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For patients with refractory epilepsy, the seizure onset zone (SOZ) plays an essential role in determining the specific regions of the brain that will be surgically resected. High-frequency oscillations (HFOs) and connectivity-based approaches have been identified among the potential biomarkers to localize the SOZ. However, there is no consensus on how connectivity between HFO events should be estimated, nor on its subject-specific short-term reliability. Therefore, we propose the channel-level connectivity dispersion (CLCD) as a metric to quantify the variability in synchronization between individual electrodes and to identify clusters of electrodes with abnormal synchronization, which we hypothesize to be associated with the SOZ. In addition, we developed a specialized filtering method that reduces oscillatory components caused by filtering broadband artifacts, such as sharp transients, spikes, or direct current shifts. Our connectivity estimates are therefore robust to the presence of these waveforms. To calculate our metric, we start by creating binary signals indicating the presence of high-frequency bursts in each channel, from which we calculate the pairwise connectivity between channels. Then, the CLCD is calculated by combining the connectivity matrices and measuring the variability in each electrode's combined connectivity values. We test our method using two independent open-access datasets comprising intracranial electroencephalography signals from 89 to 15 patients with refractory epilepsy, respectively. Recordings in these datasets were sampled at approximately 1000 Hz, and our proposed CLCDs were estimated in the ripple band (80-200 Hz). Across all patients in the first dataset, the average ROC-AUC was 0.73, and the average Cohen's d was 1.05, while in the second dataset, the average ROC-AUC was 0.78 and Cohen's d was 1.07. On average, SOZ channels had lower CLCD values than non-SOZ channels. Furthermore, based on the second dataset, which includes surgical outcomes (Engel I-IV), our analysis suggested that higher CLCD interquartile (as a measure of CLCD distribution spread) is associated with favorable outcomes (Engel I). This suggests that CLCD could significantly assist in identifying SOZ clusters and, therefore, provide an additional tool in surgical planning for epilepsy patients. [ABSTRACT FROM AUTHOR]

For fractional order systems with colored process noise, the discretization fractional order system model is used to construct the augmented vector defined by the state vector and colored process noise vector. Based on the augmented equation of fractional order systems, the robust local Kalman filtering algorithm for fractional order systems with colored process noise is derived. The matrix weighted fusion, weighted measurement fusion and centralized fusion methods were used to fuse and estimate the state of multi-sensor fractional order system. Simulation results show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract State estimation techniques appear in a plethora of engineering fields, in particular for the attitude estimation application of interest in this contribution. A number of filters have been devised for this problem, in particular Kalman-type ones, but in their standard form they are known to be fragile against outliers. In this work, we focus on error-state filters, designed for states living on a manifold, here unit-norm quaternions. We propose extensions based on robust statistics, leading to two robust M-type filters able to tackle outliers either in the measurements, in the system dynamics or in both cases. The performance and robustness of these filters is explored in a numerical experiment. We first assess the outlier ratio that they manage to mitigate, and second the type of dynamics outliers that they can detect, showing that the filter performance depends on the measurements’ properties.

State estimation techniques appear in a plethora of engineering fields, in particular for the attitude estimation application of interest in this contribution. A number of filters have been devised for this problem, in particular Kalman-type ones, but in their standard form they are known to be fragile against outliers. In this work, we focus on error-state filters, designed for states living on a manifold, here unit-norm quaternions. We propose extensions based on robust statistics, leading to two robust M-type filters able to tackle outliers either in the measurements, in the system dynamics or in both cases. The performance and robustness of these filters is explored in a numerical experiment. We first assess the outlier ratio that they manage to mitigate, and second the type of dynamics outliers that they can detect, showing that the filter performance depends on the measurements' properties. [ABSTRACT FROM AUTHOR]

This study introduces the design of a state-feedback controller for Linear Parameter Varying (LPV) systems in scenarios where exogenous parameters are not directly accessible, and the state vector is to be estimated. Instead of considering a static feedback gain, it proposes a method for estimating these parameters and synthesizing a parameter-dependent state-feedback gain that is robust against uncertainties in parameter estimation. The state vector used by the state-feedback controller, and some quantities required by the estimation law, are both obtained by a robust filter synthesized by LMI (Linear Matrix Inequalities). This paper outlines the estimation, filtering, and control laws, detailing the conditions necessary for ensuring convergence and stability. A numerical experiment and a 2 DoF torsional system application show the enhanced dynamic performance of the method when applied to uncertain dynamic systems. The findings highlight the effectiveness of the proposed approach in maintaining system stability and improving performance despite the inherent uncertainties in parameter estimation, offering a significant contribution to the field of robust control for LPV systems. [ABSTRACT FROM AUTHOR]

For patients with refractory epilepsy, the seizure onset zone (SOZ) plays an essential role in determining the specific regions of the brain that will be surgically resected. High-frequency oscillations (HFOs) and connectivity-based approaches have been identified among the potential biomarkers to localize the SOZ. However, there is no consensus on how connectivity between HFO events should be estimated, nor on its subject-specific short-term reliability. Therefore, we propose the channel-level connectivity dispersion (CLCD) as a metric to quantify the variability in synchronization between individual electrodes and to identify clusters of electrodes with abnormal synchronization, which we hypothesize to be associated with the SOZ. In addition, we developed a specialized filtering method that reduces oscillatory components caused by filtering broadband artifacts, such as sharp transients, spikes, or direct current shifts. Our connectivity estimates are therefore robust to the presence of these waveforms. To calculate our metric, we start by creating binary signals indicating the presence of high-frequency bursts in each channel, from which we calculate the pairwise connectivity between channels. Then, the CLCD is calculated by combining the connectivity matrices and measuring the variability in each electrode’s combined connectivity values. We test our method using two independent open-access datasets comprising intracranial electroencephalography signals from 89 to 15 patients with refractory epilepsy, respectively. Recordings in these datasets were sampled at approximately 1000 Hz, and our proposed CLCDs were estimated in the ripple band (80–200 Hz). Across all patients in the first dataset, the average ROC-AUC was 0.73, and the average Cohen’s d was 1.05, while in the second dataset, the average ROC-AUC was 0.78 and Cohen’s d was 1.07. On average, SOZ channels had lower CLCD values than non-SOZ channels. Furthermore, based on the second dataset, which includes surgical outcomes (Engel I-IV), our analysis suggested that higher CLCD interquartile (as a measure of CLCD distribution spread) is associated with favorable outcomes (Engel I). This suggests that CLCD could significantly assist in identifying SOZ clusters and, therefore, provide an additional tool in surgical planning for epilepsy patients.

