Linear Minimum Variance Sense Research Articles

Distributed Optimal Linear Fusion Predictors and Filters for Systems With Random Parameter Matrices and Correlated Noises

A Kalman-like recursive distributed optimal linear fusion predictor (RDOLFP) without feedback in the linear unbiased minimum variance sense is presented for multi-sensor discrete-time linear stochastic systems with random parameter matrices and correlated noises. Local predictions from sensors are sent to a fusion center to fuse with a prior fusion predictor. The proposed RDOLFP without feedback achieves better accuracy than distributed fusion predictors described in the literature that only weight fusion of local predictors, but worse accuracy than a centralized fusion predictor. A RDOLFP with feedback that has the same estimation accuracy as a centralized fusion predictor is also presented. Its optimality is strictly proven. The stability and steady-state properties of the proposed fusion predictors are analyzed. Distributed optimal linear fusion filters with and without feedback, based on the proposed RDOLFPs, are also presented. Two examples demonstrate the effectiveness of the proposed algorithms.

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

This paper studies the problem of fusion identification and estimation for multisensor multichannel autoregressive (AR) signals with unknown missing measurement rates, model parameters (MPs), sensor biases and measurement noise variances. Optimal local filters, cross-covariance matrices (CCMs), and a distributed fusion filter for AR signal are presented when the system model is accurately known, respectively. A self-tuning (ST) fusion filter is presented when MPs of AR signal, sensor biases, missing measurement rates and measurement noise variances in the system model are unknown. First, MPs of AR signal and sensor biases are identified by using a multi-dimensional recursive extended least squares (MRELS) algorithm. Further, distributed fusion estimates of MPs of AR signal are obtained by using a matrix-weighted optimal fusion estimation algorithm in the sense of linear unbiased minimum variance (LUMV). Then, receiving measurement rates and measurement noise variances are identified by correlation functions. Finally, substituting the identified parameters into the proposed optimal filtering algorithms, a matrix-weighted self-tuning (ST) fusion filtering algorithm is obtained. An example verifies the effectiveness of algorithms.

Distributed fusion cubature Kalman filters for nonlinear systems

SummaryThis paper is concerned with the distributed fusion estimation problem for multisensor nonlinear systems. Based on the Kalman filtering framework and the spherical cubature rule, a general method for calculating the cross‐covariance matrices between any two local estimators is presented for multisensor nonlinear systems. In the linear unbiased minimum variance sense, based on the cross‐covariance matrices, a distributed fusion cubature Kalman filter weighted by matrices (MW‐CKF) is presented. The proposed MW‐CKF has better accuracy and robustness. An example verifies the effectiveness of the proposed algorithms.

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

This paper is concerned with globally optimal sequential and distributed fusion estimation algorithms in the linear minimum variance (LMV) sense for multi-sensor systems with cross-correlated noises, where the measurement noises from different sensors are cross-correlated with each other at the same time step and correlated with the system noise at the previous time step. First, a globally optimal sequential fusion filter is proposed by considering the estimators for measurement noises. The equivalence on estimation accuracy of the proposed sequential fusion filter and centralized fusion filter is proven. It has reduced computational cost since it avoids the measurement augmentation. Then, a distributed fusion filter is also proposed by considering the prior fusion estimator and feedback from the fusion center. Under the condition that local gain matrices are full column rank, the proposed distributed fusion filter has the same estimation accuracy as the centralized fusion filter, that is, it also has global optimality. Their equivalence on estimation accuracy is proven. Stability and steady-state properties of the proposed algorithms are analyzed. A sufficient condition for the existence of steady-state filters is given. Finally, simulation results for a target tracking system show the effectiveness of the proposed algorithms.

Distributed Kalman filtering for time-varying discrete sequential systems

Discrete sequential system (DSS) consisting of different dynamical subsystems is a sequentially-connected dynamical system, and has found applications in many fields such as automation processes and series systems. However, few results are focused on the state estimation of DSSs. In this paper, the distributed Kalman filtering problem is studied for time-varying DSSs with Gaussian white noises. A locally optimal distributed estimator is designed in the linear minimum variance sense, and a stability condition is derived such that the mean square error of the distributed estimator is bounded. An illustrative example is given to demonstrate the effectiveness of the proposed methods.

