proved by Lyapunov theory. Finally, the Prony method is used to analyse the current signal output by the direct‐drive wind turbine, and the inherent characteristics of the negative damping of the SSO induced by the series‐compensated line of the direct‐driven wind farm are revealed. A comparative numerical simulation is carried out to demonstrate that the sub‐synchronous oscillations of the direct‐drive wind farm with series‐compensated lines can be suppressed under different operating conditions. [ABSTRACT FROM AUTHOR]

This article deals with the problem of estimating the service time distribution of the M t / G / ∞ queue from observation of the departure epochs. We develop minimax optimal estimators of G and study behavior of the minimax pointwise risk over a suitable family of service time distribution functions. In addition, we address the problem of adaptive estimation and propose a data–driven estimation procedure that adapts to unknown smoothness of the service time distribution function G. Lastly, a numerical study is presented to illustrate practical performance of the developed adaptive procedure. [ABSTRACT FROM AUTHOR]

We consider nonparametric estimation of the spectral density of a stationary time series under local differential privacy. In this framework only an appropriately anonymised version of a finite snippet from the time series can be observed and used for inference. The anonymisation procedure can be chosen in advance among all mechanisms satisfying the condition of local differential privacy, and we propose truncation followed by Laplace perturbation for this purpose. Afterwards, the anonymised time series snippet is used to define a surrogate of the classical periodogram and our estimator is obtained by projection of this privatised periodogram to a model given by a finite dimensional subspace of L 2 ([ - π , π ]) . This estimator attains nearly the same convergence rate as in the case where the original time series can be observed. However, a reduction of the effective sample size in contrast to the non-privacy framework is shown to be unavoidable. We also consider adaptive estimation and suggest to select an estimator from a set of candidate estimators by means of a penalised contrast criterion. We derive an oracle inequality which shows that the adaptive estimator attains nearly the same rate of convergence as the best estimator from the candidate set. Concentration inequalities for quadratic forms in terms of sub-exponential random variables, which have been recently derived in Götze et al. (Electron J Probab 26:1–22, 2021), turn out to be essential for our proof. Finally, we illustrate our findings in a small simulation study. [ABSTRACT FROM AUTHOR]

This article presents a novel approach for adaptive nonlinear state estimation in a modified autoregressive time series with fixed coefficients, leveraging an adaptive polynomial Kalman filter (APKF). The proposed APKF dynamically adjusts the evolving system dynamics by selecting an appropriate autoregressive time‐series model corresponding to the optimal polynomial order, based on the minimum residual error. This dynamic selection enhances the robustness of the state estimation process, ensuring accurate predictions, even in the presence of varying system complexities and noise. The proposed methodology involves predicting the next state using polynomial extrapolation. Extensive simulations were conducted to validate the performance of the APKF, demonstrating its superiority in accurately estimating the true system state compared with traditional Kalman filtering methods. The root‐mean‐square error was evaluated for various combinations of standard deviations of sensor noise and process noise for different sample sizes. On average, the root‐mean‐square error value, which represents the disparity between the true sensor reading and estimate derived from the adaptive Kalman filter, was 35.31% more accurate than that of the traditional Kalman filter. The comparative analysis highlights the efficacy of the APKF, showing significant improvements in state estimation accuracy and noise resilience. [ABSTRACT FROM AUTHOR]

Abstract Aiming at the problem of sub‐synchronous oscillations induced by direct‐drive wind farms with series‐compensated lines, this paper proposes an unknown system dynamics estimation‐based PI controller to achieve sub‐synchronous oscillation suppression. According to the mathematical model of the direct‐drive wind farm grid‐connected system, the relationship between the direct‐drive wind turbine grid‐side converter current inner‐loop PI controller and the sub‐synchronous components is first established. Secondly, the uncertain sub‐synchronous current components and voltage components in the series‐compensated lines of the direct‐drive wind farm are taken as the total disturbance, and an unknown system dynamic estimator‐based PI controller is designed by introducing the first‐order low‐pass filter operation. Then, the stability and convergence of the closed‐loop system are proved by Lyapunov theory. Finally, the Prony method is used to analyse the current signal output by the direct‐drive wind turbine, and the inherent characteristics of the negative damping of the SSO induced by the series‐compensated line of the direct‐driven wind farm are revealed. A comparative numerical simulation is carried out to demonstrate that the sub‐synchronous oscillations of the direct‐drive wind farm with series‐compensated lines can be suppressed under different operating conditions.

