Linear Minimum Variance Sense Research Articles

Secure fusion estimation against FDI sensor attacks in cyber–physical systems

This paper is concerned with the secure fusion estimation problem in cyber–physical systems (CPSs), where false data injection attack (FDIA) is able to falsify measurement signals transmitted over network. In this paper, we consider that adversaries are not able to attack all measurements, i.e., several measurements remain not being attacked. Under this condition, local augmented systems including FDIA signals are respectively constructed with un-attacked measurements. For each augmented system, we design the joint Kalman fusion estimator, under the linear minimum variance sense, to simultaneously estimate FDIA and system states, which is fulfilled by introducing a compensation factor. Finally, a simulation example is given to verify effectiveness and advantages of the secure fusion estimation method.

Fusion estimation against mixed network attacks for systems with random parameter matrices, correlated noises, and quantized measurements

This paper is concerned with the information fusion estimation problems for stochastic uncertain systems with quantized measurements and mixed network attacks including random deception attack and denial-of-service (DoS) attack. The cross-correlated random parameter matrices and addictive noises simultaneously exist in the studied system. By resorting to the optimal prediction compensation mechanism for DoS attack, an optimal centralized fusion filter in the linear minimum variance sense is proposed using an innovation analysis approach. In addition, the Kalman-like recursive distributed optimal linear fusion predictor and filter without feedback are presented based on local estimators from single-sensor subsystems. The estimation error cross-covariance matrices between two arbitrary local estimators, and those between local and prior fusion estimators are derived. They have good flexibility due to the parallel structure. However, they have lower accuracy than the centralized fusion estimators. To further improve the estimation accuracy, the distributed optimal linear fusion predictor and filter with feedback are also presented. They avoid the calculation of cross-covariance matrices. Moreover, it has been mathematically proved that they have the same estimation accuracy as the centralized fusion estimators. A simulation example demonstrates the effectiveness of the proposed algorithms.

Distributed filtering for multi-sensor networked systems with stochastic communication protocol and correlated noises

In multi-sensor networked systems, to solve data conflicts caused by limited bandwidths during measurement data exchange among sensors, a stochastic communication protocol scheduling is employed to ensure that each sensor can only receive one component of measurement vector from neighbor nodes at each instant. The measurement components selected for communication at each instant are indicated by a set of random variables. When each sensor knows which component of the measurement vector from each of its neighbor nodes is passed at each instant, an optimal distributed Kalman filter (ODKF) where both estimator and gain rely on values of random variables is designed in the linear minimum variance sense. To reduce the online computational burden, a suboptimal DKF (SDKF) where the filtering gain relies on probabilities of random variables is designed and its steady-state property is analyzed. When each sensor doesn't know which component of the measurement vector is passed at each instant, a probability-dependent DKF (PDKF) where both estimator and gain rely on probabilities of random variables is designed and its steady-state property is analyzed. Finally, the performances of the proposed three DKF algorithms are compared. Two simulation examples verify the effectiveness of algorithms.

Optimal Linear Filter Based on Feedback Structure for Sensing Network with Correlated Noises and Data Packet Dropout.

This paper is concerned with the estimation of correlated noise and packet dropout for information fusion in distributed sensing networks. By studying the problem of the correlation of correlated noise in sensor network information fusion, a matrix weight fusion method with a feedback structure is proposed to deal with the interrelationship between multi-sensor measurement noise and estimation noise, and the method can achieve optimal estimation in the sense of linear minimum variance. Based on this, a method is proposed using a predictor with a feedback structure to compensate for the current state quantity to deal with packet dropout that occurs during multi-sensor information fusion, which can reduce the covariance of the fusion results. Simulation results show that the algorithm can solve the problem of information fusion noise correlation and packet dropout in sensor networks, and effectively reduce the fusion covariance with feedback.