Self-tuning asynchronous filter for linear Gaussian system and applications

In this paper, optimal filtering problem for a class of linear Gaussian systems is studied. The system states are updated at a fast uniform sampling rate and the measurements are sampled at a slow uniform sampling rate. The updating rate of system states is several times the sampling rate of measurements and the multiple is constant. To solve the problem, we will propose a self-tuning asynchronous filter whose contributions are twofold. First, the optimal filter at the sampling times when the measurements are available is derived in the linear minimum variance sense. Furthermore, considering the variation of noise statistics, a regulator is introduced to adjust the filtering coefficients adaptively. The case studies of wheeled robot navigation system and air quality evaluation system will show the effectiveness and practicability in engineering.

Optimal Sequential Fusion Estimation With Stochastic Parameter Perturbations, Fading Measurements, and Correlated Noises

This paper focuses on the linear optimal recursive sequential fusion filter design for multisensor systems subject to stochastic parameter perturbations, fading measurements, and correlated noises. The stochastic parameter perturbations existing in the state model are described by white multiplicative noises. The fading measurement phenomena for different sensors are described by independent random variables with known statistical properties. Moreover, the measurement noises of different sensors are correlated with each other and also correlated with the system noise at the same time step. First, a model equivalent to the original system is established by transferring the multiplicative noises into the additive noises. Then, based on the equivalent model and an innovation analysis method, a sequential fusion filter in the linear minimum variance sense is proposed to solve the linear optimal state estimation problem in real time according to the arriving order of measurements from different sensors. Finally, the equivalence on estimation accuracy of the proposed sequential fusion filter and the centralized fusion filter is strictly proven, which shows the optimality of the proposed sequential fusion algorithm. Moreover, the proposed sequential fusion filter has a reduced computational burden. Compared with the distributed matrix-weighted fusion filter, the computation of cross-covariance matrices is avoided and the estimation accuracy is improved. Finally, a simulation example verifies the effectiveness of the proposed sequential fusion filtering algorithm.

Distributed Fusion Estimator for Multisensor Multirate Systems With Correlated Noises

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.

Distributed fusion filter for multi-sensor systems with finite-step correlated noises

This paper addresses the distributed fusion filtering problem for multi-sensor systems with finite-step correlated noises. The process noise and observation noises of different sensors are finite-step auto- and cross-correlated, respectively. Based on the optimal local filtering algorithms that we presented before, the filtering error cross-covariance matrices between any two local filters are derived based on an innovation analysis approach. A distributed fusion filter is put forward by using matrix-weighted fusion estimation algorithm in the linear unbiased minimum variance sense. Finally, the proposed algorithms are extended to systems with random parameter matrices. Two simulation examples are given to show the effectiveness of the proposed algorithms.

Distributed Asynchronous Fusion Estimator for Stochastic Uncertain Systems With Multiple Sensors of Different Fading Measurement Rates

This paper is concerned with the distributed fusion estimation problem for time-varying stochastic uncertain systems with multiple asynchronous sampling sensors of different fading measurement rates. Stochastic uncertainties of multiplicative noises exist in the state and measurement equations. The phenomena of fading measurements of different sensors are depicted by a group of stochastic variables with known statistics. Different sensors have different sampling rates. Sampling period of each sensor is uniform and an integer multiple of the state update period. By transforming the multiplicative noises into the additive noises, local estimators (LEs) and estimation error cross-covariance matrices between any two LEs are derived at the state update points. A real-time distributed fusion estimator (DFE) is obtained by using the matrix-weighted fusion estimation algorithm in the linear unbiased minimum variance sense. The asymptotic stability and steady-state property are analyzed. A new conception of $\boldsymbol{{period}}$ steady state is presented and the $\boldsymbol{{period}}$ steady-state properties of the LEs, cross-covariance matrices, and DFE are proven. Though DFE has lower accuracy than the centralized fusion estimator, it has better robustness and flexibility since it has a parallel structure. To avoid the calculation of cross-covariance matrices, a sequential covariance intersection fusion estimator is given by using two-sensor covariance intersection fusion algorithm. It has lower accuracy but smaller computational cost than DFE, and better accuracy than LEs. Two examples are given to show the effectiveness of the proposed algorithms.