Multiple Target Tracking (MTT) is an extensively researched field with significant importance and a wide range of applications. However, in challenging scenarios where the targets are closely spaced, and the complexity is high, many existing MTT methods often struggle to accurately distinguish and track individual targets. To address this issue, we propose an effective smoothing strategy. Our approach extends the Rauch-Tung-Striebel technique to handle multiple targets while also employing tracklet association techniques to manage dense multi-target scenarios. This strategy involves designing a smoothing multi-target distribution model using a Bayesian approach that utilizes both kinematic and identification information about multiple targets. It can be applied to all widely used MTT algorithms in the forward filtering step. The recursive smoothing algorithm we developed for the backward filtering step enhances inter-subject discrimination and improves track quality. Consequently, we achieve enhanced trajectories by integrating orbital correlation and smoothing techniques, especially when each trajectory is entangled with nearby objects. In this paper, we demonstrate a backward smoothing strategy tailored for a linear Gaussian model and present experimental results using infrared imaging that show improved tracking performance. Additionally, we illustrate its superiority over existing smoothing algorithms.

The first purpose of this paper is to propose a theoretically new robust filter method to estimate non-observable macroeconomic indicators. The second purpose is to apply the proposed method to estimate the Hungarian potential GDP in 2000–2021. The novelty of the proposed filter method is that — unlike papers published so far — it does not require the stability of the dynamic model, only a partial stability condition must be satisfied. Moreover, such time-dependent uncertainties and nonlinearities can arise in the model that satisfy a general quadratic constraint. An important advantage of the proposed robust filter method over the traditional Kalman filter is that no stochastic assumptions is needed that may not be valid for the problem at hand. The proposed filter method has never been applied to estimate the potential GDP. To estimate the Hungarian potential GDP, the proposed method is applied using uni-, bi- and trivariate models. Estimations up to 2021 has not been published yet for the Hungarian economy. The examined period includes both the financial world crisis and the Covid-19 crisis. The results of the different models are consistent. It turned out that the economic policy was very procyclical after 2012, and the GDP gap was still positive during and also after the Covid-19 crisis. [ABSTRACT FROM AUTHOR]

This study introduces the design of a state-feedback controller for Linear Parameter Varying (LPV) systems in scenarios where exogenous parameters are not directly accessible, and the state vector is to be estimated. Instead of considering a static feedback gain, it proposes a method for estimating these parameters and synthesizing a parameter-dependent state-feedback gain that is robust against uncertainties in parameter estimation. The state vector used by the state-feedback controller, and some quantities required by the estimation law, are both obtained by a robust filter synthesized by LMI (Linear Matrix Inequalities). This paper outlines the estimation, filtering, and control laws, detailing the conditions necessary for ensuring convergence and stability. A numerical experiment and a 2 DoF torsional system application show the enhanced dynamic performance of the method when applied to uncertain dynamic systems. The findings highlight the effectiveness of the proposed approach in maintaining system stability and improving performance despite the inherent uncertainties in parameter estimation, offering a significant contribution to the field of robust control for LPV systems.

Abstract The unmanned aerial vehicle (UAV) and the unmanned ground vehicle (UGV) can complete complex tasks through information sharing and ensure the mission execution capability of multiple unmanned carrier platforms. At the same time, cooperative navigation can use the information interaction between multi‐platform sensors to improve the relative navigation and positioning accuracy of the entire system. Aiming at the problem of deviation of the system model due to gross errors in sensor measurement data or strong manoeuvrability in complex environments, a robust and adaptive UGV‐UAV relative navigation and positioning algorithm is proposed. In this paper, the relative navigation and positioning of UGV‐UAV is studied based on inertial measurement unit (IMU)/Vision. Based on analyzing the relative kinematics model and sensor measurement model, a leader (UGV)‐follow (UAV) relative navigation model is established. In the implementation of the relative navigation and positioning algorithm, the robust adaptive algorithm and the non‐linear Kalman filter (extended Kalman filter [EKF]) algorithm are combined to dynamically adjust the system state parameters. Finally, a mathematical simulation of the accompanying and landing process in the UGV‐UAV cooperative scene is carried out. The relative position, velocity and attitude errors calculated by EKF, Robust‐EKF and Robust‐Adaptive‐EKF algorithms are compared and analyzed by simulating two cases where the noise obeys the Gaussian distribution and the non‐Gaussian distribution. The results show that under the non‐Gaussian distribution conditions, the accuracy of the Robust‐Adaptive‐EKF algorithm is improved by about two to three times compared with the EKF and Robust‐EKF and can almost reach the relative navigation accuracy under the Gaussian distribution conditions. The robust self‐adaptive relative navigation and positioning algorithm proposed in this paper has strong adaptability to the uncertainty and deviation of system modelling in complex environments, with higher accuracy and stronger robustness.

