This paper studies a distributed cooperative state estimation problem for nonlinear multi-agent systems based on absolute and relative measurements. Each agent achieves cooperative state estimation by integrating its own absolute measurements and relative measurements with neighboring agents. Each agent receives local estimates from neighboring agents to linearize the nonlinear function in the relative measurement equation. An optimal distributed cooperative extended Kalman filter (EKF) algorithm is proposed by minimizing the filtering error covariance matrix (FECM), which requires calculation of cross-covariance matrices (CCMs) between agents. To avoid calculation of CCMs, a suboptimal distributed cooperative EKF algorithm is also proposed by minimizing an upper bound of the FECM. The exponential mean square boundedness (MSB) of the proposed distributed filters is proven. A cooperative localization tracking system with six mobile robots is used to evaluate the effectiveness of the proposed algorithm.

The robust fusion filtering problem of multi-sensor networked uncertain descriptor systems (NUDSs) with colored noise, uncertain noise variances and cyber-attacks is investigated. During data transmission in unreliable communication networks, the data can be maliciously attacked by attackers. In other words, the local filters (LFs) may receive false data or may not receive data because of the cyber-attacks. By adopting the singular value decomposition (SVD) method, the original NUDSs can be converted into two reduced-order subsystems with uncertain correlated fictitious white noises, and the cyber-attacks are transformed into the fictitious noises. Cross-covariance matrices between local filtering errors are derived. The robust LFs are obtained according to the minimax robust estimation principle. Under the linear unbiased minimum variance criterion, three weighted fusion algorithms are applied to fuse the LFs. For all allowable uncertainties of noise variances and cyber-attacks, the minimal upper bounds of covariance matrices of the local and distributed fusion filters are guaranteed. The proof of their robustness is established through the minimax estimation principle and Lyapunov equation method. Finally, the correctness and effectiveness of the proposed algorithms are verified by a circuit system example.

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.

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.

A distributed fusion estimation algorithm is studied for multisensor multirate systems with correlated noises, where the state update rate is positive integer multiples of the measurement sampling rates and different sensors sample uniformly with different sampling rates. The measurement noises from different sensors are correlated with each other and are also correlated with the process noise. First, the state space model is established at the measurement sampling points (MSPs). Then, the optimal local filter at the MSPs and optimal local estimators (LEs) at the state update points are presented by an innovation analysis approach, respectively. Moreover, the cross-covariance matrices of estimation errors between any two LEs are derived, which involves three jointly recursive difference equations. At last, a distributed fusion estimator is proposed by applying the matrix-weighted fusion estimation algorithm in the linear minimum variance sense. The stability of the proposed algorithms is analyzed. Simulation results illustrate the effectiveness of the algorithms.

This paper is concerned with the distributed fusion estimation problem for a class of multi-sensor non-uniform sampling systems with correlated noises and fading measurements. The state is updated uniformly and the sensors sample measurement data randomly. The process noise and different measurement noises are correlated at the same instant. Moreover, the fading measurement phenomena may occur in different sensor channels. The independent random variables obeying different certain probability distributions over different known intervals are employed to describe the phenomena. Based on the measurement augmentation method, the state space model is reconstructed in which the asynchronous sampling estimation problem is transformed to the synchronous one. Afterwards, local optimal filters are designed by using an innovation analysis approach. Then, the filtering error cross-covariance matrices between any two local filters are derived. At last, the optimal matrix-weighted distributed fusion filter is given in the linear unbiased minimum variance sense. Simulation results show the effectiveness of the proposed algorithms.

This study is concerned with the linear estimation problem for networked systems with one‐step random delay and multiple packet dropouts. At each moment, the estimator may receive one or two data packets or nothing. The predictor of sensor measurement at the current instant is used as a compensator if the current measurement does not arrive at the estimator. Based on the developed compensation model, the optimal linear estimators including filter, predictor and smoother are proposed by the innovation analysis approach. Compared with the estimators based on the compensation of using the latest measurement previously received in the existing literatures, the proposed estimators have higher estimation accuracy and smaller computational burden. Simulation results show the effectiveness of the proposed algorithms.