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

This paper proposes a new packet dropout compensation framework for networked multi-sensor systems. It is more general, which includes the existing popular mechanisms such as the zero-input and hold-input mechanisms as the special cases. Based on the proposed compensation framework, the centralized fusion linear optimal full-order prior filters with compensators of different weighting factors are presented. However, it is well known that centralized fusion prior filters (CFPFs) have poor reliability. To improve the reliability, the distributed fusion prior filters (DFPFs) are also given based on the well-known matrix-weighted fusion estimation algorithm in the linear unbiased minimum variance (LUMV) sense. Moreover, the stability and steady-state property of the proposed CFPFs and DFPFs are analyzed. A numerical example is used to make the performance comparisons of the proposed and the existing compensation mechanisms. The simulation results verify the effectiveness of the proposed compensation framework and the corresponding fusion filters.

Fusion estimation for multi-sensor networked systems with packet loss compensation

This paper is concerned with information fusion estimation problems for multi-sensor networked systems with random packet losses. Based on a recent developed compensation strategy of packet losses that the predictor of lost observation is used as the observation when a packet is lost, centralized fusion estimators (CFEs), including the filter, predictor and smoother, in the linear unbiased minimum variance (LUMV) sense are first designed by completing square method. Then, local optimal estimators are designed for each sensor subsystem. Estimation error cross-covariance matrices between any two local estimators are derived. Based on local estimators and cross-covariance matrices, distributed fusion estimators (DFEs) are presented by using the matrix-weighted fusion estimation algorithm in the LUMV sense. Compared with the existing results with zero-input and hold-input compensations, the proposed algorithms with prediction compensations can obviously improve the estimation accuracy. Two simulation examples show their effectiveness.

Self-Tuning Distributed Fusion Filter for Multi-Sensor Systems Subject to Unknown Model Parameters and Missing Measurement Rates

A self-tuning fusion estimation problem is addressed for multi-sensor (MS) linear discrete-time stochastic systems subject to unknown model parameters (UMPs) and missing measurement rates. The phenomena of missing measurements for different sensors are described by random variable sequences obeying Bernoulli distributions. The UMPs and missing measurement rates are identified online by the recursive extended least squares (RELS) algorithms and correlation functions, respectively. A distributed fusion identifier for UMPs is presented by using matrix-weighted fusion estimation (MWFE) algorithm in the linear unbiased minimum variance sense. Furthermore, the corresponding self-tuning state estimation algorithms are obtained by substituting the identified model parameters and missing measurement rates into the local optimal filters, cross-covariance matrices (CCMs), and distribution optimal fusion filter. Finally, the convergence of the presented algorithms is analyzed. A numerical example shows the effectiveness of the presented algorithms.

A Solution to Estimation Fusion for Multirate Measurements with Delays

This paper presents the distributed estimation fusion algorithms for a class of multirate multisensor systems with measurement delays. Different sensors uniformly sample measurements with different sampling rates and time delays. First, a new state-space model at the measurement sampling points is constructed and the original time delayed system is transformed to a delay-free one with correlated noises in limited time intervals to obtain the real-time estimation. Based on the new state-space model, the optimal local filter at the measurement sampling points is obtained for each single-sensor subsystem, and then the local estimator at the state update points is derived by using the predictor based on the filter at the measurement sampling points. Then, the estimation error cross-covariance matrices between any two local estimators are derived. Finally, the real-time distributed fusion estimator at the state update points is obtained based on the optimal fusion criterion weighed by matrices in the linear unbiased minimum variance sense. Besides, to avoid the correlation between system and measurement noises in the developed state-space model, a simple alternative but nonreal-time estimation fusion algorithm is also presented by employing dummy measurements. A numerical example is given to illustrate the effectiveness of the proposed algorithms.