This paper analyzes the performance of Kalman filter-based estimators for robust filtering and rotor asymmetry detection in wound rotor induction machines (WRIMs) using real-time data. Filter models were designed based on an extended model of WRIMs. The detection of rotor asymmetry was achieved by estimating the states of rotor resistance and speed using four filters. The sensitivity of the parameters under healthy and asymmetry conditions was thoroughly analyzed and categorized as low, medium, and high sensitivity parameters. Robust model-based estimators were designed to minimize the probability of false alarms. The performance analysis demonstrated that the dual unscented Kalman filter (DUKF) outperformed other Kalman filters such as the extended Kalman filter (EKF), dual extended Kalman filter (DEKF), and unscented Kalman filter (UKF) for state estimation of WRIM. [ABSTRACT FROM AUTHOR]

The unmanned aerial vehicle (UAV) and the unmanned ground vehicle (UGV) can complete complex tasks through information sharing and ensure the mission execution capability of multiple unmanned carrier platforms. At the same time, cooperative navigation can use the information interaction between multi‐platform sensors to improve the relative navigation and positioning accuracy of the entire system. Aiming at the problem of deviation of the system model due to gross errors in sensor measurement data or strong manoeuvrability in complex environments, a robust and adaptive UGV‐UAV relative navigation and positioning algorithm is proposed. In this paper, the relative navigation and positioning of UGV‐UAV is studied based on inertial measurement unit (IMU)/Vision. Based on analyzing the relative kinematics model and sensor measurement model, a leader (UGV)‐follow (UAV) relative navigation model is established. In the implementation of the relative navigation and positioning algorithm, the robust adaptive algorithm and the non‐linear Kalman filter (extended Kalman filter [EKF]) algorithm are combined to dynamically adjust the system state parameters. Finally, a mathematical simulation of the accompanying and landing process in the UGV‐UAV cooperative scene is carried out. The relative position, velocity and attitude errors calculated by EKF, Robust‐EKF and Robust‐Adaptive‐EKF algorithms are compared and analyzed by simulating two cases where the noise obeys the Gaussian distribution and the non‐Gaussian distribution. The results show that under the non‐Gaussian distribution conditions, the accuracy of the Robust‐Adaptive‐EKF algorithm is improved by about two to three times compared with the EKF and Robust‐EKF and can almost reach the relative navigation accuracy under the Gaussian distribution conditions. The robust self‐adaptive relative navigation and positioning algorithm proposed in this paper has strong adaptability to the uncertainty and deviation of system modelling in complex environments, with higher accuracy and stronger robustness. [ABSTRACT FROM AUTHOR]

This article introduces an alternative and less conservative ℋ∞$$ {\mathscr{H}}_{\infty } $$ filter design procedure applied to continuous time uncertain systems. In order to provide a reduction in conservatism and an ℋ∞$$ {\mathscr{H}}_{\infty } $$ norm improvement, the proposed technique avoids the conventional convexification procedure—which uses structure restrictions and slack variables. Instead, it defines an unconstrained structure. The proposed technique consists of a hybrid procedure, combining the application of linear matrix inequalities (LMIs) with heuristic optimization algorithms (HOAs). The HOAs, specifically genetic algorithms, are used to optimize terms that could cause bilinearities, subsequently evaluated by LMIs and generating the desired filter. Numerical examples and a comparison with other methodologies are presented, testifying to the proposed method's efficacy and the performance. [ABSTRACT FROM AUTHOR]

The natural instability of an inverted pendulum and its dynamics richness, in terms of nonlinearity, provide a nice apparatus to reproduce behaviors of analogous systems. In this way, it is useful to perform benchmark tests for new control approaches developed. In this paper, we address the main inverted pendulum problems: pendulum stabilization, tracking, and catching swing‐up control. We show how robust recursive, control and filtering, techniques improve the system performance. They are developed to solve stochastic problems based on deterministic approaches, in order to decrease the worst influence of uncertainties. Experimental results of the proposed robust approach provide robust stability and performance despite parametric uncertainties, disturbances, and noise effects. [ABSTRACT FROM AUTHOR]

A multivariate score-driven filter is developed to extract signals from noisy vector processes. By assuming that the conditional location vector from a multivariate Student's t distribution changes over time, we construct a robust filter which is able to overcome several issues that naturally arise when modeling heavy-tailed phenomena and, more in general, vectors of dependent non-Gaussian time series. We derive conditions for stationarity and invertibility and estimate the unknown parameters by maximum likelihood. Strong consistency and asymptotic normality of the estimator are derived. Analytical formulae are derived which consent to develop estimation procedures based on a fast and reliable Fisher scoring method. An extensive Monte–Carlo study is designed to assess the finite samples properties of the estimator, the impact of initial conditions on the filtered sequence, the performance when some of the underlying assumptions are violated, such as symmetry of the underlying distribution and homogeneity of the degrees of freedom parameter across marginals. The theory is supported by a novel empirical illustration that shows how the model can be effectively applied to estimate consumer prices from home scanner data. [ABSTRACT FROM AUTHOR]

