Trace Of Covariance Research Articles

Data-Based Tampered-Data Recovery Strategy With Encoding Against Stealthy Attack for Unknown Discrete-Time Systems.

This study addresses a tampered-data recovery problem for linear discrete-time systems with completely unknown system dynamics under stealthy attacks. The basic idea is to identify the stealthy attack, that lies in any of attack-stealthy subspaces, and compensate for it. Different from the existing sparse recovery methods which are applicable to nonstealthy sparse attacks, a novel encoding scheme, where a set of subdecoding matrices is designed specifically for each 1-D attack-stealthy subspace, is developed so that the parameters of the stealthy attack can be identified via a subspace projection technique. A necessary and sufficient condition of determining the targeted subspace by using n parallel attack identification filters is established for this encoding scheme. Especially, a composite encoding matrix characterizes the lower and upper boundaries of the recovery error covariance's trace. A simulation example of a flight vehicle illustrates the efficiency of the proposed approach.

Distributed fusion filtering for multi-rate nonlinear systems with random sensor failures under event-triggering round-robin-like scheme

The distributed fusion filtering problem is addressed for the multi-rate nonlinear systems with random sensor failures (RSFs) over sensor networks, where a prediction compensation approach is proposed to transform the system unlike the lifting technique. The RSFs are portrayed by using stochastic variables with known statistical properties that satisfy certain probability distribution. In order to prevent data conflicts and reduce unnecessary data transmission, the event-triggering round-robin-like scheme (ETRRLS) is introduced to schedule the data transmission among sensor nodes. The main objectives of this paper are to design a local distributed filtering scheme based on the information of itself and ETRRLS scheduled neighboring nodes, and obtain an upper bound on the local filtering error (LFE) covariance which is minimized based on the filter gains design. Afterward, the local filters are fused by using the sequential covariance intersection fusion criterion. Moreover, we provide a sufficient condition, which can ensure the boundedness of the trace of LFE covariance. Finally, a simulation example is presented to illustrate the effectiveness and superiority of the newly proposed distributed fusion estimation algorithm.

Minimum Regularized Covariance Trace Estimator and Outlier Detection for Functional Data

We propose the Minimum Regularized Covariance Trace (MRCT) estimator, a novel method for robust covariance estimation and functional outlier detection designed primarily for dense functional data. The MRCT estimator employs a subset-based approach that prioritizes subsets exhibiting greater centrality based on the generalization of the Mahalanobis distance, resulting in a fast-MCD type algorithm. Notably, the MRCT estimator handles high-dimensional datasets without the need for preprocessing or dimension reduction techniques, due to the internal smoothening whose amount is determined by the regularization parameter α > 0 . The selection of α is automated. An extensive simulation study demonstrates the efficacy of the MRCT estimator in terms of robust covariance estimation and automated outlier detection, emphasizing the balance between noise exclusion and signal preservation achieved through appropriate selection of α. The method converges fast in practice and performs favorably when compared to other functional outlier detection methods.

Multi-Measurement Kalman-Filtering-Based Neural Network Estimator for SOC of Lithium Batteries

State of charge (SOC) refers to the remaining capacity of the battery, which cannot be measured directly. A multi-measurement Kalman filter which is composed of two sub Kalman filters is constructed to improve the estimation accuracy of SOC. The two sub filters share the same state function but have different measurements, namely the terminal voltage and the SOC estimation from neural network, respectively. Based on minimizing the trace of error covariance, an optimal weighted matrix is computed to fuse the estimates of the two sub filters. The training dataset of neural network is collected from mixed discharging cycles experiment and corresponding charging process. By comparing the results with model-based methods, such as H-infinity filter, unscented Kalman filter, data-driven methods, like neural networks and hybrid method, the multi-measurement Kalman filter is verified by both the root mean square error and mean absolute error that are less than 2% in different drive cycles.

Event-Based Optimal Stealthy False Data-Injection Attacks Against Remote State Estimation Systems.

Security is a crucial issue for cyber-physical systems, and has become a hot topic up to date. From the perspective of malicious attackers, this article aims to devise an efficient scheme on false data-injection (FDI) attacks such that the performance on remote state estimation is degraded as much as possible. First, an event-based stealthy FDI attack mechanism is introduced to selectively inject false data while evading a residual-based anomaly detector. Compared with some existing methods, the main advantage of this mechanism is that it decides when to launch the FDI attacks dynamically according to real-time residuals. Second, the state estimation error covariance of the compromised system is used to evaluate the performance degradation under FDI attacks, and the larger the state estimation error covariance, the more the performance degradation. Moreover, under attack stealthiness constraints, an optimal strategy is presented to maximize the trace of the state estimation error covariance. Finally, simulation experiments are carried out to illustrate the superiority of the proposed method compared with some existing ones.