Abstract This article presents a novel approach for adaptive nonlinear state estimation in a modified autoregressive time series with fixed coefficients, leveraging an adaptive polynomial Kalman filter (APKF). The proposed APKF dynamically adjusts the evolving system dynamics by selecting an appropriate autoregressive time‐series model corresponding to the optimal polynomial order, based on the minimum residual error. This dynamic selection enhances the robustness of the state estimation process, ensuring accurate predictions, even in the presence of varying system complexities and noise. The proposed methodology involves predicting the next state using polynomial extrapolation. Extensive simulations were conducted to validate the performance of the APKF, demonstrating its superiority in accurately estimating the true system state compared with traditional Kalman filtering methods. The root‐mean‐square error was evaluated for various combinations of standard deviations of sensor noise and process noise for different sample sizes. On average, the root‐mean‐square error value, which represents the disparity between the true sensor reading and estimate derived from the adaptive Kalman filter, was 35.31% more accurate than that of the traditional Kalman filter. The comparative analysis highlights the efficacy of the APKF, showing significant improvements in state estimation accuracy and noise resilience.

Abstract Suitable and effective matching area selection is crucial for gravity matching‐aided navigation. In this paper, an all‐field extended extremum algorithm based on an adaptive threshold (AT‐AEE) is proposed for matching area selection in the Arctic Sea. The gradient data is obtained by using the convolution of gravity reference graph data and all‐field extended extremum parameters. Then, the adaptive threshold method was employed to determine the optimal gradient threshold based on gravity anomaly data across various test areas. Data points with gradients exceeding the specified threshold are identified as local candidate points for matching areas. The test areas containing a certain proportion of local candidate points are designated as the suitable matching areas. Nine test areas in the Arctic Sea with different gravity change characteristics were chosen for simulation experiments to verify the performance of the proposed algorithm. Simulation experiments showed that superior navigation positioning results could be obtained in the matching areas selected by the AT‐AEE algorithm. Compared to traditional algorithm, the matching areas derived from the AT‐AEE algorithm performed with a better consistency in the gravity matching navigation results. In suitable matching areas with the proportion of local candidate points reaching 70%, the average positioning errors could be reduced to less than 1.5 n miles.

Abstract Recent advances in concurrent learning based adaptive controllers have relaxed the persistency of excitation condition required to achieve exponential tracking and parameter estimation error convergence. This was made possible via the use of additional concurrent learning stacks in the parameter estimation algorithm. However, the proposed concurrent learning components, that is, the history stacks, needed to be filled with “selected” values dependent on the actual system states. Therefore, the previously proposed concurrent learning adaptive controllers required the system to be stable initially for a finite time so that the corresponding history stacks can be filled (finite excitation condition). In this work, motivated to remove the finite excitation condition, a novel desired system state based concurrent learning adaptive controller is proposed. In order to remove the system state dependencies in the controller and estimation algorithms, a filtered version of the dynamics and a novel prediction error formulation have been designed. The overall exponential stability, parameter error convergence and boundedness of the system states during closed loop operations are ensured via Lyapunov based arguments. The main advantages of the proposed method are its dependence on the desired system states and the overall stability results that paved the way in removing the need for finite excitation condition. Numerical studies performed on a two link robotic device are also presented to illustrate the feasibility of the proposed method.

Suitable and effective matching area selection is crucial for gravity matching‐aided navigation. In this paper, an all‐field extended extremum algorithm based on an adaptive threshold (AT‐AEE) is proposed for matching area selection in the Arctic Sea. The gradient data is obtained by using the convolution of gravity reference graph data and all‐field extended extremum parameters. Then, the adaptive threshold method was employed to determine the optimal gradient threshold based on gravity anomaly data across various test areas. Data points with gradients exceeding the specified threshold are identified as local candidate points for matching areas. The test areas containing a certain proportion of local candidate points are designated as the suitable matching areas. Nine test areas in the Arctic Sea with different gravity change characteristics were chosen for simulation experiments to verify the performance of the proposed algorithm. Simulation experiments showed that superior navigation positioning results could be obtained in the matching areas selected by the AT‐AEE algorithm. Compared to traditional algorithm, the matching areas derived from the AT‐AEE algorithm performed with a better consistency in the gravity matching navigation results. In suitable matching areas with the proportion of local candidate points reaching 70%, the average positioning errors could be reduced to less than 1.5 n miles. [ABSTRACT FROM AUTHOR]

This study addresses the state estimation problem of discrete‐time non‐linear stochastic systems with non‐Gaussian noises, particularly impulsive noises. Instead of minimizing the mean square error of the state estimate, which tends to excessively focus on outliers caused by non‐Gaussian noises, the ℓ1${\ell }_1$ norm‐based non‐linear recursive filter (L1KF) is put forward in this paper. Here, minimizing the ℓ1${\ell }_1$ norm of model errors is actually to pursue the minimum sum of absolute values of all errors, which is equitable to all model errors rather than paying much attention on outliers. To further improve estimation accuracy, a recursive nonlinear smoother (L1KS) is proposed, based on minimizing the ℓ1${\ell }_1$ norm of model errors. The proposed ℓ1${\ell }_1$ norm‐based filter and smoother are implemented using unscented transformation for statistical linear regression applied to nonlinear models. Additionally, the computational complexity of the proposed method is analysed. Simulation results of tracking a radar target with impulsive noises demonstrate the effectiveness and robustness of the proposed estimator. [ABSTRACT FROM AUTHOR]

