Search

This paper is concerned with the secure estimation problem for the state of charge of Lithium-ion batteries subject to malicious attacks during the data transmission from sensors to cloud-based battery management system terminal. First, the second-order resistance-capacitance equivalent circuit model, whose parameters are identified by Kalman filter in an off-line manner, is introduced to describe the internal dynamics of lithium-ion batteries. Then, by applying the $\chi ^{2}$ detection mechanism, real-time malicious attacks are first detected and then a secure estimator is designed to suppress the influence of attacks on the estimation performance. An upper bound of the filtering error covariance is determined by solving certain coupled Riccati-like equations, and the filter parameter is obtained by minimizing such an upper bound at each time step. Finally, the validity of the proposed attack detection approach and the effectiveness of the developed estimation scheme are verified by experiment results under Federal Urban Driving Schedule condition. [ABSTRACT FROM AUTHOR]

This paper proposes a new nonlinear filtering technique under the Gaussian filtering approach, which is based on the numerical approximation of intractable integrals. The proposition is in the category of spherical-radial rule based Gaussian filtering (dominated by cubature Kalman filter), which is most commonly used in practical applications. The existing Gaussian filters with spherical-radial rule are accurate only for the systems modelled with polynomials of a certain order and suffer from poor estimation accuracy for the oscillatory systems. The proposed method, however, provides an efficient approach for estimation and filtering in oscillatory environment. It introduces an exponentially-fitted spherical-radial rule of numerical approximation, which is accurate for oscillatory functions. The exponentially-fitted spherical-radial rule is composed of a third-degree spherical-cubature rule and an exponentially-fitted Gauss-Laguerre quadrature rule. The proposed filter is named as exponentially-fitted cubature Kalman filter (ECKF). The estimation accuracy of the ECKF is analyzed for nonlinear filtering problems related to the Duffing and Coulomb oscillators in terms of root mean square error (RMSE). The RMSE analysis concludes an improved estimation accuracy for the proposed ECKF compared to the existing Gaussian filters. [ABSTRACT FROM AUTHOR]

In this paper, a novel ANOVA Kernel Kalman Filter (AKKF)-based adaptive control algorithm is introduced which is used for accurate harmonics support during operation of grid-integrated solar energy conversion system (SECS). For grid integrated SECS, a single-phase two-stage topology is considered, where local loads are attached on common point of interconnection (CPI), and a battery is attached on DC link. The AKKF is the improved form of Kalman Filter (KF), where the ANOVA Kernel (AK) trick is hybridized to improve the estimation accuracy of the KF. The objective of proposed control technique is to use this solar power to fulfil the load requirement. After satisfying the load requirement, the rest of solar power is fed to the grid. However, when the solar power is not available (in nighttime), then the system operates as Distribution Static Compensator (DSTATCOM), which provides reactive power support to the grid. The performance of the developed control technique is validated through experimentation on a developed prototype. During testing, adverse grid conditions, solar insolation variation, and load unbalance conditions are considered for satisfying the motive of the developed control technique. [ABSTRACT FROM AUTHOR]

The Hilbert space embedding provides a powerful and flexible tool for dealing with the nonlinearity and high-order statistics of random variables in a dynamical system. The kernel Kalman filtering based on the conditional embedding operator (KKF-CEO) shows significant performance improvements over the traditional Kalman filters in the noisy nonlinear time-series prediction. However, KKF-CEO based on the minimum mean-square-error (MMSE) criterion is sensitive to the outliers or heavy-tailed noises. In contrast to the MMSE criterion, the maximum correntropy criterion (MCC) can achieve more robust performance in the presence of outliers. In this paper, we develop a novel kernel Kalman-type filter based on MCC, referred to kernel Kalman filtering with conditional embedding operator and maximum correntropy criterion (KKF-CEO-MCC). The proposed KKF-CEO-MCC can capture higher order statistics of errors and is robust to outliers. In addition, two simplified versions of KKF-CEO-MCC are developed, namely, KKF-CEO-MCC-O and KKF-CEO-MCC-NA. The former is an online approach and the latter is based on Nyström approximation. Simulations on noisy nonlinear time-series prediction confirm the desirable accuracy and robustness of the new filters. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of continuous-time nonlinear filtering of stochastic processes evolving on connected Riemannian manifolds without boundary. The main contribution of this paper is to derive the feedback particle filter (FPF) algorithm for this problem. In its general form, the FPF is shown to provide an intrinsic description of the filter that automatically satisfies the geometric constraints of the manifold. The particle dynamics are encapsulated in a Stratonovich stochastic differential equation that retains the feedback structure of the original (Euclidean) FPF. The implementation of the filter requires a solution of a Poisson equation on the manifold, and a numerical algorithm is described for this purpose. For the special case when the manifold is a matrix Lie group, explicit formulae for the filter are derived, using the matrix coordinates. Filters for two example problems are presented: the attitude estimation problem on $SO(3)$ and the robot localization problem in $SE(3)$. Comparisons are also provided between the FPF and popular algorithms for attitude estimation, namely the multiplicative extended Kalman filter (EKF), the invariant EKF, the unscented quaternion estimator, the invariant ensemble Kalman filter, and the bootstrap particle filter. Numerical simulations are presented to illustrate these comparisons. [ABSTRACT FROM AUTHOR]