A simultaneous autoregressive score-driven model with autoregressive disturbances is developed for spatio-temporal data that may exhibit heavy tails. The model specification rests on a signal plus noise decomposition of a spatially filtered process, where the signal can be approximated by a nonlinear function of the past variables and a set of explanatory variables, while the noise follows a multivariate Student-t distribution. The key feature of the model is that the dynamics of the space-time varying signal are driven by the score of the conditional likelihood function. When the distribution is heavy-tailed, the score provides a robust update of the space-time varying location. Consistency and asymptotic normality of maximum likelihood estimators are derived along with the stochastic properties of the model. The motivating application of the proposed model comes from brain scans recorded through functional magnetic resonance imaging when subjects are at rest and not expected to react to any controlled stimulus. We identify spontaneous activations in brain regions as extreme values of a possibly heavy-tailed distribution, by accounting for spatial and temporal dependence. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite Systems (GNSS) Precise Point Positioning (PPP) is a great precision positioning method based on GNSS. PPP based on multi-constellation GNSS uses the extended Kalman filter (EKF). Inappropriately, the measurement outliers and the system's dynamic model might produce mistakes in the positioning accuracy acquired using this method. An adaptive robust Kalman filter (RKF) was recently developed in order to alleviate these errors. In addition, the preceding variance is sometimes used to determine the weights of different categories of observations, which has an effect on PPP performance. A novel developed robust adaptive filtering (DRKF) has been developed to provide better placement results. For the equivalent weight matrix to be generated, an equivalent weight model that is statistically robust by the chi-square test for classification is constructed in this technique. According to prior Kalman filter models employing International GNSS Service (IGS) final clock and orbit products, the performance of GNSS PPP using the DRKF is confirmed in contrast to those produced using the current model. DRKF surpasses traditional robust adaptive filters in terms of positioning accuracy, convergence time, and PPP sturdiness according to the results of this study. In comparison to RKF, DRKF improves the positioning solution by 201 mm with 119.10 %, 77 mm with 164.86 %, and 160 mm with 211.74 % in the east, north, and up (ENZ) directions, respectively. It is recommended to use the newly developed robust adaptive Kalman filter in kinematic mode, especially in urban areas, due to the noticeable improvement in position accuracy.

Aiming at the problems of Non-Line-of-Sight (NLOS) observation errors and inaccurate kinematic model in ultra-wideband (UWB) systems, this paper proposed an improved robust adaptive cubature Kalman filter (IRACKF). Robust and adaptive filtering can weaken the influence of observed outliers and kinematic model errors on filtering, respectively. However, their application conditions are different, and improper use may reduce positioning accuracy. Therefore, this paper designed a sliding window recognition scheme based on polynomial fitting, which can process the observation data in real-time to identify error types. Simulation and experimental results indicate that compared to the robust CKF, adaptive CKF, and robust adaptive CKF, the IRACKF algorithm reduces the position error by 38.0%, 45.1%, and 25.3%, respectively. The proposed IRACKF algorithm significantly improves the positioning accuracy and stability of the UWB system. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite Systems (GNSS) Precise Point Positioning (PPP) is a great precision positioning method based on GNSS. PPP based on multi-constellation GNSS uses the extended Kalman filter (EKF). Inappropriately, the measurement outliers and the system's dynamic model might produce mistakes in the positioning accuracy acquired using this method. An adaptive robust Kalman filter (RKF) was recently developed in order to alleviate these errors. In addition, the preceding variance is sometimes used to determine the weights of different categories of observations, which has an effect on PPP performance. A novel developed robust adaptive filtering (DRKF) has been developed to provide better placement results. For the equivalent weight matrix to be generated, an equivalent weight model that is statistically robust by the chi-square test for classification is constructed in this technique. According to prior Kalman filter models employing International GNSS Service (IGS) final clock and orbit products, the performance of GNSS PPP using the DRKF is confirmed in contrast to those produced using the current model. DRKF surpasses traditional robust adaptive filters in terms of positioning accuracy, convergence time, and PPP sturdiness according to the results of this study. In comparison to RKF, DRKF improves the positioning solution by 201 mm with 119.10 %, 77 mm with 164.86 %, and 160 mm with 211.74 % in the east, north, and up (ENZ) directions, respectively. It is recommended to use the newly developed robust adaptive Kalman filter in kinematic mode, especially in urban areas, due to the noticeable improvement in position accuracy. [ABSTRACT FROM AUTHOR]

This paper analyzes the performance of Kalman filter-based estimators for robust filtering and rotor asymmetry detection in wound rotor induction machines (WRIMs) using real-time data. Filter models were designed based on an extended model of WRIMs. The detection of rotor asymmetry was achieved by estimating the states of rotor resistance and speed using four filters. The sensitivity of the parameters under healthy and asymmetry conditions was thoroughly analyzed and categorized as low, medium, and high sensitivity parameters. Robust model-based estimators were designed to minimize the probability of false alarms. The performance analysis demonstrated that the dual unscented Kalman filter (DUKF) outperformed other Kalman filters such as the extended Kalman filter (EKF), dual extended Kalman filter (DEKF), and unscented Kalman filter (UKF) for state estimation of WRIM.

Combining a global navigation satellite system (GNSS) and microelectromechanical technology-based inertial system (MINS) has become essential in land vehicle navigation systems. In an urban environment, the error of position output by GNSS receiver increases because of the blocking and reflection of the signal by buildings, which affects the positioning accuracy of the integrated system. In order to improve the positioning accuracy under these scenarios, this paper proposed a new robust method based on the estimation of the standard deviation of GNSS positioning error. In our study, a method for estimating the standard deviation ${\boldsymbol{\sigma}}^p$ (or variance) of the position error of GNSS receiver is firstly proposed. Then a robust filtering method combined multi-factor scaling and bias estimation is proposed based on the estimation of ${\boldsymbol{\sigma}}^p$. The simulations and vehicle navigation test show that the proposed method has a robust positioning effect. When ${\boldsymbol{\sigma}}^p$ increases, the position accuracy is closed to the Sage-Husa filtering method with boundary constraint (SH-KF). Simulations also indicate that the proposed method has better robust effect than the traditional Kalman filter and SH-KF when a large bias error of position exists. [ABSTRACT FROM AUTHOR]

Soft-sensing and state-space-based methods play crucial roles in fault-tolerant sensor fusion schemes. Kalman filtering is one of the most employed sensor fusion methods. In practice, filtering (or state estimation) is sensitive to initial conditions, variations in model parameters, and faults in sensors and actuators. Cumulatively, these uncertainties that affect the state estimator can be modeled as unknown parameters. In this article, we present the development of a discrete-time minimum variance unbiased estimator (MVUE) that is robust to a class of unknown parameters. The estimation gain of MVUE is designed to facilitate unbiased state estimates in the presence of unknown parameters. We then use the innovations that are generated by the proposed state estimator (MVUE) to estimate the unknown parameters, thus proposing a sequential state and unknown parameter estimation strategy. The development of the decoupled state and unknown parameter estimation strategy is motivated by the fault-tolerant sensor fusion exercise for railway track geometry inspection. This exercise aims to formulate the state-space realization of the track geometry inspection problem to enable sequential state and unknown parameter estimation. The track geometry parameters, initial conditions, and sensor faults are considered unknown parameters for the application. The simulation analysis shows the importance of developing the trinity of the state-space realization for track geometry inspection, the state estimation framework, and the decoupled unknown parameter estimator. [ABSTRACT FROM AUTHOR]