Recent advances in concurrent learning based adaptive controllers have relaxed the persistency of excitation condition required to achieve exponential tracking and parameter estimation error convergence. This was made possible via the use of additional concurrent learning stacks in the parameter estimation algorithm. However, the proposed concurrent learning components, that is, the history stacks, needed to be filled with "selected" values dependent on the actual system states. Therefore, the previously proposed concurrent learning adaptive controllers required the system to be stable initially for a finite time so that the corresponding history stacks can be filled (finite excitation condition). In this work, motivated to remove the finite excitation condition, a novel desired system state based concurrent learning adaptive controller is proposed. In order to remove the system state dependencies in the controller and estimation algorithms, a filtered version of the dynamics and a novel prediction error formulation have been designed. The overall exponential stability, parameter error convergence and boundedness of the system states during closed loop operations are ensured via Lyapunov based arguments. The main advantages of the proposed method are its dependence on the desired system states and the overall stability results that paved the way in removing the need for finite excitation condition. Numerical studies performed on a two link robotic device are also presented to illustrate the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

In statistical process control, accurately estimating in-control (IC) parameters is crucial for effective monitoring. This typically requires a Phase I analysis to obtain estimates before monitoring commences. The traditional "fixed" estimate (FE) approach uses these estimates exclusively, while the "adaptive" estimate (AE) approach updates the estimates with each new observation. Such extreme criteria reflect the traditional bias-variance tradeoff in the framework of the sequential parameter learning schemes. This paper proposes an intermediate update rule that generalizes two ad hoc criteria for monitoring univariate Gaussian data, by giving a lower probability to parameter updates when an out-of-control (OC) situation is likely, therefore updating more frequently when there is no evidence of an OC scenario. The simulation study shows that this approach improves the detection power for small and early shifts, which are commonly regarded as a weakness of control charts based on fully online adaptive estimation. The paper also shows that the proposed method performs similarly to the fully adaptive procedure for larger or later shifts. The proposed method is illustrated by monitoring the sudden increase in ICU counts during the 2020 COVID outbreak in New York. [ABSTRACT FROM AUTHOR]

Abstract This article proposes an online solution to address the problem of closed‐loop system identification using multiple recursive least squares estimation protocols. Some control systems cannot be analysed in an open‐loop form for stability reasons or the requirement for online control system operation. So, it is necessary to identify plant dynamics and controller parameters based on input–output data from the feedback structure. The presented method identifies real‐time parameters of plant dynamics and controller parameters by utilising a series of recursive least square estimation algorithms that estimate open‐loop data from noisy input–output data measured from the closed‐loop feedback structure. The proposed method can effectively identify abrupt variations in both the controller parameters and plant dynamics. This capability makes it valuable for deployment as a supervisory component, enabling the detection of any faults that may arise in operating systems. Mathematical formulations and theorems are developed, and two numerical case studies are presented to examine the feasibility and performance of the presented closed‐loop system identification protocol.

This paper presents a new model-based fault resilient control scheme for a class of nonlinear distributed parameter systems (DPS) represented by parabolic partial differential equations (PDE) in the presence of actuator faults. A Luenberger-like observer on the basis of nonlinear PDE representation of DPS is developed with boundary measurements. A detection residual is generated by taking the difference between the measured output of the DPS and the estimated one given by the observer. Once a fault is detected, an unknown actuator fault parameter vector together with a known basis function is utilized to adaptively estimate the fault dynamics. A novel tuning algorithm is derived to estimate the unknown actuator fault parameter vector. Next, in order to achieve resilience, the controller from the healthy scenario is adjusted to mitigate the faults by using both estimated fault dynamics and a secondary measurement. Subsequently, an explicit formula is developed to estimate the time-to-resilience (TTR). Finally, a nonlinear example is utilized to illustrate the effectiveness of the proposed scheme.

High precision navigation and positioning technology, as a fundamental function, is gradually occupying an indispensable position in the various fields. However, a single sensor cannot meet the navigation requirements in different scenarios. This paper proposes a "plug and play" Vision/IMU/UWB multi-sensor tightly-coupled system based on factor graph. The difference from traditional UWB-based tightly-coupled models is that the Vision/IMU/UWB tightlycoupled model in this study uses UWB base station coordinates as parameters for real-time estimation without pre-calibrating UWB base stations. Aiming at the dynamic change of sensor availability in multi-sensor integrated navigation system and the serious problem of traditional factor graph in the weight distribution of observation information, this study proposes an adaptive robust factor graph model. Based on redundant measurement information, we propose a novel adaptive estimation model for UWB ranging covariance, which does not rely on prior information of the system and can adaptively estimate realtime covariance changes of UWB ranging. The algorithm proposed in this study was extensively tested in real-world scenarios, and the results show that the proposed system is superior to the most advanced combination method in all cases. Compared with the visual-inertial odometer based on the factor graph (FG-VIO), the RMSE is improved by 62.83 and 64.26% in scene 1 and 82.15, 70.32, and 75.29% in scene 2 (non-line-of-sight environment). [ABSTRACT FROM AUTHOR]