This article considers a nonlinear filtering method for handling outliers. The presence of outliers that are gross observation errors can greatly reduce the accuracy of filtering methods that assume Gaussian distributed errors. There are some existing methods that assume a Gaussian observation error, and estimate the error covariance matrix at each time step to avoid overfitting to the outliers. However, the estimates of the covariance matrix under such methods can become unstable. This results in underfitting or overfitting to observations when filtering. This paper presents a new method for handling outliers in nonlinear filtering problems by extending the unscented Kalman filter. In this method, two Gaussian observation error models with distinct covariance matrices are used: one for observations with regular errors, and another with a larger variance specified by a scale parameter for outliers. In addition to the system state, this method estimates an indicator variable that switches between the two models and the scale parameter for outliers. With the inclusion of the indicator variable and scale parameter, the estimated error covariance matrix can handle both regular observations and outliers appropriately at each time step. Furthermore, by estimating the scale parameter, the proposed method can be applied to a dataset without additional tuning to account for outlier characteristics. Through numerical experiments, we find that our method can estimate the system state better than existing methods for both datasets with and without outliers. [ABSTRACT FROM AUTHOR]

In this paper, we focus on extended Kalman filtering (EKF), in the difficult case where a function of the state has been perfectly observed, and is thus known with certainty, while the full state still has unobserved degrees of freedom. In the linear case, the Kalman filter seamlessly handles such constraints, which result in the state being in an affine subspace. Yet, in the nonlinear case, the EKF poorly handles such type of constraints. As a remedy, we propose a novel general methodology of EKF based on an (arbitrary) nonlinear error $e$. And we prove that under compatibility of the error $e$ with the constraints, the EKF based on $e$ seamlessly handles the constraints. Furthermore, when the state space is a Lie group, we prove the EKF based on invariant errors is exactly the invariant EKF (IEKF), and we prove further properties. The theory is applied to the problem of simultaneous localization and mapping, where the IEKF is shown to perfectly handle some partial deterministic information about the map. As a byproduct, the theory is also shown to readily allow devising EKFs on state spaces defined by a class of equality constraints. [ABSTRACT FROM AUTHOR]

This paper addresses the robust optimal filtering design over unreliable networks, where the data packet dropouts occur during the signal transmission from the sensor side to the filter. The designed filter is expected, under communication data loss, to provide a guaranteed robustness against disturbance/model uncertainty while achieving the minimized variance of the estimation error under Gaussian white noises and the worst case of the disturbance. The Nash game approach is adopted to deal with such a multiobjective filtering problem. Based on the concept of the mean-square stability, Nash equilibrium strategies are analytically applied in terms of two cross-coupled modified algebraic Riccati equations. The presented design method provides a systematic way to achieve a tradeoff of the estimation performance in the $\mathcal {H}_2$ and $\mathcal {H}_\infty$ senses in the presence of data loss. [ABSTRACT FROM AUTHOR]

This paper is concerned with the distributed set-membership filtering problem for a class of general discrete-time nonlinear systems under event-triggered communication protocols over sensor networks. To mitigate the communication burden, each intelligent sensing node broadcasts its measurement to the neighboring nodes only when a predetermined event-based media-access condition is satisfied. According to the interval mathematics theory, a recursive distributed set-membership scheme is designed to obtain an ellipsoid set containing the target states of interest via adequately fusing the measurements from neighboring nodes, where both the accurate estimate on Lagrange remainder and the event-based media-access condition are skillfully utilized to improve the filter performance. Furthermore, such a scheme is only dependent on neighbor information and local adjacency weights, thereby fulfilling the scalability requirement of sensor networks. In addition, an optimization algorithm is developed to minimize the trace of the estimated ellipsoid set, and the effect from the adopted event-triggered threshold is thoroughly discussed as well. Finally, a simulation example is utilized to illustrate the usefulness of the proposed distributed set-membership filtering scheme. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of distributed federated Kalman filter fusion (DFKFF) for a class of multi- sensor unreliable networked systems (MUNSs) with uncorrelated noises. An optimal DFKFF algorithm of MUNSs without buffer is presented, and rigorously proved to be equivalent to centralized optimal Kalman filter fusion (COKFF) algorithm of MUNSs without buffer. Finite length buffers deal with measurement delay or loss, and a suboptimal DFKFF algorithm of MUNSs with finite length buffers is proposed based on the optimal local Kalman filter with a buffer of finite length for each subsystem. Compared with COKFF algorithm of MUNSs with buffers, the proposed DFKFF algorithm of MUNSs with buffers has stronger fault-tolerance ability. Two simulation examples are given to illustrate the effectiveness of the proposed approaches. [ABSTRACT FROM PUBLISHER]