Globally optimal distributed and sequential state fusion filters for multi-sensor systems with correlated noises

The problem concerning the multi-sensor fusion filtering for systems with correlated system and measurement noises is studied in this paper. Each sensor produces a local predictor by using its own measurements and then sends it to a fusion center. In the fusion center, by applying the projection theory and difference technology, the globally optimal distributed state fusion filter without feedback and sequential state fusion filter with recursive estimators of noises are presented in the sense of linear minimum variance by using all received local predictors, respectively. Under the condition that local prediction gain matrices are of full column rank, the proposed distributed and sequential state fusion filters can achieve the same estimation accuracy as the centralized fusion filter, i.e., they both have global optimality. The optimality is strictly proved. The corresponding steady-state fusion filters are also explored. A sufficient condition for the convergence of the proposed fusion filters is given. A target tracking example verifies the effectiveness of the proposed algorithms.

An order insensitive optimal generalised sequential fusion estimation for stochastic uncertain multi‐sensor systems with correlated noise

AbstractThe globally optimal generalised sequential fusion (GSF) algorithm in the sense of linear minimum variance for multi‐sensor stochastic uncertain systems is investigated by the authors. Specifically, in the GSF algorithm, the estimation of measurement noise is considered, and ma (ma ≥ 1) sensors' measurement data are fused at the ath reception instant, which makes it very flexible and suitable for practical applications. The centralised and sequential fusion algorithms are special cases of the proposed GSF algorithm. Furthermore, for any ma, a = 1, 2, …, M, the estimated values of the GSF algorithm remain invariant and globally optimal. Moreover, the independence between the estimated values and fusion order is proved in the proposed GSF algorithm. Finally, simulation results are given to demonstrate the usefulness of the developed algorithm.

Delay-Dependent Distributed Kalman Fusion Estimation With Dimensionality Reduction in Cyber-Physical Systems.

This article studies the distributed dimensionality reduction fusion estimation problem with communication delays for a class of cyber-physical systems (CPSs). The raw measurements are preprocessed in each sink node to obtain the local optimal estimate (LOE) of a CPS, and the compressed LOE under dimensionality reduction encounters with communication delays during the transmission. Under this case, a mathematical model with compensation strategy is proposed to characterize the dimensionality reduction and communication delays. This model also has the property of reducing the information loss caused by the dimensionality reduction and delays. Based on this model, a recursive distributed Kalman fusion estimator (DKFE) is derived by optimal weighted fusion criterion in the linear minimum variance sense. A stability condition for the DKFE, which can be easily verified by the exiting software, is derived. In addition, this condition can guarantee that the estimation error covariance matrix of the DKFE converges to the unique steady-state matrix for any initial values and, thus, the steady-state DKFE (SDKFE) is given. Note that the computational complexity of the SDKFE is much lower than that of the DKFE. Moreover, a probability selection criterion for determining the dimensionality reduction strategy is also presented to guarantee the stability of the DKFE. Two illustrative examples are given to show the advantage and effectiveness of the proposed methods.

Recursive distributed fusion estimation for multi-sensor systems with missing measurements, multiple random transmission delays and packet losses

This paper is concerned with the recursive distributed fusion estimation problems for networked multi-sensor systems with missing measurements, multiple random transmission delays, and packet losses. There exist missing measurements in the observation equations due to unpredictable sensor faults. Moreover, there are often random delays and losses during data transmissions from sensors to the fusion center due to limited communication bandwidths of the network. The Kalman-like recursive distributed fusion predictor and filter in the linear unbiased minimum variance (LUMV) sense are, respectively presented based on local estimates, cross-covariance matrices between local estimates, and cross-covariance matrices between the prior fusion estimate and local estimates. The stability and steady-state property of the proposed algorithms are analyzed. Their estimation accuracy is better than that of local estimates and distributed fusion estimates by matrix-weighting local estimates. A simulation example shows the effectiveness of the proposed algorithms.

Globally Optimal Distributed Fusion Filter for Descriptor Systems with Time-Correlated Measurement Noises.

