Fusion identification and estimation of multisensor multichannel AR signals with missing measurements and sensor biases

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.

This paper is concerned with the distributed fusion filtering problem for descriptor systems with multiple sensors and multiple packet dropouts. When a packet is lost from a sensor to a local processor over an unreliable network, the predictor of the lost packet is used as a compensator. The original high-order descriptor system is transformed into two reduced-order subsystems (ROSs) by a non-singular linear transformation. By using projection theory, local filters (LFs) are presented for two ROSs in the linear unbiased minimum variance (LUMV) sense. The cross-covariance matrices between any two sensor subsystems and between two ROSs are derived to compute fusion weights, respectively. The distributed fusion filters (DFFs) weighted by matrices are presented for two ROSs in the LUMV sense. Then, DFF for the original descriptor system is obtained. A numerical example is used to show the effectiveness of the presented algorithm.

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

A general packet dropout compensation framework for optimal prior filter of networked multi-sensor systems

Multi-sensor information fusion estimators for stochastic uncertain systems with correlated noises

This paper presents a distributed optimal predictor (DOP) with the Kalman-like form for time-invariant system with communication noises, i.e., a prior filter, considering cross-covariance matrices between sensor nodes in sensor networks, where each sensor exchanges local estimates with its neighbor nodes. To obtain the DOP, an optimal Kalman predictor gain for each sensor node and different optimal consensus gains for state estimates of its neighbor nodes are designed in the linear unbiased minimum variance (LUMV) sense. Stability and steady-state property of DOP are analyzed. An example for target tracking based on a directed topology in sensor networks demonstrates effectiveness of the proposed algorithm.

This paper is concerned with the design of networked multi-sensor fusion estimation system (NMFES). The Kalman filtering problem is considered for the NMFES with random observation delays, packet dropouts and missing measurements caused by sensor failures. For each observation subsystem, the sensor failure phenomenon is described by a Bernoulli distributed white sequence with a known conditional probability, and the packet dropout phenomenon and randomly delayed measurements are described by multiple binary random variables. Without resorting to the augmentation technique, an optimal recursive fusion filter for NMFES is obtained in the linear minimum variance sense by using the innovation analysis method. The dimension of the designed filter is the same to the original system, which can help reduce computation costs as compared with the augmentation method. Moreover, the performance of the designed Kalman filter is dependent on the missing rates of the measurements, the upper bounds of random delays and the occurrence probabilities of delays. Finally, the effectiveness of the proposed results is demonstrated by an illustrative example.

This study addresses the challenge of developing a robust, time‐varying fusion Kalman estimator for multi‐sensor networks with compound indeterminacies, including multiplicative noises, two‐step stochastic delays, missing measurements, and variations in uncertain noise. To tackle this problem, a model transformation strategy that includes the augmentation method, the de‐randomization method, and the fictional noise method is employed. This approach converts the original multi‐sensor system into an equivalent system with constant parameters and unknown noise variances, laying the foundation for subsequent estimator design. Within a unified framework, three robust fusion time‐varying Kalman estimators—predictor, filter, and smoother—are derived based on the minimax robust estimation principle and the worst‐case system with the conservative upper bounds of the noise variances. The design of this robust fusion Kalman estimator utilizes the robust fusion Kalman predictor, further derives the corresponding weighted fusion filter and smoother, and adopts three weighting rules: matrix weighting, diagonal matrix weighting and scalar weighting. The robustness of the proposed fusion estimators is verified through the augmented noise method, the non‐negative definite matrix decomposition method, and the global Lyapunov equation method, which also reveal the accuracy correlation between robust local estimates and fused time‐varying Kalman estimates. Specifically, “robustness” herein refers to ensuring that the actual estimation error variances maintain corresponding minimum upper bounds for all admissible uncertainties. Finally, simulation experiments on autoregressive (AR) signal processing and the original system demonstrate that robust fusion state estimation can solve the problem of robust fusion signal estimation and verify the effectiveness and accuracy of the proposed method.

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

Probability hypothesis density (PHD) filter has been demonstrated a promising algorithm for tracking an unknown number of targets in real time. However, this method can only be used in the multi‐target tracking systems with known measurement noise variances; otherwise, the tracking performance will decline greatly. To solve this problem, an adaptive PHD filter algorithm is proposed based on the variational Bayesian approximation technique to recursively estimate the joint PHDs of the multi‐target states and the time‐varying measurement noise variances. First, the variational calculus method is employed to derive the multi‐target estimate recursions, and then the Gaussian and the inverse Gamma distributions are introduced to approximate the joint posterior PHD, and achieve a closed‐form solution. Simulation results show that the proposed algorithm can effectively estimate the unknown measurement noise variances and has a good performance of multi‐target tracking with a strong robustness.

This paper is concerned with the information fusion estimation problem about the white noise. White noise estimator has an important application in oil seismic exploration. The centralized fusion white noise estimator in least mean square sense is presented for multi-sensor discrete-time stochastic linear systems with missing measurements based on the innovation analysis method, where different sensors have different missing measurement rates. Compared to local estimators, the proposed centralized fusion estimator has better estimation accuracy. An example shows the effectiveness.

Multi-sensor distributed fusion estimation algorithms based on machine learning are proposed in this paper. Firstly, using local estimations as inputs and estimations of three classic distributed fusion (weighted by matrices, by diagonal matrices and by scalars) as the training sets, three distributed fusion algorithms based on BP network (BP net-based fusion weighted by matrices, by diagonal matrices and by scalar) are proposed and the selection basis of the number of nodes in hidden layer is given. Furthermore, by using local estimations as inputs and centralized fusion estimation as training set, another recurrent net-based distributed fusion algorithm is proposed, in the case that neither true states nor cross-covariance matrices is available. This method is not limited to the linear minimum variance (LMV) criterion, so its accuracy is higher than the classical three distributed fusion algorithms. A radar tracking simulation verifies the effectiveness of the proposed fusion networks.

Information Fusion Identification Method for the Multidimension ARMA Signal with Sensor Bias and Common Disturbance Noise

Particle filters for probability hypothesis density filter with the presence of unknown measurement noise covariance

This paper shows that a general multisensor unbiased linearly weighted estimation fusion essentially is the linear minimum variance (LMV) estimation with linear equality constraint, and the general estimation fusion formula is developed by extending the Gauss-Markov estimation to the random parameter under estimation. First, we formulate the problem of distributed estimation fusion in the LMV setting. In this setting, the fused estimator is a weighted sum of local estimates with a matrix weight. We show that the set of weights is optimal if and only if it is a solution of a matrix quadratic optimization problem subject to a convex linear equality constraint. Second, we present a unique solution to the above optimization problem, which depends only on the covariance matrix C k . Third, if a priori information, the expectation and covariance, of the estimated quantity is unknown, a necessary and sufficient condition for the above LMV fusion becoming the best unbiased LMV estimation with known prior information as the above is presented. We also discuss the generality and usefulness of the LMV fusion formulas developed. Finally, we provide an off-line recursion of C k for a class of multisensor linear systems with coupled measurement noises.