The fusion estimation problem for a class of multi‐sensor asynchronous sampling linear stochastic systems with missing measurements is considered, where the state is updated uniformly and each sensor non‐uniformly samples one measurement at most within a state update period. Based on the sampled measurement data of each sensor, the optimal local state estimators are designed at the state and measurement points by using the projection theory. The cross‐covariance matrices between estimation errors of any two local estimators are derived. Based on the obtained local estimators and cross‐covariance matrices, the distributed optimal fusion estimator is given by using matrix‐weighted fusion estimation algorithm in the linear minimum variance sense. A simulation example verifies the effectiveness of the algorithms.

This study is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with multiplicative noise uncertainties in state and measurement matrices and with multiple packet dropouts from a sensor to an estimator. Based on the projection theory, the optimal linear estimators including filter, predictor and smoother are derived in the linear minimum variance sense. In the absence of stochastic uncertainties and/or packet dropouts, the corresponding results can be obtained as the special cases of the proposed estimators. Steady-state property is also analysed. A sufficient condition for the existence of the steady-state estimators is obtained. They can be computed offline. So they have the reduced online computational cost. Simulation examples are given to demonstrate the effectiveness of the proposed estimators.

This study is concerned with the optimal linear estimation problems for multi-sensor autoregressive moving average (ARMA) signals with missing measurements, which can be converted into estimation problems of the state and white noise in the state space representation. The missing measurements from different sensors are described by a group of Bernoulli distributed random variables. Using the projection theory, the optimal linear estimators including filter, predictor and smoother for the state and white noise are derived in the linear minimum variance sense. Furthermore, the centralised optimal estimators for ARMA signals with multiple sensors of different missing measurement rates are obtained. The previous estimation algorithms under complete measurement data in references have lost the optimality when there are missing measurements of sensors. At last, the stability of the proposed estimators is analysed. Simulation results show the effectiveness of the proposed optimal linear estimators.

This paper is concerned with the optimal estimation problem for discrete-time stochastic linear systems with finite consecutive packet dropouts. By introducing a set of new variables, a state augmented system with a lower order is obtained. Based on the new model, the optimal estimators including filter, predictor and smoother are readily solved in the least-mean-square sense via the innovation analysis approach. The solutions depend on the recursion of a Riccati equation and a Lyapunov equation. The steady-state estimators have also been investigated. A sufficient condition for the convergence of the optimal estimators has been given. A simulation shows the effectiveness of the proposed algorithms.

Based on the optimal fusion algorithm weighted by scalars in the linear minimum variance sense, a distributed optimal fusion reduced-order Kalman filter with scalar weights is presented for discrete-time stochastic singular systems with multiple sensors and correlated noises. It has higher accuracy than any local filter does. Compared with the distributed fusion filter weighted by matrices, it has lower accuracy but has reduced computational burden. Computation formula of cross-covariance matrix of the filtering errors between any two sensors is given. An example with three sensors shows the effectiveness

Based on the multi-sensor optimal information fusion criterion weighted by scalars in the linear minimum variance sense, the distributed optimal fusion Kalman multi-step predictor is given for discrete multi-channel ARMA (autoregressive moving average) signals. The precision of the fusion predictor is higher than that of any local predictor. It only requires the computation of scalar weights, the computational burden can be reduced comparing with one weighted by matrices. An example of double-channel signal system with three sensors shows the effectiveness.

The unified multisensor optimal information fusion criterion weighted by matrices is rederived in the linear minimum variance sense, where the assumption of normal distribution is avoided. Based on this fusion criterion, the optimal information fusion input white noise deconvolution estimators are presented for discrete time-varying linear stochastic control system with multiple sensors and correlated noises, which can be applied to seismic data processing in oil exploration. A three-layer fusion structure with fault tolerant property and reliability is given. The first fusion layer and the second fusion layer both have netted parallel structures to determine the first-step prediction error cross-covariance for the state and the estimation error cross-covariance for the input white noise between any two sensors at each time step, respectively. The third fusion layer is the fusion center to determine the optimal matrix weights and obtain the optimal fusion input white noise estimators. The simulation results for Bernoulli-Gaussian input white noise deconvolution estimators show the effectiveness.