Summary: An adaptive fractional‐order unscented particle filter (FOUPF) and an adaptive FOUPF with the estimations of the noise covariance matrices (NCMs) are proposed to estimate the state of charge (SOC) of lithium‐ion batteries (LIBs) in this study. The Grünwald–Letnikov difference is employed to establish the corresponding discrete‐time equation of the fractional‐order system (FOS). The order and SOC of FOS of LIBs are controlled within an appropriate interval by a mapping function. In order to achieve a joint estimation of order and unknown parameters for a FOS, an augmented vector method is applied in this study. Compared with the adaptive fractional‐order unscented Kalman filter and adaptive fractional‐order cubature Kalman filter, the proposed adaptive FOUPF has a higher accuracy for estimating SOC. Besides, an iterative approach that accommodates the NCMs is proposed to improve the estimation accuracy of SOC. Finally, the availability of the proposed algorithms is tested by several experiments. [ABSTRACT FROM AUTHOR]

Kalman filter has emerged as a powerful tool for unbalance identification in rotating machinery. Recently, the augmented Kalman filter combined with the finite element model has grown up and projects its potential for complex rotor systems. This paper investigates the application of the augmented Kalman filter (AKF) to a practical turbofan engine. The current study reveals that using steady-state responses as measurements can cause fluctuation in the estimated results, even divergence for some cases, while the available signals in practice are steady-state responses generally. To the authors' knowledge, this practical problem is revealed for the first time. To address the problem, the convergence criterion is employed to improve the AKF and formulates the adaptive fading augmented Kalman filter (AFAKF) proposed in this paper. Results indicate that the increase of the amplification factor, the insufficient measurement points, and the complexity of the dynamic model can all lead to the deterioration of the estimated unbalance. The proposed AFAKF method shows favorable convergence and can achieve accurate estimation with less than 5% relative errors, and the superiority over AKF in computation cost is also observed. [ABSTRACT FROM AUTHOR]

This article proposes an online solution to address the problem of closed‐loop system identification using multiple recursive least squares estimation protocols. Some control systems cannot be analysed in an open‐loop form for stability reasons or the requirement for online control system operation. So, it is necessary to identify plant dynamics and controller parameters based on input–output data from the feedback structure. The presented method identifies real‐time parameters of plant dynamics and controller parameters by utilising a series of recursive least square estimation algorithms that estimate open‐loop data from noisy input–output data measured from the closed‐loop feedback structure. The proposed method can effectively identify abrupt variations in both the controller parameters and plant dynamics. This capability makes it valuable for deployment as a supervisory component, enabling the detection of any faults that may arise in operating systems. Mathematical formulations and theorems are developed, and two numerical case studies are presented to examine the feasibility and performance of the presented closed‐loop system identification protocol. [ABSTRACT FROM AUTHOR]

We study parameter estimation for a linear parabolic second-order stochastic partial differential equation (SPDE) in two space dimensions with a small dispersion parameter using high frequency data with respect to time and space. We set two types of Q-Wiener processes as a driving noise. We provide minimum contrast estimators of the coefficient parameters of the SPDE appearing in the eigenfunctions of the differential operator of the SPDE based on the thinned data in space, and approximate the coordinate process based on the thinned data in time. Moreover, we propose an estimator of the drift parameter using the fact that the coordinate process is the Ornstein-Uhlenbeck process and statistical inference for diffusion processes with a small noise. We also give an example and simulation results for the proposed estimators. [ABSTRACT FROM AUTHOR]

This paper proposes a new secure distributed estimation for cyber‐physical systems against adversarial attacks with noisy input. To mitigate the effect of attacks, a novel distributed attack detection based on a reliable reference estimation obtained by temporal convex combination is proposed. Furthermore, for more effective and robust performance, an adaptation rule to adjust convex combination weights is presented, in which the generalized correntropy method with nonlinear loss function and stochastic gradient descent are utilized. Besides, to eliminate input noise, a bias‐compensation method in local adaptation of the secure distributed estimation is proposed. Simulations show superior dynamic and real‐time adaptability of the proposed algorithm under complex attacking scenarios. [ABSTRACT FROM AUTHOR]

This article discusses the nonparametric estimation of a bivariate density function using copula information under right censoring. We propose an adaptive estimator based on wavelet methods and the formulae for the asymptotic mean integrated squared error(MISE) is used to get the near optimal rate on a large functional class of regular densities. In particular, the asymptotic formulae for MISE in the context of kernel density estimators is derived in the case of censoring. Finally, the consistency of the proposed estimators is established and its effectiveness is validated through a numerical simulations. [ABSTRACT FROM AUTHOR]