The time and measurement update for the discrete time Kalman filter can be formulated in terms of conditional means and covariances. The unscented Kalman filter can be interpreted as calculating these conditional means and covariances by using the unscented transform. This approach can also be directly applied to nonlinear models as an alternative to the discrete time extended Kalman filter. In this paper, a novel method for computing the unscented Kalman filter for a nonlinear model with continuous time dynamics and discrete time measurements is presented. Compared to the existing approaches, this method is far simpler and less computationally demanding, and it performs at least as well. [ABSTRACT FROM AUTHOR]

The problem of the stochastic event-based distributed fusion estimation for a class of Gaussian systems is investigated. Considering the deterministic event-triggers destroying the Gaussian property of system states, the stochastic event-triggered mechanisms (SETMs) are used, which also can relieve the network transmission burden. Under the stochastic transmission schedules, a two-step fusion estimation method is developed. The first step, with the consideration of channel fading, the local estimation of each sensor is proposed by using the measurements from itself and its neighbors. The second step, the fusion algorithm is designed to eliminate the disagreements among local estimations of each sensor. Finally, experiment is carried out to demonstrate the advantages of the proposed distributed fusion estimation. [ABSTRACT FROM AUTHOR]

In this paper, an enhanced unscented Kalman filter is used for the estimation of non-idealities in sigma-delta modulators. As sigma-delta modulator based analog-to-digital converters are known to be prone to performance degradation from many circuit non-idealities, testing and selection of the manufactured chips as well as post-correction procedures are required to ensure a reliable performance. In contrast to most state-of-the art techniques, the proposed estimator is capable of simultaneously tracking a large set of non-ideal parameters with high accuracy and in a very short offline time within the range of microseconds. Three possible implementations are proposed and it is shown how the technique is used to perform an in situ non-ideality estimation and subsequent calibration of a manufactured chip, bringing the modulator back into its designed performance range. It is further demonstrated that the estimator can reliably detect the non-idealities over a wide range when intentionally degrading the performance of the chip by manually sweeping its trimming parameters. The presented hardware measurement results prove that the proposed technique is practically applicable to the test and/or calibration of sigma-delta data converters. [ABSTRACT FROM AUTHOR]

In this  paper, we study the prediction performance of the Kalman filter (KF) in a worst case minimax setting as studied in online machine learning, information, and game theory. The aim is to predict the sequence of observations almost as well as the best reference predictor (comparator) sequence in a comparison class. We prove worst-case bounds on the cumulative squared prediction errors using a priori knowledge about the complexity of reference predictor sequence. In fact, the performance of the KF is derived as a function of the performance of the best reference predictor and the total amount of drift that occurs in the schedule of the best comparator. [ABSTRACT FROM AUTHOR]

This paper investigates the stability of Kalman filtering over Gilbert–Elliott channels where random packet drops follow a time-homogeneous two-state Markov chain whose state transition is determined by a pair of failure and recovery rates. First of all, we establish a relaxed condition guaranteeing peak-covariance stability described by an inequality in terms of the spectral radius of the system matrix and transition probabilities of the Markov chain. We further show that the condition can be interpreted using a linear matrix inequality feasibility problem. Next, we prove that the peak-covariance stability implies mean-square stability, if the system matrix has no defective eigenvalues on the unit circle. This connection between the two stability notions holds for any random packet drop process. We prove that there exists a critical curve in the failure-recovery rate plane, below which the Kalman filter is mean-square stable and no longer mean-square stable above. Finally, a lower bound for this critical failure rate is obtained making use of the relationship we establish between the two stability criteria, based on an approximate relaxation of the system matrix. [ABSTRACT FROM PUBLISHER]

In this paper, an iterative residual generator (IRG) is proposed for discrete time-invariant state–space model with the aim of detecting faulty signals. By minimizing the mean square errors subject to unbiasedness constraint, a new filter with finite impulse response structure is derived. The resulting IRG is then obtained by extracting residual signal from the batch filter through several predictor/corrector iterations. It shows that IRG can provide a zero-mean Gaussian process regardless of previous estimation errors. More importantly, it includes the residual generation process in the Kalman filter as its special case. With the chi-square test, a numerical example is simulated to demonstrate that IRG can reduce the false alarm significantly compared with the traditional recursive strategy in the presence of actuator or sensor faults, and the estimation horizon length in IRG serves as a tuning parameter providing a tradeoff between the missed alarm and false alarm. [ABSTRACT FROM AUTHOR]