This paper concerns the distributed fusion filtering problem for descriptor systems with time-correlated measurement noises. The original descriptor is transformed into two reduced-order subsystems (ROSs) based on singular value decomposition. For the first ROS, a new measurement is obtained using measurement difference technology. Each sensor produces a local filter based on the fusion predictor from the fusion center and its own new measurement and then sends it to the fusion center. In the fusion center, based on local filters, a distributed fusion filter with feedback (DFFWF) in the linear minimum variance (LMV) sense is proposed by applying an innovative approach. The DFFWF for the second ROS is also obtained based on the DFFWF for the first ROS. Then, the DFFWF for the original descriptor is obtained. The proposed DFFWF can achieve the same estimation accuracy as the centralized fusion filter (CFF) under the condition that all local filter gain matrices are of full column rank. Its optimality is strictly proved. Moreover, it has robustness and reliability due to the parallel processing of local filters. Two simulation examples demonstrate the effectiveness of the developed fusion algorithm.

Distributed Filtering for Multi-sensor Systems with Missing Data

This paper studies distributed estimation problems for multi-sensor systems with missing data. Missing data may occur during sensor measuring or data exchanging among sensor nodes due to unreliability of communication links or external disturbances. Missing data include random missing measurements of sensor itself and random missing estimates of neighbor nodes. Three distributed Kalman filter (DKF) algorithms with the Kalman-like form are designed for each sensor node. When it is available whether a datum is missing or not at each time, an optimal DKF (ODKF) dependent on the knowledge of missing data is presented, where filter gains and covariance matrices require online computing. To reduce online computational cost, a suboptimal DKF (SDKF) is presented, where filter gains and covariance matrices dependent on missing probabilities can be computed offline. When it is unavailable whether a datum is missing or not, a probability-based DKF (PDKF) dependent on missing probabilities is presented. For each DKF algorithm, an optimal Kalman filter gain for measurements of sensor itself and different optimal consensus filter gains for state estimates of its neighbor nodes are designed in the linear unbiased minimum variance (LUMV) sense, respectively. Mean boundedness of covariance matrix of the proposed ODKF is analyzed. Stability and steady-state properties of the proposed SDKF and PDKF are analyzed. Also, the performance of three DKF algorithms is compared. Simulation examples demonstrate effectiveness of the proposed algorithms.

Optimal input filtering for networked iterative learning control systems with packet dropouts and channel noises in both sides

AbstractThis article is concerned with the convergence performance of wireless networked iterative learning control (ILC) systems with data dropouts and channel noises in both sensor‐to‐controller and controller‐to‐actuator channels. In order to improve the convergence performance of such ILC systems, an optimal input filter is developed at the actuator side to estimate controller updated input with the effect of these network uncertainties. Specifically, a filtering model is constructed only by using the learning process of P‐type controllers and the transmission process of both measured output data and updated input data. On the basis of this model and the orthogonality principle, the filter in the sense of linear minimum variance is designed at the actuator side so that the controller updated input could be estimated in iteration domain. The convergence performance of filtering error covariance matrix is analyzed theoretically. Moreover, because the filter design does not employ plant information, the tracking performance of any plant with P‐type learning controllers can be improved by driving with the filtered input. Simulation results show that the proposed filtering method is effective.

Optimized distributed fusion filtering for singular systems with fading measurements and stochastic nonlinearity

<abstract><p>In this paper, the problem of optimized distributed fusion filtering is considered for a class of multi-sensor singular systems in the presence of fading measurements and stochastic nonlinearity. By utilizing the standard singular value decomposition, the multi-sensor stochastic singular systems are simplified to two reduced-order nonsingular subsystems (RONSs). The local filters (LFs) with corresponding error covariance matrices are proposed for RONSs via the innovation analysis approach. Then, on the basis of the matrix-weighted fusion estimation algorithm, the distributed fusion filters (DFFs) are designed for RONSs with multiple sensors in the linear minimum variance sense. Moreover, the DFFs are obtained by utilizing the state transformation for original singular systems. It can be observed that the DFFs have better accuracy in contrast with the LFs. Finally, an illustrate example is put forward to verify the feasibility of the proposed fusion filtering scheme.</p></abstract>

Globally Optimal Centralized and Sequential Fusion Filters for Uncertain Systems With Time-Correlated Measurement Noises