In this article, an observer-based adaptive non-singular fast-reaching terminal sliding mode control strategy is proposed to tackle the problem of actuator faults and uncertain disturbance in aerial robot systems. Firstly, a model of an aerial robot system is established through dynamic analysis. Next, an adaptive observer, combined with a fast adaptive fault estimation (FAFE) algorithm, is proposed to estimate system states and actuator failure and compensate for faults in a precise and prompt manner. In addition, a non-singular fast terminal sliding surface is defined, taking into account the fast convergence of the tracking errors in order to provide appropriate trajectory tracking results. Since the upper bounds of the disturbances caused by the manipulator of the system in practice are unknown, the control approach may benefit from the addition of an adaptive control strategy that can suppress the influence of uncertain disturbances. The Lyapunov stability theory demonstrates that tracking errors are able to converge stably and quickly. In the end, the contrast experiment is conducted to exhibit the effectiveness of the proposed control strategy. The results demonstrate quicker convergence and improved estimating accuracy. [ABSTRACT FROM AUTHOR]

The adaptive single-mode fiber (SMF) coupling technique is normally adopted since the coupling efficiency (CE) significantly determines the performance of the free-space optical communication (FSOC) systems. The stochastic parallel gradient descent (SPGD) algorithm is the most commonly used control algorithm in adaptive SMF fiber coupling system. This paper proposes an improved SPGD algorithm named estimation-based stochastic parallel gradient descent (ESPGD) algorithm to accelerate the sytem convergence when applied to a practical adaptive SMF coupling system based on fast steering mirror (FSM). Applying the perturbed voltages, FSM dynamic response and then recording the performance metrics is the basic and most time-consuming process in actual adaptive SMF coupling system control. The ESPGD algorithm uses a different gradient estimation method based on adaptive parameter estimation method. The algorithm only needs to perform this process once in one iteration while the original SPGD algorithm needs to perform it twice to obtain the estimated gradient. This greatly reduce the time consumed by one iteration of the algorithm, thereby reducing the convergence time. The simulation and experimental results show that the ESPGD algorithm reduces the system convergence time by nearly half when correcting static angular errors and more than doubles the control bandwidth when correcting sinusoidal angular jitters.

A precise dynamic model and exact statistical information are required in a standard Kalman filter to ensure optimal performance. Without these, degraded performance may be obtained. In this paper, an improved adaptive estimation approach for uncertain models is proposed, and the fading matrix is adaptively estimated according to the observability of the system state. Meanwhile, a sequential way to calculate the covariance matrix of the measurement noises is performed, thereby strengthening its ability to resist disturbances further. The proposed algorithm was implemented in practical data processing of GNSS (Global Navigation Satellite System) and INS (Inertial Navigation System) integrated systems. The measurement sensors were equipped on aircraft and land vehicles to test their stability and robustness. Comparisons with existing fading filters and conventional nonlinear Kalman filters show that the proposed algorithm controls model errors, weakens influences of constantly changing and abrupt outliers, achieves relatively high precision, and restrains filter divergence effectively.

State estimation is paramount in control, monitoring, and fault management across various domains. Uncertainty in model parameters and changing system dynamics pose significant challenges to accurate state estimation. This paper proposes a novel adaptive estimation strategy called the Moving Window Interacting Multiple Model (MWIMM). Using a moving window improves identifiability and computational efficiency of the multiple model algorithms by focusing on a subset of possible models, rather than considering all models at each stage. MWIMM enables the estimation of gradual changes in the system, making it valuable for fault intensity and Remaining Useful Life (RUL) estimation. The paper provides an overview of adaptive estimation strategies, presents the formulation of MWIMM for fault intensity and RUL estimation, and investigates the parameter estimation problem. Results are compared with those of augmented state Extended Kalman Filter (EKF) estimation, and it is shown that the proposed MWIMM approach offers a promising alternative for effectively handling extensive parameter uncertainty and accommodating gradual changes in system parameters.

We consider parameter estimation for a linear parabolic second‐order stochastic partial differential equation (SPDE) in two space dimensions driven by two types of Q$$ Q $$‐Wiener processes based on high frequency data in time and space. We first estimate the parameters which appear in the eigenfunctions of the differential operator of the SPDE using the minimum contrast estimator based on the thinned data with respect to space, and then construct an approximate coordinate process of the SPDE. Furthermore, we propose estimators of the coefficient parameters of the SPDE utilizing the approximate coordinate process based on the thinned data with respect to time. We also give some simulation results. [ABSTRACT FROM AUTHOR]

Quantum state tomography (QST) is essential for characterizing unknown quantum states. Several methods of estimating quantum states already exist and can be classified mainly into three broad classes. They are based on the criteria like maximum likelihood, linear inversion, and Bayesian framework. The Bayesian framework for QST gives a better reconstruction performance. However, the existing methods of the Bayesian frameworks are computationally extensive and, most of the time require knowledge about the prior distribution of the quantum state. In this paper, we propose a Bayesian method of QST based on the linear minimum mean square error criterion, where the prior statistics are estimated and the computational complexity is comparable to that of the linear inversion based QST method. We also propose an adaptive version based on the block estimation of parameters. Extensive numerical simulations are conducted to demonstrate its efficacy over the linear inversion-based QST regarding trace distance error metric. [ABSTRACT FROM AUTHOR]

Abstract A robust interacting multiple model approach is proposed to address the problem of accuracy and non‐Gaussian measurement noise in manoeuvering target tracking. The proposed approach introduces multiple fading factors into the prediction covariance matrix and adjusts each channel of the gain matrix in real time to improve the accuracy caused by model mismatch and enhance state transition capability. Considering the non‐Gaussian noise, an improved IMM filter is constructed to further improve the robustness using the maximum correntropy criterion. The simulation results show that the proposed approach can effectively suppress the non‐Gaussian noise and improve the accuracy with adaptability and robustness.

