Reduced dimension weighted measurement fusion Kalman filtering algorithm

For the multisensor linear discrete time-invariant systems with correlated measurement noises and with different measurement matrices, based on weighted least squares (WLS) method, applying orthogonal transformation, two weighted measurement fusion Kalman filtering algorithms are presented. Using information filter, it is proved that they are functionally equivalent to the centralized fusion Kalman filtering algorithm, i.e. the corresponding two weighted measurement fusion Kalman filtering algorithms are numerically identical to the centralized fusion Kalman filtering algorithm, so that they have global optimality. Compared with the centralized Kalman filtering algorithm, they can significantly reduce the computational load. A numerical simulation example in the tracking systems verifies their functional equivalence and gives the comparison of their operation counts.

For the multisensor systems with correlated noises and identical measurement matrices, based on linear unbiased minimum variance (LUMV) criterion, a weighted measurement fusion (WMF) Kalman filter is presented, where the optimal weights is given by the Lagrange multiplier method. By using the information filter, it is proved that it is functionally equivalent to the centralized fusion Kalman filter, i.e. it is numerically identical to the centralized fusion Kalman filter, so that they have the global optimality. In order to reduce the computational burden, another simple algorithm for computing the optimal weights is also derived, and comparison of computational counts of two algorithms for computing optimal weights is given. A numerical simulation example verifies their functional equivalence. The proposed results can be applied to solve the information fusion filtering problem for the autoregressive moving average (ARMA) signals.

For the multisensor system with different measurement matrices, correlated measurement noises and unknown noise variances, by correlated method, the online identifiers of the noise variances are obtained. Based on ARMA innovation model, a self-tuning weighted measurement fusion Kalman filter is presented, which avoids Lyapunov and Riccati equations, reduces the computational burden and is suitable for real time application. By dynamic error system analysis (DESA) method, it is rigorously proved that the proposed self-tuning fused Kalman filter converges to the corresponding optimal fused Kalman filter with probability one or in a realization, i.e. it has asymptotical global optimality. A simulation example for a target tracking systems with 3 sensors shows its effectiveness.

For the multisensor systems with unknown noise variances, using correlation method and least squares fusion criterion, information fusion noise variance estimators are presented by the average of local noise variance estimators, which have the consistence. Substituting the fused noise variance online estimators into the optimal Riccati equation and the optimal weighted measurement fusion Kalman filter, a self-tuning Riccati equation and a new self-tuning weighted measurement fusion Kalman filter are presented. In order to prove the convergence of the self-tuning Riccati equation, a dynamic variance error system analysis (DVSEA)method is presented, which converts the convergence problem to the stability problem of a time-varying Lyapunov equation. A stability decision criterion is presented for the Lyapunov equation. By the dynamic error system analysis (DESA) method and DVSEA method, it proves that the self-tuning weighted measurement fusion Kalman filter converges to the globally optimal weighted measurement fusion Kalman filter in a realization, so that it has asymptotic global optimality. A simulation example for target tracking system with 3-sensor shows its effectiveness.

Self-tuning weighted measurement fusion Kalman filtering algorithm

For the multisensor systems with companion form and unknown model parameters and noise variances, using recursive instrumental variable(RIV) algorithm, the local and fused model parameter estimators are obtained. Based on the fused model parameter estimators, the information fusion noise variance estimators are presented by using correlation method. They have strong consistence. Further, a self-tuning weighted measurement fusion Kalman filter based on a self-tuning Riccati equation is presented. By the dynamic error system analysis (DESA) method, it is rigorously proved that the self-tuning weighted measurement fusion Kalman filter converges to the optimal weighted measurement fusion Kalman filter in a realization, so that it has asymptotic global optimality. A simulation example applied to signal processing shows its effectiveness.

In this paper, a constrained weighted least squares (CWLS) problem with two quadratic constraints for hybrid AOA, TDOA, and RSS localization is formulated. The Lagrange multiplier method cannot be efficiently used in this situation, so we provide four methods to solve the CWLS problem: 1) weighted least squares (WLS); 2) iterative constrained weighted least squares (ICWLS); 3) Lagrange multiplier method combined with Newton’s method (LMM+NM); 4) semidefinite programming (SDP). Furthermore, in order to obtain a good balance between accuracy and computational burden, we develop a fixed point iteration (FPI)-based algorithm that is derived from an approximate maximum likelihood estimator (MLE). Simulation results show that the accuracy of the proposed FPI method is better than the other four methods; besides, its computational burden is one in ten of the SDP algorithm.