This paper is concerned with the fusion filtering problem for stochastic uncertain multi-sensor systems with time-correlated measurement noises, where the stochastic uncertainties are described by white multiplicative noises, and the additive measurement noises are first-order Gauss-Markov Processes. By introducing the recursive measurement noise estimators, the centralized fusion filter (CFF) based on the idea of batch process and sequential fusion filter (SFF) based on the idea of sequential process are designed in the linear minimum variance (LMV) sense by an innovation analysis approach, respectively. The proposed SFF can achieve the same estimation accuracy as the CFF. It is also globally optimal. The equivalence on estimation accuracy of the SFF and CFF is strictly proved by mathematical induction method. The stability and steady-state properties of the proposed fusion filters are analyzed. Two examples show the effectiveness of the proposed fusion algorithms.

Optimal input filters for iterative learning control systems with additive noises, random delays, and data dropouts in both channels

The convergence performance of wireless networked iterative learning control systems is affected by additive noises, random delays, and data dropouts in both sensor‐to‐controller and controller‐to‐actuator channels. In order to guarantee the convergence performance of such systems, an input filter is designed in front of actuators to estimate the controller updated input under the effect of those uncertainties. Specifically, a P‐type learning controller is considered firstly, and then a model is developed to describe the transmission of sensor measured output data and controller updated input data under the mixed effect of those uncertainties. On the basis of state augmentation, the two developed data transmission processes are further combined with the controller learning process to build a unified filtering model. According to this filtering model and the projection theory, an optimal filter in linear minimum variance sense is designed at the actuator side to estimate the controller updated input in iteration domain. The convergence performance of the norm of filtering error covariance matrix is proved theoretically, which means driven by this accurately estimated input, the convergence performance of networked systems adopting the P‐type learning controller is guaranteed. Finally, some numerical results are given to illustrate the effectiveness of the proposed method.

Distributed Kalman Filters With Random Sensor Activation and Noisy Channels

This paper studies distributed Kalman filtering problems for sensor networks with random sensor activation and noisy channels. Each sensor measures the target state with a random activation and receives state estimates of its neighbor nodes. Communication noises are considered in communication links between sensors and their neighbor nodes. Considering cross-covariance matrices between sensors, an optimal distributed Kalman filter (ODKF) with a given recursive structure is proposed for each sensor, which depends on the knowledge whether a sensor itself is activated to measure the target state or not and whose filter gains and covariance matrices depend on random activation rate of the sensor. In the ODKF algorithm, optimal Kalman filter gain for each sensor and different optimal consensus filter gains for state estimates of its neighbor nodes are designed in the linear unbiased minimum variance (LUMV) sense. To reduce computational cost, a suboptimal distributed Kalman filter (SDKF) is also presented by considering a locally minimum upper bound of the filtering error covariance matrix, where the calculation of cross-covariance matrices among sensor nodes is avoided. The stability and steady-state property of the proposed ODKF and SDKF algorithms are explored. Finally, the proposed methods are also extended to the nonlinear scenarios. Simulation examples show the effectiveness of the proposed algorithms.

An optimal filter for updated input of iterative learning controllers with multiplicative and additive noises

Multiplicative and additive noises, arising from both sensor-to-controller and controller-to-actuator channels, affect the convergence performance of wireless networked iterative learning control (ILC) systems. In order to guarantee the convergence performance of such ILC systems, this paper designs an input filter at the actuator side for estimating the controller updated input. Specifically, a P-type learning controller is considered firstly, and then a mathematical model is developed to describe the transmission processes of both measured output data and updated input data with the effect of those noises. On the basis of state augmentation, these two data transmission processes are further combined with the controller learning process to build a filtering model. Finally, according to this filtering model and the orthogonality projection theory, the optimal input filter in the sense of linear minimum variance is designed in front of actuators. The convergence performance of the filtering error covariance matrix is analysed theoretically. Furthermore, because the input filter is designed only with the controller learning process and the two data transmission processes, the convergence performance of any system with the considered controller can be improved by driving with the filtered input. Finally, numerical results are given to illustrate the effectiveness of the proposed method.