Abstract This paper proposes a new secure distributed estimation for cyber‐physical systems against adversarial attacks with noisy input. To mitigate the effect of attacks, a novel distributed attack detection based on a reliable reference estimation obtained by temporal convex combination is proposed. Furthermore, for more effective and robust performance, an adaptation rule to adjust convex combination weights is presented, in which the generalized correntropy method with nonlinear loss function and stochastic gradient descent are utilized. Besides, to eliminate input noise, a bias‐compensation method in local adaptation of the secure distributed estimation is proposed. Simulations show superior dynamic and real‐time adaptability of the proposed algorithm under complex attacking scenarios.

Abstract The authors propose a computationally efficient approach to estimate the directions of arrival of far‐field sources impinging on a sensor array. The proposed estimator is formed using a sparse reconstruction framework, employing a novel adaptive grid selection technique to reduce the dimensionality of the used dictionary matrix. The method further makes use of a SPICE‐inspired dictionary to adaptively select an appropriate regularisation parameter and to select the active grid set. An adaptive stepsize selection strategy is also introduced to reduce computation complexity further. The proposed method allows for accurate direction‐of‐arrival (DOA) estimates using even a single snapshot, also from weak sources. Numerical simulations indicate that the method offers preferable performance in comparison to existing state‐of‐the‐art DOA estimation algorithms.

Abstract In order to solve the problems of difficult control, poor stability, and low control precision in complex autonomous non‐linear systems, and some sensors have non‐linear errors in special environments. Based on the PSO (Particle Swarm Optimization) algorithm, an PSO‐BP‐PID (Particle Swarm Optimization Back Propagation neural network PID) control method and a sensor error compensation algorithm based on BP (Back Propagation) neural network are designed for optimal temperature and humidity control and sensor error compensation in the autonomous greenhouse system. The error between the average temperature value and the target value after steady state is 0.5°C, and the error between the average humidity value and the target value is 1% RH. The results show that the control method can effectively compensate the non‐linear error of the sensor and improve the performance of the control system in a complex environment, which is suitable for the stable and control of actuators in autonomous systems. The error of temperature and humidity sensor is compensated by BP neural network; PSO (Particle Swarm Optimization) was used to optimize the BP‐PID parameters of the automatic greenhouse system.

A robust interacting multiple model approach is proposed to address the problem of accuracy and non‐Gaussian measurement noise in manoeuvering target tracking. The proposed approach introduces multiple fading factors into the prediction covariance matrix and adjusts each channel of the gain matrix in real time to improve the accuracy caused by model mismatch and enhance state transition capability. Considering the non‐Gaussian noise, an improved IMM filter is constructed to further improve the robustness using the maximum correntropy criterion. The simulation results show that the proposed approach can effectively suppress the non‐Gaussian noise and improve the accuracy with adaptability and robustness. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with parameter estimate of deterministic autoregressive moving average (DARMA) systems with uniform quantized output observations. By designing system input signals, the recursive least‐squares algorithm with designed weights is proved to have convergence properties under the uniform output signal quantizer. The authors analyse the properties of the size of quantization error, which implies that the convergence properties can be achieved when the quantization error satisfies some conditions. A numerical example is supplied to demonstrate the theoretical results.

Abstract This paper investigates a fault‐tolerant fixed‐time prescribed performance microelectromechanical system gyroscope using the adaptive backstepping method. The control protocol is designed such that not only is the system robust to even extremely harsh conditions of disturbance and actuator faults but also the performance and its settling time are user‐adjustable. Also, the system itself along with the external disturbances and actuator faults are assumed to be uncertain. Two case studies have been analyzed; the controller performance in the presence of very severe while uncertain disturbance and actuator faults, and a comparison between fixed‐time and finite‐time in this model in terms of their performance and convergence rate. First, the dynamics of the system are derived, and the prescribed performance error is defined for the analysis. Then, using the backstepping method, and adaptive estimations for the uncertainties, the algorithm is designed to converge the errors to a small set near zero with a fixed‐time convergence rate after which the stability of the system is verified via Lyapunov theory. In the end, a simulation example is presented in each case study to represent the efficacy of the proposed control scheme.