Complete stealthiness false data injection attack design in multisensor systems with attack resource constraints

AbstractThis article is concerned with the attack design problem of multisensor cyber‐physical systems. Compared with the existing results developed for the single‐sensor system, the attacker is limited to modify partial sensors. To avoid generating alarm for the given detect mechanism, the correlation influence between the attacked and normal sensors is eliminated in the designed stealthiness condition. Then the trace of error covariance is used to measure the attack effect and the coupling information between sensors is also involved. By using the design freedom of stealthiness condition, the detailed attack parameters design and attacked channels selection strategy are derived to achieve the optimal attack performance via a two‐stage method including backstepping and eigenvalue sorting techniques. Finally, numerical simulation examples are provided to verify the effectiveness and advantages of the proposed attack method.

Maximum logarithmic derivative bound on quantum state estimation as a dual of the Holevo bound

In quantum estimation theory, the Holevo bound is known as a lower bound of weighed traces of covariances of unbiased estimators. The Holevo bound is defined by a solution of a minimization problem, and in general, explicit solution is not known. When the dimension of Hilbert space is two and the number of parameters is two, a explicit form of the Holevo bound was given by Suzuki. In this paper, we focus on a logarithmic derivative lies between the symmetric logarithmic derivative (SLD) and the right logarithmic derivative (RLD) parameterized by $\beta\in[0,1]$ to obtain lower bounds of weighted trace of covariance of unbiased estimator. We introduce the maximum logarithmic derivative bound as the maximum of bounds with respect to $\beta$. We show that all monotone metrics induce lower bounds, and the maximum logarithmic derivative bound is the largest bound among them. We show that the maximum logarithmic derivative bound has explicit solution when the $d$ dimensional model has $d+1$ dimensional $\mathcal{D}$ invariant extension of the SLD tangent space. Furthermore, when $d=2$, we show that the maximization problem to define the maximum logarithmic derivative bound is the Lagrangian duality of the minimization problem to define Holevo bound, and is the same as the Holevo bound. This explicit solution is a generalization of the solution for a two dimensional Hilbert space given by Suzuki. We give also examples of families of quantum states to which our theory can be applied not only for two dimensional Hilbert spaces.

Flexible optimal Kalman filtering in wireless sensor networks with intermittent observations

This paper is concerned with the distributed Kalman filtering over the wireless sensor networks (WSNs) in the presence of intermittent observations and different sensing states, where only task nodes are required to estimate the state of a linear time-invariant discrete-time system. A class of flexible binary values is used to develop the adaptability of flexible optimal Kalman filtering (FOKF) for variable sensing states. Based on the minimum error covariance trace principle, two classes of FOKFs have optimal collaborative estimation via their own and community observations, including the original FOKF and the FOKF with uncertain noise variance. The performance analysis of these two types of filters show that they have high estimation accuracy, strong robustness, low energy consumption and user-friendliness. The proposed algorithms are applied to estimate and track the position of a moving target in WSNs. The simulation illustrates that the proposed filters have superior performance, compared with the existing algorithms.

Recursive filtering for time-varying systems under duty cycle scheduling based on collaborative prediction

In this paper, a novel recursive filtering scheme combined with collaborative prediction (CP) method is proposed for a class of linear time-varying systems under duty cycle communication scheduling. The communication between the sensor nodes and the remote filter is implemented through wireless networks. In order to save energy even further, the working states of sensor nodes alternate between activation and dormancy depending on the preset duty cycle. The aim of this paper is to design a usable recursive filtering scheme for linear time-varying system subject to the duty cycle scheduling (DCS) in the case of limited energy. The DCS is modeled according to the corresponding scheduling rule. The unsent measurement outputs due to sensors being dormancy state are predicted by CP algorithm, based on which a recursive filtering scheme is developed. Also, the filter gain is calculated by minimizing the trace of error covariance. Subsequently, the boundedness of the designed filtering algorithm is analyzed. Finally, a numerical simulation example is presented to illustrate the effectiveness of the proposed recursive filtering approach based on CP algorithm subject to the DCS.