Summary: To avert catastrophic failure in the structures, joints are typically designed to yield, but not fail, so that energy accumulated under cyclic loading is dissipated. Eventually, this renders the structural joints to be characteristically weaker and more vulnerable than the members. Yet, damage detection research mostly assumes damage in the members only. This article proposes a model‐based predictor–corrector algorithm that uses an interacting filtering approach to efficiently estimate joint damage in the presence of input and measurement uncertainties. For the predictor model, a novel strain‐displacement relationship specific to semi‐rigid frames is developed to map nodal displacements to corresponding strain measurements. The proposed estimation method embeds robustness against non‐stationary input (e.g., seismic excitation) in the state filter, itself. For this, an output injection technique is integrated within the state filter. The modified state filter (robust Kalman filter) runs within an enveloping parameter filter (particle filter) to simultaneously estimate the system states and joint damage parameters, respectively, using the response signal. Strain has been adopted as measurement since it is frame independent (beneficial for seismic activity) and also comparatively cheaper to use. Numerical studies are performed on a two‐dimensional (2‐D) three‐story three‐bay shear frame for different joint damage locations and severities. The sensitivity and the stability of the proposed approach are further investigated. Experimental validation of the proposed algorithm is carried out on a 2‐D steel frame. [ABSTRACT FROM AUTHOR]

We consider linear continuous-time retarded systems with multiplicative noise and polytopic type parameter uncertainty and we address the problems of H ∞ and H 2 general filtering of these systems. These problems are solved by applying a modified version of the descriptor method that leads to a considerable reduction in the over-design associated with the "quadratic" solution that assigns a single Lyapunov function to all the points in the uncertainty polytope. The theory is extended to the robust gain-scheduling case where on-line parameter measurement is exercised in the estimation process. Two examples are given that demonstrate the superiority of our solution method. The first example relates to a simple second order system whereas the second example is one of altitude estimation taken from the field of aerospace engineering. [ABSTRACT FROM AUTHOR]

As to an aerospace vehicle, the flight span is large and the flight environment is complex. More than that, the existing navigation algorithms cannot meet the needs to provide accurate navigation parameters for aerospace vehicles, which results in the decline of navigation accuracy. This paper proposes a multi-layer, fault-tolerant robust filtering algorithm of aerospace vehicle in the launch inertial coordinate system to address this problem. Firstly, the launch inertial coordinate system is used as the reference coordinate system for navigation calculation, and the state equation and measurement equation of the navigation system are established in this coordinate system to improve the modeling accuracy of the navigation system. On this basis, a multi-layer, fault-tolerant robust filtering algorithm is designed to estimate and compensate the unknown input in the state equation in real time and adjust the noise variance matrix in the measurement equation adaptively. Simulation results show that the errors about the integrated navigation system output parameters are reduced, through this algorithm, which improves the attitude, velocity and position estimation accuracy of the integrated navigation system. In addition, the algorithm enhances the fault tolerance and robustness of the filtering algorithm. [ABSTRACT FROM AUTHOR]

In this article, a consensus-based robust regularized least-squares filter is designed for multi-sensor systems with norm-bounded uncertainties. In this approach, a min-max optimization problem is presented based on a consensus protocol on estimates. The advantage of a consensus filter is that each node estimates its local states, in addition to reaching an agreement on estimatesmade by all sensors on the network. By introducing appropriate conversions the proposed optimization problem is converted to a robust regularized least-squares problem. Solving this problem results in the structure of the proposed filter. Then, the recursive formulation of the filter is obtained in measurement form and information form. Finally, in order to investigate the efficacy, good proficiency, and robustness of the proposed consensus-based robust least-squares filter, it has been applied to an uncertain multi-sensor system with 100 nodes and its results have been compared with existing consensus filters. [ABSTRACT FROM AUTHOR]

With the expansion of the exploration scope of underwater vehicles and the improvement of their safety requirements, integrated navigation under passive conditions has become a hot topic in the field of navigation. Due to the stability and detectability of the Earth’s gravity field, the use of a matching result for external correction of inertial navigation systems (INSs) can be effective. For practical navigation applications, an inertial gravity matching integrated navigation algorithm must be designed for real-time applicability, diversified output information capability, and anti-interference capability. In this paper, an INS/gravity matching (INS-GM) integrated navigation algorithm is improved to extract the information of gravity fields in real time and correct the navigation results, and a robust integrated algorithm is proposed. Through two-hierarchy filtering, correction of the gravity field to the carrier position and of the integrated navigation system is obtained. According to the first-hierarchy filtering noise characteristics of gravity matching, the robustness of the algorithm to a complex environment is improved by second-hierarchy filtering. The ocean experiment data processing results show that the algorithm can effectively handle a certain degree of initial error, and an integrated navigation accuracy of 205 m is achieved in a good experimental environment. In the case of severe test conditions, the accuracy of the robust integrated navigation algorithm is 72% higher than that of the ordinary navigation algorithm, and it has a strong anti-jamming ability, which can meet the requirements of marine inertial gravity matching integrated navigation tasks. [ABSTRACT FROM AUTHOR]