Abstract This paper proposes an adaptive observer‐based scheme to control fractional‐order chaotic micro‐electro‐mechanical‐systems (MEMS). The fractional‐order model of a system exhibits the dynamic behaviour of a physical system more accurately than a similar integer‐order one. An observer‐based control considering the unknown parameters is presented for a fractional‐order chaotic micro‐electro‐mechanical‐system. To handle the existence of the unknown parameters, the control law consists of both estimated parameters and also estimated states that have been designed. First, a fractional‐order observer is designed to estimate the state variables. The asymptotic convergence to zero of the estimation state error is proved using the Lyapunov scheme. After that, with the designed observer as a foundation, adaptive control is expanded for the closed‐loop system to ensure its asymptotic stability. An evaluation of the proposed method shows its efficacy via simulations for two case studies.

Abstract This paper proposes a novel variational Bayesian (VB) adaptive Kalman filter with mismatched process noise covariance matrix (PNCM). Firstly, this paper explains the reason why the predicted error covariance matrix (PECM) is chosen for variational inference. Secondly, compared with the earlier VB adaptive Kalman filter (VB‐AKF‐Q), the proposed filter calculate the dynamic model of the PECM with its historical estimation information. Therefore, the proposed filter can overcome the influence of mismatched PNCM on the initial value setting of PECM in the VB‐AKF‐Q. Finally, we use the evidence lower bound for the proposed filter and give the convergence criterion on this basis. Some examples with a target tracking simulation are carried out to demonstrate the superiority of the proposed filter.

Abstract The trajectory prediction of the hypersonic glide vehicle (HGV) can provide hit point information for early warning systems, which is of great significance for near‐space defence operations. However, the heavy‐tailed noise caused by abnormal environmental disturbance and abrupt changes in vehicle trajectory seriously affects the accuracy of HGV trajectory prediction. To solve the problem of trajectory prediction for HGV under heavy‐tailed noise, we propose an adaptive multivariate Student's t‐process regression method called aEM‐MVTPR. Firstly, a heavy‐tailed noise model is developed using the Student's t‐distribution. Secondly, a multivariate Student's t‐process regression (MVTPR) for HGV trajectory prediction is derived, and the method can learn the HGV trajectory time series features and mine the correlations among the trajectory variables. Finally, to further improve the method's robustness, we use the accelerated expectation maximisation algorithm and Pearson correlation analysis to adaptively estimate and adjust the initial values of the MVTPR parameters. The simulation experimental results show that the proposed method has more accurate predicted values of trajectory variables than multivariate Gaussian process regression (MVGPR) under heavy‐tailed noise conditions. In addition, the ability of the aEM‐MVTPR to adaptively adjust the parameter makes it more robust than the MVTPR under different noise environments.

Abstract This paper develops a novel Taylor‐based adaptive sliding mode control method (ASMC) for robot manipulators. In the first new scheme, sliding mode control (SMC) is effectively enhanced using the Taylor expansion for achieving a less conservative sign‐function gain that enables chattering attenuation. After that, a new Taylor‐based adaptive SMC scheme is proposed without prior knowledge of the upper bound of uncertainty and the Taylor expansion coefficients. Then, a new Taylor‐based boundary layer ASMC scheme is proposed for chattering attenuation. As a fact, no chattering is expected to be observed as long as the sliding surface remains an invariant set. However, the sliding surface will not be an invariant set unless the sign‐function is precisely determined on the sliding surface. It is verified that the sign‐function cannot be precisely determined on the sliding surface due to the presence of uncertainty, hence, the chattering phenomenon. In the new Taylor‐based boundary layer ASMC scheme, the conventional ASMC is modified by removing the sign‐function in the vicinity of the sliding surface and using the Taylor expansion to estimate and compensate for the uncertainty. Compared to a time‐delay ASMC applied to a robot manipulator, the Taylor‐based ASMC scheme exhibits a less conservative sign‐function gain resulting in chattering attenuation.

In this article, we investigate a fault‐tolerant control (FTC) for a class of quadrotors with variable mass and actuator faults. Firstly, a mathematical model of quadrotors considered variable‐mass factor is established based on Euler Newton's formula. Secondly, an adaptive estimation algorithm based on a fault observer is designed to achieve the estimations of variable mass and actuator fault, respectively. With the aim of obtaining satisfactory trajectory tracking performance, utilizing the variable mass estimation, a nonsingular terminal sliding mode controller is designed to track desired position. Meanwhile, utilizing the information of actuator fault estimation, an integral sliding mode controller is designed to track desired attitude. Finally, by comparison with the existing sliding mode control (SMC) and other FTC algorithm, the results show that the proposed FTC method has better tracking performance in the case of variable mass, fault and disturbance. [ABSTRACT FROM AUTHOR]