In allusion to the defect that conventional weight least squares (WLS), when applied to the power system state estimation, generally takes the same weight. It causes large state estimation error. A state estimation method combining optimal weight setting with weighted least squares is proposed. On the basis of weighted least squares state estimation models, through the theoretical analysis of different kinds of voltage measurements, power injection measurements and power flow measurements data, which impact differently on the results, different weights are set corresponding to their measurement sensitivity in order to reduce the estimation errors. Finally, the algorithm is tested on IEEE14 bus system by MATLAB. Compared with the traditional weighted least squares, this method is similar with regard to iteration time. However, the voltage and phase angle state estimation accuracy can be improved by about 0.16 and 4.66 percentage points. Therefore, the algorithm has certain advantages and application value.

In order to handle the fusion estimation problem for the multi-sensor systems with multiple time delayed measurements, a steady-state suboptimal Kalman filter is derived, and then a sequential covariance intersection (SCI) fusion Kalman filtering algorithm is presented, which can avoid large computational burden and handle the fusion problem for the systems with unknown cross-covariances. The simulation example shows the effectiveness, consistency and the geometric interpretation of the accuracy relation. The accuracy of the presented SCI fusion Kalman filter is higher than each of local estimators and is close to that of the Kalman fuser weighted by matrices, so it has good performance.

Multi-sensor information fusion white noise filter weighted by scalars based on Kalman predictor

Under certain environmental conditions, the unknown system errors often occur and yield to larger filtering errors when the unverified or uncalibrated measurement equation is used. Incremental equation can be introduced, which will effectively solve the problem of state estimation for the systems under poor observation condition. For the linear discrete descriptor systems under poor observation condition, a descriptor incremental Kalman estimation algorithm is firstly presented under the canonical form. It solves the state estimation problem for the descriptor systems with unknown measurement errors, which doesn't meet the requirements of classical Kalman filter. Furthermore, an optimal weighted fusion descriptor incremental Kalman estimator is given based on the linear minimum variance optimal fusion criterion. Compared with the existing augmented dimension-enlarged processing methods, the proposed algorithms are simple in form and small in computational burden so as to be easily applied in engineering practice. A simulation example shows its effectiveness and feasibility.

For the multisensor system with identical measurement matrix and correlated measurement noises, by correlated method, the online estimators of the noise statistics are obtained. Based on modern time series analysis method, a self-tuning weighted measurement fusion Wiener filter is presented, which avoids Lyapunov and Riccati equations, reduces the computational burden and is suitable for real time application. By dynamic error system analysis (DESA) method, it is rigorously proved that the proposed self-tuning Wiener filter converges to the optimal Wiener filter in a realization or with probability one, i.e. it has asymptotical global optimality. A simulation example for a target tracking systems with 3 sensors shows its effectiveness.

For the multisensor linear discrete time‐invariant stochastic systems with unknown noise variances, using the correlation method, the information fusion noise variance estimators with consistency are given by taking the average of the local noise variance estimators. Substituting them into two optimal weighted measurement fusion steady‐state Kalman filters, two new self‐tuning weighted measurement fusion Kalman filters with a self‐tuning Riccati equation are presented. By the dynamic variance error system analysis (DVESA) method, it is rigorously proved that the self‐tuning Riccati equation converges to the steady‐state optimal Riccati equation. Further, by the dynamic error system analysis (DESA) method, it is proved that the steady‐state optimal and self‐tuning Kalman fusers converge to the global optimal centralized Kalman fuser, so that they have the asymptotic global optimality. Compared with the centralized Kalman fuser, they can significantly reduce the computational burden. A simulation example for the target tracking systems shows their effectiveness. Copyright © 2010 John Wiley & Sons, Ltd.

New approach to information fusion steady-state Kalman filtering

For multi-sensor system with colored measurement noises, using the observation transformation, the system can be converted into an equivalent system with correlated measurement noises. Based on this method, using the classical Kalman filtering, this paper proposed a covariance intersection (CI) fusion Kalman estimator, which can handle the fused filtering, prediction and smoothing problems. The advantage of the proposed method is that it can avoid the computation of the cross co-variances among the local filtering errors and can reduce the computational burden significantly, as well as the CI fusion algorithm can be used in the uncertain system with unknown cross covariances. Based on classical Kalman filtering theory, the centralized fusion and three weighted fusion (weighted by matrices, scalars and diagonal) estimators are also presented respectively. Their accuracy comparisons are given. The geometric interpretations based on covariance ellipses are also given. A Monte-Carlo simulation example shows that the accuracy relations.