Secure Fusion Estimation for Bandwidth Constrained Cyber-Physical Systems Under Replay Attacks

State estimation plays an essential role in the monitoring and supervision of cyber-physical systems (CPSs), and its importance has made the security and estimation performance a major concern. In this case, multisensor information fusion estimation (MIFE) provides an attractive alternative to study secure estimation problems because MIFE can potentially improve estimation accuracy and enhance reliability and robustness against attacks. From the perspective of the defender, the secure distributed Kalman fusion estimation problem is investigated in this paper for a class of CPSs under replay attacks, where each local estimate obtained by the sink node is transmitted to a remote fusion center through bandwidth constrained communication channels. A new mathematical model with compensation strategy is proposed to characterize the replay attacks and bandwidth constrains, and then a recursive distributed Kalman fusion estimator (DKFE) is designed in the linear minimum variance sense. According to different communication frameworks, two classes of data compression and compensation algorithms are developed such that the DKFEs can achieve the desired performance. Several attack-dependent and bandwidth-dependent conditions are derived such that the DKFEs are secure under replay attacks. An illustrative example is given to demonstrate the effectiveness of the proposed methods.

State estimators for systems with random parameter matrices, stochastic nonlinearities, fading measurements and correlated noises

Using the innovation analysis approach, the optimal linear state estimators, including the filter, predictor and smoother, in the linear minimum variance (LMV) sense are presented for a class of nonlinear discrete-time stochastic uncertain systems with fading measurements and correlated noises. Stochastic uncertainties of parameter matrices are depicted by correlated multiplicative noises. Stochastic nonlinearities are characterized by a known conditional mean and covariance. Different sensor channels have different fading measurement rates. The process and measurement noises are finite-step auto- and/or cross-correlated with each other. Two simulation examples verify the effectiveness of the proposed algorithms.

Optimal Linear Estimators for Systems With Finite-Step Correlated Noises and Packet Dropout Compensations

This paper is concerned with the optimal estimation problem for discrete-time stochastic systems with finite-step auto- and cross-correlated noises and multiple packet dropouts induced by the unreliable networks. When a packet transmitted from the sensor to the data processing center is lost, its predictor is used as the compensation. The optimal linear estimators including filter, predictor and smoother that depend on the packet arriving rate are proposed in the linear minimum variance sense via an innovative analysis approach. They are computed in terms of the solutions of some auto- and cross-covariance matrices. A tracking system example is given to demonstrate the effectiveness of the proposed algorithms.

Distributed fusion estimation for multi-sensor asynchronous sampling systems with correlated noises

ABSTRACTThis paper is concerned with the distributed fusion estimation problem for a class of multi-sensor asynchronous sampling systems with correlated noises. The state updates uniformly and the sensors sample randomly. Based on the measurement augmentation method, the asynchronous sampling system is transformed to the synchronous sampling one. Local filter is designed by using an innovation analysis approach. Then, the filtering error cross-covariance matrix between any two local filters is derived. Finally, the optimal distributed fusion filter is proposed by using matrix-weighted fusion algorithm in the linear minimum variance sense. Simulation results show the effectiveness of the proposed algorithms.

Distributed fusion estimator for multi‐sensor asynchronous sampling systems with missing measurements

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.

Distributed fusion filter for networked stochastic uncertain systems with transmission delays and packet dropouts

This paper is concerned with the distributed fusion filtering problem for networked stochastic uncertain systems with white multiplicative noises. The measured data of each sensor are transmitted to the local processor over different communication channels with different one-step delay and packet dropout rates. At each moment, the local processor may receive one or two data packets or nothing. Local filters at individual local processors are transmitted to the fusion center to produce a fusion filter. First, a new augmented model with a lower-dimension state vector is developed. Based on the new augmented model, the local optimal linear filter is designed in the linear minimum variance sense. Then, the cross-covariance matrices between any two local filtering errors are derived to compute the fusion weights. At last, the distributed fusion filter is obtained based on the well-known fusion algorithm weighted by matrices in the linear minimum variance sense. Moreover, the steady-state behavior of the proposed distributed fusion filter is analyzed.