Optimal experimental design under irreducible uncertainty for linear inverse problems governed by PDEs

We present a method for computing A-optimal sensor placements for infinite-dimensional Bayesian linear inverse problems governed by PDEs with irreducible model uncertainties. Here, irreducible uncertainties refers to uncertainties in the model that exist in addition to the parameters in the inverse problem, and that cannot be reduced through observations. Specifically, given a statistical distribution for the model uncertainties, we compute the optimal design that minimizes the expected value of the posterior covariance trace. The expected value is discretized using Monte Carlo leading to an objective function consisting of a sum of trace operators and a binary-inducing penalty. Minimization of this objective requires a large number of PDE solves in each step. To make this problem computationally tractable, we construct a composite low-rank basis using a randomized range finder algorithm to eliminate forward and adjoint PDE solves. We also present a novel formulation of the A-optimal design objective that requires the trace of an operator in the observation rather than the parameter space. The binary structure is enforced using a weighted regularized ℓ0-sparsification approach. We present numerical results for inference of the initial condition in a subsurface flow problem with inherent uncertainty in the flow fields and in the initial times.

Innovation-Based Fusion of Multiple Satellite Positioning Systems for Minimizing Uncertainty

Redundant outputs from multiple positioning systems are not typically fused together on moving vehicles, resulting in unrealized opportunities in minimizing any combined position error and uncertainty. Satellite navigation is commonly used in timing and positioning applications, and combined with complementary inertial information to generate a more complete solution. However, the use of multiple Global Positioning System (GPS) outputs has not been thoroughly explored within a decentralized fusion context for reducing the uncertainty and position error. To prospect any such improvements, a federated architecture using the position outputs of multiple GPS with an inertial measurement unit is considered for a ground vehicle. The innovations are derived from extended Kalman filters and used in weighting the combination of outputs, under conditions of independence, estimated correlations, and unknown cross covariance. The methods of averaging, maximum likelihood estimation, covariance trace optimization, and covariance intersection are compared. As the number of systems grows, simulations show that the root mean squared (horizontal) position error decreases. The methods that account for nonzero correlations provide the most improved fused mean position error. As redundant position data become more ubiquitous, it can be used to improve the fused estimate over any single system alone, while further increasing overall robustness.

FD-ZKF: A Zonotopic Kalman Filter optimizing fault detection rather than state estimation

Enhancing the sensitivity to faults with respect to disturbances, rather than optimizing the precision of the state estimation using Kalman Filters (KF) is the subject of this paper. The stochastic paradigm (KF) is based on minimizing the trace of the state estimation error covariance. In the context of the bounded-error paradigm using Zonotopic Kalman Filters (ZKF), this is analog to minimize the covariation trace. From this analogy and keeping a similar observer-based structure as in ZKF, a criterion jointly inspired by set-membership approaches and approximate decoupling techniques coming from parity-space residual generation is proposed. Its on-line maximization provides an optimal time-varying observer gain leading to the so-called FD-ZKF filter that allows enhancing the fault detection properties. The characterization of minimum detectable fault magnitude is done based on a sensitivity analysis. The effect of the uncertainty is addressed using a set-membership approach and a zonotopic representation reducing set operations to simple matrix calculations. A case study based on a quadruple-tank system is used both to illustrate and compare the effectiveness of the results obtained from the FD-ZKF approach compared to a pure ZKF approach.

Optimal Scheduling for Resource-Constrained Multirobot Cooperative Localization

Typically, localization algorithms focus on maximizing estimation accuracy, often while neglecting some of the real-world costs of achieving such performance. In this letter, we formulate optimal scheduling problems of multirobot localization to investigate the tradeoff between estimate accuracy and its corresponding cost. We derive the continuous-time approximation to explicitly represent the rates of distinct operations in a multirobot localization scheme, which we then use to define the optimization problems for scheduling those operations. For a given accuracy requirement, we can solve the cost minimization problem to find the lowest cost schedule satisfying the prescribed error expectation; similarly, for a given cost budget, we can solve the trace minimization problem to find a schedule for the best achievable error performance. While the interplay between the localization error and the operation parameters is described by a Riccati equation, the Frechet derivative is applied to shed the light on their implicit relationship. In a localization example grounded in a realistic setting, we show that by solving these optimal scheduling problems, power consumption can be reduced by $64\%$ through cost minimization, or the bounding covariance trace can be reduced by $15\%$ through trace minimization.

Desensitized cubature Kalman filter with uncertain parameters

In this study, a robust desensitized cubature Kalman filtering (DCKF) is proposed for nonlinear systems with uncertain parameters. Unlike the cubature Kalman filtering, the desensitized cost function is introduced by penalizing the posterior covariance trace with a weighted sum of the posteriori sensitivities. The sensitivity of the root square matrix is obtained by solving a Lyapunov-like linear equation, and the sensitivity propagation of the state estimate errors is presented. The effectiveness of the proposed DCKF is demonstrated by two numerical examples in which models with uncertain parameters are considered.