The paper deals with decentralized state estimation for spatially distributed systems described by linear partial differential equations from discrete in-space-and-time noisy measurements provided by sensors deployed over the spatial domain of interest. A fully scalable approach is pursued by decomposing the domain into possibly overlapping subdomains assigned to different processing nodes interconnected to form a network. Each node runs a local finite-dimensional discrete-time Kalman filter which exploits the finite element approach for spatial discretization, a backward Euler method for time-discretization and the parallel Schwarz method to iteratively enforce continuity of the field predictions over the boundaries of adjacent subdomains. Numerical stability of the adopted approximation scheme and stability of the proposed distributed finite element Kalman filter are mathematically proved. The effectiveness of the proposed approach is then demonstrated via simulation experiments concerning the estimation of a bi-dimensional temperature field. [ABSTRACT FROM PUBLISHER]

For linear discrete state-space models, under certain conditions, the linear least-mean-squares filter estimate has a convenient recursive predictor/corrector format, aka the Kalman filter. The purpose of this paper is to show that the linear minimum variance distortionless response (MVDR) filter shares exactly the same recursion, except for the initialization which is based on a weighted least-squares estimator. If the MVDR filter is suboptimal in mean-squared error sense, it is an infinite impulse response distortionless filter (a deconvolver) which does not depend on the prior knowledge (first- and second-order statistics) on the initial state. In other words, the MVDR filter can be pre-computed and its behaviour can be assessed in advance independently of the prior knowledge on the initial state. [ABSTRACT FROM AUTHOR]

In this paper, we propose a systematization of the (discrete-time) Unscented Kalman Filter (UKF) theory. We gather all available UKF variants in the literature, present corrections to theoretical inconsistencies, and provide a tool for the construction of new UKF's in a consistent way. This systematization is done, mainly, by revisiting the concepts of Sigma-Representation, Unscented Transformation (UT), Scaled Unscented Transformation (SUT), UKF, and Square-Root Unscented Kalman Filter (SRUKF). Inconsistencies are related to 1) matching the order of the transformed covariance and cross-covariance matrices of both the UT and the SUT; 2) multiple UKF definitions; 3) issue with some reduced sets of sigma points described in the literature; 4) the conservativeness of the SUT; 5) the scaling effect of the SUT on both its transformed covariance and cross-covariance matrices; and 6) possibly ill-conditioned results in SRUKF's. With the proposed systematization, the symmetric sets of sigma points in the literature are formally justified, and we are able to provide new consistent variations for UKF's, such as the Scaled SRUKF's and the UKF's composed by the minimum number of sigma points. Furthermore, our proposed SRUKF has improved computational properties when compared to state-of-the-art methods. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the Gaussian approximation (GA) smoothing estimation for the nonlinear system with the colored measurement noise modeled as an autoregressive process. Firstly, based on measurement differencing scheme, designing the GA smoothers with the colored measurement noise is transformed into deriving the GA ones with delayed state. Secondly, the novel fixed- interval, fixed-point and fixed-lag GA smoothers are proposed via the recursive operation of analytical computation and nonlinear integrals, as the general and unifying frameworks: they are applicable for both linear and nonlinear systems; by setting the noise correlation parameter as zero, they can automatically reduce to the standard GA smoothers with uncorrelated white noises; many implementations of the GA frameworks can be developed through utilizing different numerical technologies for computing such nonlinear integrals, e.g., the cubature rule based cubature Kalman smoothers (CKSs) with the colored measurement noise. Finally, the superior performance in estimation accuracy and computation efficiency of the proposed smoothing methods is demonstrated with a multi-sensor target tracking example. [ABSTRACT FROM PUBLISHER]

This paper proposes a probabilistic approach to the problem of intrinsic filtering of a system on a matrix Lie group with invariance properties. The problem of an invariant continuous-time model with discrete-time measurements is cast into a rigorous stochastic and geometric framework. Building upon the theory of continuous-time invariant observers, we introduce a class of simple filters and study their properties (without addressing the optimal filtering problem). We show that, akin to the Kalman filter for linear systems, the error equation is a Markov chain that does not depend on the state estimate. Thus, when the filter's gains are held fixed, the noisy error's distribution is proved to converge to a stationary distribution, under some convergence properties of the filter with noise turned off. We also introduce two novel tools of engineering interest: the discrete-time invariant extended Kalman filter, for which the trusted covariance matrix is shown to converge, and the invariant ensemble Kalman filter. The methods are applied to attitude estimation, allowing to derive novel theoretical results in this field, and illustrated through simulations on synthetic data. [ABSTRACT FROM AUTHOR]