In this paper, a generalized maximum Versoria criterion algorithm (GMVC) based on wiener spline adaptive filter, called SAF–GMVC, is proposed. The proposed algorithm is used for nonlinear system identification under non-Gaussian environment. To improve the convergence performance of the SAF–GMVC, the momentum stochastic gradient descent (MSGD) is introduced. In order to further reduce the steady-state error, the variable step-size algorithm is introduced, called as SAF–GMVC–VMSGD. Simulation results demonstrate that SAF–GMVC–VMSGD achieves better filtering effective against non-Gaussian noise. [ABSTRACT FROM AUTHOR]

In this paper, we propose CE-BASS, a particle mixture Kalman filter which is robust to both innovative and additive outliers, and able to fully capture multi-modality in the distribution of the hidden state. Furthermore, the particle sampling approach re-samples past states, which enables CE-BASS to handle innovative outliers which are not immediately visible in the observations, such as trend changes. The filter is computationally efficient as we derive new, accurate approximations to the optimal proposal distributions for the particles. The proposed algorithm is shown to compare well with existing approaches and is applied to both machine temperature and server data. [ABSTRACT FROM AUTHOR]

In the tomographic reconstruction of seismic travel time data, care must be taken to keep the propagation of data errors to the model space under control. The non-Gaussian noise distribution—especially the outliers in the data sets- can cause appreciable distortions in the tomographic imaging. To reduce the noise sensitivity well-developed tomography algorithms can be used. On the other hand, the quality of the tomogram can further be improved by using image processing tools. In the paper, a newly developed robust filter is presented, in which the Most Frequent Value (MFV) method developed by Steiner is applied. To analyze the noise reduction capability of the new filter (called Steiner-filter) and to compare it to smoothing filters based on arithmetic- and binomial mean, as well as median, medium-sized tomographic images are used. The MFV-based filter is successfully tested also in edge detection procedures. [ABSTRACT FROM AUTHOR]

Aiming at the problems of Non-Line-of-Sight (NLOS) observation errors and inaccurate kinematic model in ultra-wideband (UWB) systems, this paper proposed an improved robust adaptive cubature Kalman filter (IRACKF). Robust and adaptive filtering can weaken the influence of observed outliers and kinematic model errors on filtering, respectively. However, their application conditions are different, and improper use may reduce positioning accuracy. Therefore, this paper designed a sliding window recognition scheme based on polynomial fitting, which can process the observation data in real-time to identify error types. Simulation and experimental results indicate that compared to the robust CKF, adaptive CKF, and robust adaptive CKF, the IRACKF algorithm reduces the position error by 38.0%, 45.1%, and 25.3%, respectively. The proposed IRACKF algorithm significantly improves the positioning accuracy and stability of the UWB system.

Multi-constellation GNSS precise point positioning (PPP) typically uses the extended Kalman filter (EKF) for kinematic applications. Unfortunately, the obtained positioning accuracy in this approach is prone to errors caused by measurement outliers and the system's dynamic model. An adaptive robust Kalman filter (RKF) was recently developed to mitigate these errors. However, RKF uses empirical values as detection thresholds for the outliers, which requires the measurements to be from the same constellation and of equal precision to obtain an optimal PPP solution. The classification robust adaptive Kalman filter (CAKF) has subsequently been developed to deal with measurements of different precisions, namely pseudorange and carrier-phase measurements. This paper proposes a real-time GPS/Galileo PPP system, which employs a modified version of CAKF called the Improved Robust adaptive Kalman Filter (IRKF). The positioning performance of GPS/Galileo PPP through the IRKF is initially verified in comparison with those obtained through the EKF, RKF, and CAKF using the Centre for Orbit Determination in Europe (CODE) final orbit and clock products in both of static and kinematic modes. The real-time GPS/Galileo PPP solution through the IRKF is then assessed in comparison with its near-real-time counterpart. The results indicate that when the IRKF approach is utilised, the positioning accuracy is significantly improved and the convergence behaviour is enhanced compared with results from EKF, conventional RKF, and CAKF. In the real-time mode, centimeter-level horizontal positioning accuracy is achieved under an open sky environment, while decimeter-level horizontal positioning accuracy is achieved under a challenging environment. On the other hand, decimeter-level accuracy is achieved for the vertical positioning component under all environmental scenarios. Moreover, the positioning accuracy of the real-time solution is comparable to the near-real-time counterpart. [ABSTRACT FROM AUTHOR]

Basing on the weighted maximum likelihood method and the correntropy cubature Kalman filter, we develop some software for solving the problem of parametric estimation of the models for the stochastic nonlinear continuous-discrete systems in presence of anomalous observations in measurement data. The effectiveness of the proposed procedure is demonstrated by two model structures for the stochastic and the grouped nature of anomalous data location. [ABSTRACT FROM AUTHOR]

In this survey, we discuss various approaches to control theory that have arisen in the recent decades and reflect the desire to reach a trade-off between the -control theory and the -control theory. The theories of the kind include the theory of risk-sensitive controllers, the theory of suboptimal control with a constraint on the -entropy functional, the mixed -control theory, the minimax -control theory, the anisotropy-based theory, and some others. The survey discusses in more detail the anisotropy-based control theory, which includes both the - and the -theory within a single statement of the problem. [ABSTRACT FROM AUTHOR]

As to an aerospace vehicle, the flight span is large and the flight environment is complex. More than that, the existing navigation algorithms cannot meet the needs to provide accurate navigation parameters for aerospace vehicles, which results in the decline of navigation accuracy. This paper proposes a multi-layer, fault-tolerant robust filtering algorithm of aerospace vehicle in the launch inertial coordinate system to address this problem. Firstly, the launch inertial coordinate system is used as the reference coordinate system for navigation calculation, and the state equation and measurement equation of the navigation system are established in this coordinate system to improve the modeling accuracy of the navigation system. On this basis, a multi-layer, fault-tolerant robust filtering algorithm is designed to estimate and compensate the unknown input in the state equation in real time and adjust the noise variance matrix in the measurement equation adaptively. Simulation results show that the errors about the integrated navigation system output parameters are reduced, through this algorithm, which improves the attitude, velocity and position estimation accuracy of the integrated navigation system. In addition, the algorithm enhances the fault tolerance and robustness of the filtering algorithm.