Kalman Filtering With Intermittent Observations: Tail Distribution and Critical Value

In this paper, we analyze the performance of Kalman filtering for discrete-time linear Gaussian systems, where packets containing observations are dropped according to a Markov process modeling a Gilbert-Elliot channel. To address the challenges incurred by the loss of packets, we give a new definition of non-degeneracy, which is essentially stronger than the classical definition of observability, but much weaker than one-step observability, which is usually used in the study of Kalman filtering with intermittent observations. We show that the trace of the Kalman estimation error covariance under intermittent observations follows a power decay law. Moreover, we are able to compute the exact decay rate for non-degenerate systems. Finally, we derive the critical value for non-degenerate systems based on the decay rate, improving upon the state of the art.

Short Data Record Adaptive Filtering: The Auxiliary-Vector Algorithm

Karystinos, G. N., Qian, H., Medley, M. J., and Batalama, S. N., Short Data Record Adaptive Filtering: The Auxiliary-Vector Algorithm, Digital Signal Processing 12 (2002) 193–222 Based on statistical conditional optimization criteria, we developed an iterative algorithm that starts from the matched filter (or constraint vector) and generates a sequence of filters that converges to the minimum variance distortionless response (MVDR) solution for any positive definite input autocorrelation matrix. Computationally, the algorithm is a simple recursive procedure that avoids explicit matrix inversion, decomposition, or diagonalization operations. When the input autocorrelation matrix is replaced by a conventional sample-average (positive definite) estimate, the algorithm effectively generates a sequence of MVDR filter estimators: The bias converges rapidly to zero and the covariance trace rises slowly and asymptotically to the covariance trace of the familiar sample matrix inversion (SMI) estimator. For short data records, the early, nonasymptotic, elements of the generated sequence of estimators offer favorable bias–covariance balance and are seen to outperform in mean-square estimation error constraint-LMS, RLS-type, and orthogonal multistage decomposition estimates (also called nested Wiener filters) as well as plain and diagonally loaded SMI estimates. The problem of selecting the most successful (in some appropriate sense) filter estimator in the sequence for a given data record is addressed and two data-driven selection criteria are proposed. The first criterion minimizes the cross-validated sample average variance of the filter estimator output. The second criterion maximizes the estimated J-divergence of the filter estimator output conditional distributions. Illustrative interference suppression examples drawn from the communications literature are followed throughout this presentation.

An iterative algorithm for the computation of the MVDR filter

Statistical conditional optimization criteria lead to the development of an iterative algorithm that starts from the matched filter (or constraint vector) and generates a sequence of filters that converges to the minimum-variance-distortionless-response (MVDR) solution for any positive definite input autocorrelation matrix. Computationally, the algorithm is a simple, noninvasive, recursive procedure that avoids any form of explicit autocorrelation matrix inversion, decomposition, or diagonalization. Theoretical analysis reveals basic properties of the algorithm and establishes formal convergence. When the input autocorrelation matrix is replaced by a conventional sample-average (positive definite) estimate, the algorithm effectively generates a sequence of MVDR filter estimators; the bias converges rapidly to zero and the covariance trace rises slowly and asymptotically to the covariance trace of the familiar sample-matrix-inversion (SMI) estimator. In fact, formal convergence of the estimator sequence to the SMI estimate is established. However, for short data records, it is the early, nonasymptotic elements of the generated sequence of estimators that offer favorable bias covariance balance and are seen to outperform in mean-square estimation error, constraint-LMS, RLS-type, orthogonal multistage decomposition, as well as plain and diagonally loaded SMI estimates. An illustrative interference suppression example is followed throughout this presentation.

Robust Adaptive Control for Hydraulic Servosystems

The application of an indirect (self-tuning) adaptive controller to an electro-hydraulic positioning system is described. The underlying control method is pole placement, with the addition of a demand filter to allow noise effects to be reduced without degrading closed-loop performance. Recursive least squares is used to estimate the plant parameters, but the data is pre-filtered to reduce bias. A novel covariance trace limiting algorithm provides estimator reliability despite periods of insufficient excitation. Off-line system identification is employed to help controller design for the electro-hydraulic servosystem. The resulting controller performs well, and adapts rapidly to changes in load stiffness and supply pressure.