The authors propose a computationally efficient approach to estimate the directions of arrival of far‐field sources impinging on a sensor array. The proposed estimator is formed using a sparse reconstruction framework, employing a novel adaptive grid selection technique to reduce the dimensionality of the used dictionary matrix. The method further makes use of a SPICE‐inspired dictionary to adaptively select an appropriate regularisation parameter and to select the active grid set. An adaptive stepsize selection strategy is also introduced to reduce computation complexity further. The proposed method allows for accurate direction‐of‐arrival (DOA) estimates using even a single snapshot, also from weak sources. Numerical simulations indicate that the method offers preferable performance in comparison to existing state‐of‐the‐art DOA estimation algorithms. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive distributed hybrid control approach to investigate the output containment tracking problem of heterogeneous wide-area networks with intermittent communication. First, a clustered network is modeled for a wide-area scenario. An aperiodic intermittent communication mechanism is exerted on the clusters such that clusters only communicate through leaders. Second, in order to remove the assumption that each follower must know the system matrix of the leaders and achieve output containment, a distributed adaptive hybrid control strategy is proposed for each agent under the internal model and adaptive estimation mechanism. Third, sufficient conditions based on average dwell-time are provided for the output containment achievement using a Lyapunov function method, from which the exponential stability of the closed-loop system is analyzed. Finally, simulation results are presented to demonstrate the effectiveness of the proposed adaptive distributed intermittent control strategy. [ABSTRACT FROM AUTHOR]

In order to solve the problems of difficult control, poor stability, and low control precision in complex autonomous non‐linear systems, and some sensors have non‐linear errors in special environments. Based on the PSO (Particle Swarm Optimization) algorithm, an PSO‐BP‐PID (Particle Swarm Optimization Back Propagation neural network PID) control method and a sensor error compensation algorithm based on BP (Back Propagation) neural network are designed for optimal temperature and humidity control and sensor error compensation in the autonomous greenhouse system. The error between the average temperature value and the target value after steady state is 0.5°C, and the error between the average humidity value and the target value is 1% RH. The results show that the control method can effectively compensate the non‐linear error of the sensor and improve the performance of the control system in a complex environment, which is suitable for the stable and control of actuators in autonomous systems. The error of temperature and humidity sensor is compensated by BP neural network; PSO (Particle Swarm Optimization) was used to optimize the BP‐PID parameters of the automatic greenhouse system. The error of temperature and humidity sensor is compensated by BP neural network; Particle Swarm Optimization (PSO) was used to optimize the BP‐PID parameters of the automatic greenhouse system. [ABSTRACT FROM AUTHOR]

Standard methods, such as sequential procedures based on Johansen's (pseudo-)likelihood ratio (PLR) test, for determining the co-integration rank of a vector autoregressive (VAR) system of variables integrated of order one can be significantly affected, even asymptotically, by unconditional heteroskedasticity (non-stationary volatility) in the data. Known solutions to this problem include wild bootstrap implementations of the PLR test or the use of an information criterion, such as the BIC, to select the co-integration rank. Although asymptotically valid in the presence of heteroskedasticity, these methods can display very low finite sample power under some patterns of non-stationary volatility. In particular, they do not exploit potential efficiency gains that could be realized in the presence of non-stationary volatility by using adaptive inference methods. Under the assumption of a known autoregressive lag length, Boswijk and Zu develop adaptive PLR test based methods using a non-parametric estimate of the covariance matrix process. It is well-known, however, that selecting an incorrect lag length can significantly impact on the efficacy of both information criteria and bootstrap PLR tests to determine co-integration rank in finite samples. We show that adaptive information criteria-based approaches can be used to estimate the autoregressive lag order to use in connection with bootstrap adaptive PLR tests, or to jointly determine the co-integration rank and the VAR lag length and that in both cases they are weakly consistent for these parameters in the presence of non-stationary volatility provided standard conditions hold on the penalty term. Monte Carlo simulations are used to demonstrate the potential gains from using adaptive methods and an empirical application to the U.S. term structure is provided. [ABSTRACT FROM AUTHOR]

Most of the works on estimating winds from the Doppler information provided by the very high frequency (VHF) radars use either parametric or nonparametric techniques. The studies using nonparametric signal processing techniques have tried to interpret the radar returns from higher altitudes where the signal to noise (SNR) is weak. It may be challenging to cover higher altitudes accurately without actually boosting signal strength by increasing transmit power and processing gain. The studies using parametric techniques have assumed data from a particular model to carry out pattern recognition and ascertain accuracy for a single frame of data, which does not guarantee consistency for an extended dataset. The present study introduces the empirical Bayesian approach for processing the radar data in near real-time to achieve higher altitude coverage. The eBayes adaptive estimation technique is a data-aware technique that learns from informative prior. It implements a hybrid model for data analytics, incorporating a nonparametric model to improve signal strength and a parametric model to reduce noise variance. It derives wind accurately from the Doppler, which is cross-validated with the wind information obtained from several GPS radiosonde simultaneous observations. In addition, the eBayes approach incorporates a modified version of classical moments estimation and introduces new quality parameters to quantify SNR characteristics. The study concludes that the eBayes analytical approach can accurately derive 3D winds consistently, covering higher altitudes of 25.2–28.8 km, improving the typical MST (Mesosphere Stratosphere and Troposphere) radar reference range of 21 km. This approach is helpful for several scientific investigations using measurements from VHF radars. [ABSTRACT FROM AUTHOR]