Summary: Standard state estimation techniques, ranging from the linear Kalman filter (KF) to nonlinear extended KF (EKF), sigma‐point or particle filters, assume a perfectly known system model, that is, process and measurement functions and system noise statistics (both the distribution and its parameters). This is a strong assumption which may not hold in practice, reason why several approaches have been proposed for robust filtering, mainly because the filter performance is particularly sensitive to different model mismatches. In the context of linear filtering, a solution to cope with possible system matrices mismatch is to use linear constraints. In this contribution we further explore the extension and use of recent results on linearly constrained KF for robust nonlinear filtering under both process and measurement model mismatch. We first investigate how linear equality constraints can be incorporated within the EKF and derive a new linearly constrained extended KF (LCEKF). Then we detail its use to mitigate parametric modeling errors in the nonlinear process and measurement functions. Numerical results are provided to show the performance improvement of the new LCEKF for robust vehicle navigation. [ABSTRACT FROM AUTHOR]

State estimation is a fundamental task in many engineering fields, and therefore robust nonlinear filtering techniques able to cope with misspecified, uncertain and/or corrupted models must be designed for real-life applicability. In this contribution we explore nonlinear Gaussian filtering problems where measurements may be corrupted by outliers, and propose a new robust variational-based filtering methodology able to detect and mitigate their impact. This method generalizes previous contributions to the case of multiple outlier indicators for both independent and dependent observation models. An illustrative example is provided to support the discussion and show the performance improvement. [ABSTRACT FROM AUTHOR]

Summary: The paper introduces a general class of heavy‐tailed auto‐regressions for modelling integer‐valued time series with outliers. The specification proposed is based on a heavy‐tailed mixture of negative binomial distributions that features an observation‐driven dynamic equation for the conditional expectation. The existence of a stationary and ergodic solution for the class of auto‐regressive processes is shown under general conditions. The estimation of the model can be easily performed by maximum likelihood given the closed form of the likelihood function. The strong consistency and the asymptotic normality of the estimator are formally derived. Two examples of specifications illustrate the flexibility of the approach and the relevance of the theoretical results. In particular, a linear dynamic equation and a score‐driven equation for the conditional expectation are studied. The score‐driven specification is shown to be particularly appealing as it delivers a robust filtering method that attenuates the effect of outliers. Empirical applications to the series of narcotics trafficking reports in Sydney and the euro–pound sterling exchange rate illustrate the effectiveness of the method in handling extreme observations. [ABSTRACT FROM AUTHOR]

Abstract The classical Kalman smoother recursively estimates states over a finite time window using all observations in the window. In this paper, we assume that the parameters characterizing the second-order statistics of process and observation noise are unknown and propose an optimal Bayesian Kalman smoother (OBKS) to obtain smoothed estimates that are optimal relative to the posterior distribution of the unknown noise parameters. The method uses a Bayesian innovation process and a posterior-based Bayesian orthogonality principle. The optimal Bayesian Kalman smoother possesses the same forward-backward structure as that of the ordinary Kalman smoother with the ordinary noise statistics replaced by their effective counterparts. In the first step, the posterior effective noise statistics are computed. Then, using the obtained effective noise statistics, the optimal Bayesian Kalman filter is run in the forward direction over the window of observations. The Bayesian smoothed estimates are obtained in the backward step. We validate the performance of the proposed robust smoother in the target tracking and gene regulatory network inference problems.

Summary: The problem of robust H∞ estimation of stochastic, state‐delayed, uncertain, linear, discrete‐time systems is solved by applying a vertex dependent Lyapunov function. In this problem, a cost function is defined, which is the expected value of the standard H∞ performance index with respect to the uncertain parameters. The optimal estimator is obtained by solving a simple set of linear matrix inequalities (LMIs) for either the case where the filter matrices are constant or for the case where these matrices are gain scheduled. The solutions to the corresponding minimum error variance estimation problems are also obtained for the nominal and the uncertain cases, where an additional set of conditions is introduced that guarantees the minimization of the estimation error variance. Two examples are given. The first is a numerical example that demonstrates the advantage of the new design method. The second is an example of a practical nature that is taken from the field of guidance control and estimation. [ABSTRACT FROM AUTHOR]

We propose a new approach for solving the filtering problem in linear systems based on incomplete measurements, where the characteristics of the dynamic noise are not known exactly, and measurements may contain anomalous non-Gaussian errors. The proposed algorithm is based on the idea of using the adaptive Kalman filter and the generalized least absolute deviations method jointly. With numerical modeling, we show that, compared to the classical optimal linear filtering method, our solution has lower sensitivity to short-term outliers in measurements and provides a quick adjustment of the parameters of the system dynamics. The proposed algorithm can be used to solve onboard navigation and tracking problems on aircrafts. To implement the method of least absolute deviations, we use an efficient L1-optimization algorithm. [ABSTRACT FROM AUTHOR]

We investigate a new sampling scheme aimed at improving the performance of particle filters whenever (a) there is a significant mismatch between the assumed model dynamics and the actual system, or (b) the posterior probability tends to concentrate in relatively small regions of the state space. The proposed scheme pushes some particles toward specific regions where the likelihood is expected to be high, an operation known as nudging in the geophysics literature. We reinterpret nudging in a form applicable to any particle filtering scheme, as it does not involve any changes in the rest of the algorithm. Since the particles are modified, but the importance weights do not account for this modification, the use of nudging leads to additional bias in the resulting estimators. However, we prove analytically that nudged particle filters can still attain asymptotic convergence with the same error rates as conventional particle methods. Simple analysis also yields an alternative interpretation of the nudging operation that explains its robustness to model errors. Finally, we show numerical results that illustrate the improvements that can be attained using the proposed scheme. In particular, we present nonlinear tracking examples with synthetic data and a model inference example using real-world financial data. [ABSTRACT FROM AUTHOR]