Estimation for Networked Random Sampling Systems With Packet Losses

The state estimation problem is investigated in this article for networked random sampling linear stochastic systems. In the system, the system state uniformly updates and the measurement is randomly sampled. Packet losses induced by unreliable networks from a controller to an actuator and from a sensor to an estimator under the TCP protocol are tackled by employing two independent Bernoulli distributed stochastic variables. A state space model (SSM) at successfully received measurement sampling (SRMS) points is developed under the condition of known sampling time. Using an innovation analysis approach, a recursive nonaugmented optimal estimator is proposed in the linear minimum variance (LMV) sense. It can obtain state estimates at state update (SU) points and SRMS points. In addition, for multisensor systems, a centralized fusion estimator by reordering measurement data from sensors and a suboptimal distributed covariance intersection fusion estimator are proposed, respectively. The effectiveness of the proposed algorithms is verified through an example.

Estimator for Multirate Sampling Systems With Multiple Random Measurement Time Delays

The optimal linear estimation problem is studied for multirate sampling systems with multiple random measurement time delays (TDs). The considered multirate sampling scheme is that the sensor uniformly samples at a slow rate and the state uniformly updates at a fast rate. Known stochastic variable sequences obeying Bernoulli distributions are adopted to depict random measurement TDs, including missing measurements as a special case. First, using a state iterating method, the original system with multirate sampling and delayed measurements is transformed into a state-space model with single-rate sampling and delay-free measurements at measurement sampling (MS) instants. Then, by utilizing projection theory, a nonaugmented recursive optimal linear state filter is presented based on the established model in the linear minimum variance sense, where the estimators for the process noise are involved. Furthermore, the state estimator at state update instants is achieved through filtering or prediction based on the filter at MS instants. Finally, the centralized fusion estimator and the distributed covariance intersection fusion estimator are proposed for the multisensor case. Simulation research on a vehicle suspension system verifies the effectiveness of the algorithms.

Distributed Fusion Estimation for Multisensor Multirate Systems With Packet Dropout Compensations and Correlated Noises

This article investigates distributed fusion estimation problems for multisensor multirate (MSMR) stochastic systems with correlated noises (CNs) and packet dropouts (PDs). The state updates at the fast rate while sensors uniformly sample at positive integer multiples of the state updating period. Different sensors may have different sampling rates. The system noise and measurement noises are auto- and cross-correlated at the same instant. The phenomenon of PDs randomly occurs during data transmission from a sensor to a data processor through unreliable networks. A recent developed compensation strategy that a predictor of a lost packet is employed as a compensator is adopted to optimize the tracking process. First, an optimal linear local filter (LF) for each sensor at measurement sampling points (MSPs) is presented by using an innovation analysis approach. Then, a local estimator (LE) at state updating points (SUPs) is proposed by filtering or prediction based on the LF at MSPs. Furthermore, estimation error cross-covariance matrices (CCMs) between arbitrary two LEs at SUPs are deduced, which can recursively be calculated by three joint difference equations. Finally, a distributed fusion filter (DFF) weighted by matrices in the sense of linear unbiased minimum variance (LUMV) is addressed. Period steady-state (PSS) property of the LEs, CCMs, and DFF is proved. A simulation example verifies the effectiveness of algorithms.

Distributed Fusion Filter for Nonlinear Multi-Sensor Systems With Correlated Noises

This paper is concerned with distributed fusion (DF) estimation problem for nonlinear multi-sensor systems with correlated noises. Based on a recursive linear minimum variance estimation (RLMVE) framework, a novel filter is developed. It is proved that the RLMVE-based filter and the existing de-correlated filter have the functional equivalence. Then, for multi-sensor cases, cross-covariance matrices between any two local filters are derived. Based on the RLMVE-based filter and cross-covariance matrices, a DF filter weighted by matrices is proposed in the sense of linear minimum variance. Finally, based on the existing de-correlated filter, the algorithm of cross-covariance for de-correlated systems and the DF algorithm weighted by matrices, a de-correlated DF filtering algorithm is proposed. An example verifies the effectiveness of the proposed RLMVE-based DF filter.