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This paper considers the problem of robust H2 and H∞ filter design for uncertain continuous‐time linear systems. Linear fractional transformation (LFT) representation is considered for the uncertainty modeling and by definition of large number of slack variables, extra free dimensions are provided to the H2 and H∞ filter design optimization problem, so method presented in this paper expected to be less conservative than the existing methods for the polytopic uncertain systems and its efficiency for filter design is illustrated by means of numerical comparisons with some benchmark examples from the literature. [ABSTRACT FROM AUTHOR]

The paper deals with robust filtering algorithms for discrete systems with unknown inputs (disturbances) and Markovian jump parameter. The proposed filtering algorithm is based on the separation principle, minimization of a quadratic criterion and the use of Kalman filters with unknown input and smoothing procedures. Solving a non-stationary problem is represented solving a two-point boundary value problem in kind of difference matrix equations. In the stationary case problem is represented matrix algebraic equations. Robustness ensures the stability of the filter dynamics when errors occur in identifying the jump parameter. An example is provided to illustrate the proposed approach, which showed that the use of smoothing procedures for estimating an unknown input improves the accuracy of estimates. [ABSTRACT FROM AUTHOR]

This paper proposes a novel robust adaptive filter that combines smooth variable structure filter and extended Kalman filter for the spacecraft attitude estimation with model uncertainty originating from gyro drift, parameter error, and installation error. The proposed filter employs the extended Kalman filter based on quaternion and fuses an adaptive factor and smooth variable structure filter to improve robustness to the model uncertainty and noise. To improve the robustness of the extended Kalman filter, an adaptive factor that tunes the predicted covariance matrix is utilized to design the attitude estimation strategy. Moreover, to further decrease the impact of the suddenly rapid maneuvering and improve its robust effect of model uncertainty induced by dynamic error, gyro drift, and so on, a smooth variable structure estimation strategy founded on sliding mode theory is derived and utilized for the satellite attitude estimation. Thereby, a novel filtering algorithm is proposed by incorporating an adaptive factor and a smooth variable structure estimation strategy. Simulation results indicate that our proposed algorithm delivers exceptional robustness and achieves high precision and accuracy in satellite attitude estimation compared with the traditional extended Kalman filter. [ABSTRACT FROM AUTHOR]

China is promoting the construction of an integrated positioning, navigation, and timing (PNT) systems with the BeiDou Navigation Satellite System (BDS) as its core. To expand the positioning coverage area and improve the positioning performance by taking advantage of device-to-device (D2D) and self-organizing network (SON) technology, a BDS/SON integrated positioning system is proposed for the fifth-generation (5G) networking environment. This system relies on a combination of time-of-arrival (TOA) and BeiDou pseudo-range measurements to effectively supplement BeiDou signal blind spots, expand the positioning coverage area, and realize higher precision in continuous navigation and positioning. By establishing the system state model, and addressing the single-system positioning divergence and insufficient accuracy, a robust adaptive fading filtering (RAF) algorithm based on the prediction residual is proposed to suppress gross errors and filtering divergence in order to improve the stability and accuracy of the positioning results. Subsequently, a federated Kalman filtering (FKF) algorithm operating in fusion-feedback mode is developed to centrally process the positioning information of the combined system. Considering that the prediction error can reflect the magnitude of the model error, an adaptive information distribution coefficient is introduced to further improve the filtering performance. Actual measurement and significance test results show that by integrating BDS and SON positioning data, the proposed algorithm realizes robust, reliable, and continuous high precision location services with anti-interference capabilities and good universality. It is applicable in scenarios involving unmanned aerial vehicles (UAVs), autonomous driving, military, public safety and other contexts and can even realize indoor positioning and other regional positioning tasks.

It is well known that the standard state estimation technique performance is particularly sensitive to perfect system knowledge, where the underlying assumptions are: (i) Process and measurement functions and parameters are known, (ii) inputs are known, and (iii) noise statistics are known. These are rather strong assumptions in real-life applications; therefore, a robust filtering solution must be designed to cope with model misspecifications. A possible way to design robust filters is to exploit linear constraints (LCs) within the filter formulation. In this contribution we further explore the use of LCs, derive a linearly constrained extended Kalman filter (LCEKF) for systems affected by non-additive noise and system inputs, and discuss its use for model mismatch mitigation. Numerical results for a robust tracking and navigation problem are provided to show the performance improvement of the proposed LCEKF, with respect to state-of-the-art techniques, that is, a benchmark EKF without mismatch and a misspecified EKF not accounting for the mismatch.

Noise reduction methods have a great impact on the performance of all EEG signal processing systems. The work involves the reduction in impulsive interferences. It is impossible to suppress effectively such a noise using linear filtering approach. The work presents the properties of a cascaded filter based on the ordered weighted aggregation (OWA) operator and its application to improve the electroencephalogram (EEG) signal. The OWA operator is a class of mean-like aggregation operators. By introducing a nonlinear sorting process and by assigning appropriate values of weights to the sorted samples, the improvement in filtering in the impulsive environment is achieved. The structure of the proposed cascade consists of two layers. The first layer contains two OWA filters that share a certain number of signal samples. The second layer averages the outputs of the first layer. The algorithm for the rise of filtering efficiency has been introduced. The performance of the new method has been experimentally compared with the traditional methods of impulsive noise reduction, using synthetic as well as real signals from the CHB-MIT database. The obtained results demonstrate that in the field of impulsive noise suppression and preprocessing, the proposed cascaded OWA filter brings about a significant improvement in the signal-to-noise ratio. [ABSTRACT FROM AUTHOR]