Multichannel Autoregressive Moving Average Signal Research Articles

Covariance Intersection Fusion Smoothers for Multichannel ARMA Signal with Colored Measurement Noises

For multichannel autoregressive moving average (ARMA) signal with colored measurement noises, based on classical Kalman filtering theory, a covariance intersection (CI) fusion smoother without cross-covariances is presented by the augmented state space model. It has the advantage that the computation of cross-covariances is avoid, so it can significantly reduce the computational burden, and it can solve the fusion problem for multi-sensor systems with unknown cross-covariances. Under the unbiased linear minimum variance (ULMV) criterion, three optimal weighted fusion smoothers with matrix weights, scalar weights and diagonal weights are also presented respectively. The accuracy comparison of the CI fuser with the other three weighted fusers is given. It is shown that its accuracy is higher than that of each local smoother, and is lower than or close to that of the optimal fuser weighted by matrices. So the presented fusion smoother is better in performance.

Multichannel ARMA signal covariance intersection fusion Wiener filter for the two-sensor system with time-delayed measurements

For the two-sensor, multi-channel autoregressive moving average (ARMA) signals with measurement delays, the system with measurement delays is converted into the system without measurement delays by the measurement transformation method. When the filtering error cross-covariances are known, by the Kalman filtering method, based on the white noise Wiener filters and measure- ment Wiener predictors, the optimal fusion Wiener signal filters weighted by matrices, diagonal matrices and scalars are presented. When the filtering error cross-covariances are unknown, by the covariance intersection (CI) fusion method, the CI fusion Wiener signal filter is presented. It is rigorously proven that the actual accuracy of the CI Wiener signal fuser is higher than that of each local Wiener signal filter, and is lower than that of the optimal Wiener signal fuser with the matrix weights. The geometric interpretation of the above accuracy relations are presented based on the covariance ellipses. A Monte-Carlo simulation example shows that the actual accuracy of the CI fuser is close to that of the fuser with the matrix weights, so that it has higher accuracy and good performance.

Information Fusion Kalman Predictor for Two-Sensor Multichannel ARMA Signal System with Time-Delayed Measurements

For the two-sensor multichannel autoregressive moving average (ARMA) signals with time-delayed measurements, an equivalent state space model with time-delayed measurements is obtained. Then a measurement transformation method is presented, which can transform this state space model with measurement delays into the state space model without measurement delays. Furthermore, based on the modern time series analysis method, local Kalman predictors are obtained. Then the covariance intersection (CI) fusion Kalman predictor is presented, which avoids computing the cross-covariance compared with the fused Kalman predictor weighted by matrices. It is proved that its accuracy is higher than each local predictor, and lower than that of the fused Kalman predictor weighted by matrices. The geometric interpretations of the local and fused predictors’ accuracy relation are given based on covariance ellipses. A Monte-Carlo simulation example shows that the CI Kalman fuser has higher accuracy and good performance.

Self-tuning distributed measurement fusion Kalman estimator for the multi-channel ARMA signal

For the multisensor multi-channel autoregressive moving average (ARMA) signal with white measurement noises and a common disturbance measurement white noise, when the model parameters and the noise variances are all unknown, a multi-stage information fusion identification method is presented, where the consistent fused estimates of the model parameters and noise variances are obtained by the multi-dimension recursive instrumental variable (RIV) algorithm, correlation method and Gevers–Wouters algorithm with a dead band. Substituting these estimates into the optimal distributed measurement fusion Kalman signal estimator, a self-tuning distributed measurement fusion Kalman signal estimator is presented. Its convergence is proved by the dynamic error system analysis (DESA) method, so that it has asymptotical global optimality. In order to reduce computational load, a fast recursive inversion algorithm for a high-dimension matrix is presented by the inversion formula of partitioned matrix. Especially, when the process and measurement noise variance matrices are all diagonal matrices, the inversion formula of a high-dimension matrix is presented, which extends the formula of the inverse of Pei–Radman matrix. Applying the proposed inversion algorithm, the computation of the fused measurement and fused noise variance is simplified and their computational burden is reduced. A simulation example shows effectiveness of the proposed method.

Information fusion Wiener filter for the multisensor multichannel ARMA signals with time-delayed measurements

For the multisensor multichannel autoregressive moving average (ARMA) signals with time-delayed measurements, a measurement transformation approach is presented, which transforms the equivalent state space model with measurement delays into the state space model without measurement delays, and then using the Kalman filtering method, under the linear minimum variance optimal weighted fusion rules, three distributed optimal fusion Wiener filters weighted by matrices, diagonal matrices and scalars are presented, respectively, which can handle the fused filtering, prediction and smoothing problems. They are locally optimal and globally suboptimal. The accuracy of the fuser is higher than that of each local signal estimator. In order to compute the optimal weights, the formulae of computing the cross-covariances among local signal estimation errors are given. A Monte Carlo simulation example for the three-sensor target tracking system with time-delayed measurements shows their effectiveness.

Optimal and self-tuning weighted measurement fusion Wiener filter for the multisensor multichannel ARMA signals

For the multisensor multichannel autoregressive moving average (ARMA) signals with white measurement noises, using the modern time series analysis method, based on the ARMA innovation models, white noise estimators, and measurement predictors, an optimal weighted measurement fusion Wiener filter is presented by the weighted least squares (WLS) method. It can handle the fused filtering, smoothing and prediction problems in a unified framework. When the noise variances and model parameters are unknown, based on the on-line identification of the local and fused ARMA innovation models, a self-tuning weighted measurement fusion Wiener filter is presented. By the dynamic error system analysis (DESA) method, it is rigorously proved that the self-tuning fuser converges to the optimal fuser in a realization, so that it has the asymptotic optimality. Compared with the globally optimal centralized fusion time-varying Kalman filter, the proposed optimal and self-tuning Wiener fusers have the asymptotic global optimality, whose accuracies are higher than these of the optimal and self-tuning distributed Wiener fusers and local Wiener filters, respectively. A simulation example shows their effectiveness.

OPTIMAL FUSION DISTRIBUTED FILTER FOR DISCRETE MULTICHANNEL ARMA SIGNALS

Based on the multi-sensor optimal information fusion criterion weighted by matrices in the linear minimum variance sense, an optimal information fusion distributed Kalman filter is given for discrete multi-channel ARMA (autoregressive moving average) signals with correlated noises. When all subsystems have the steady-state filters, a steady-state information fusion filter is also given. It has the reduced computation burden compared with the optimal fusion filter. The precision of the fusion filter is higher than that of any local filter, but is lower than that of the centralized filter. The filtering error cross-covariance matrix between any two subsystems is given for discrete multichannel ARMA signals. Applying it to a four-channel ARMA signal system with three sensors shows its effectiveness.

Optimal multi-sensor Kalman smoothing fusion for discrete multichannel ARMA signals

Based on the multi-sensor optimal information fusion criterion weighted by matrices in the linear minimum variance sense, using white noise estimators, an optimal fusion distributed Kalman smoother is given for discrete multi-channel ARMA (autoregressive moving average) signals. The smoothing error cross-covariance matrices between any two sensors are given for measurement noises. Furthermore, the fusion smoother gives higher precision than any local smoother does.

Optimal information fusion distributed smoother for discrete multichannel ARMA signals

Based on the multisensor optimal information fusion criterion weighted by matrices in the linear minimum variance sense, using estimators of white measurement noise, an optimal information fusion distributed Kalman smoother is given for discrete time multichannel autoregressive moving average (ARMA) signals with correlated noise. It has a three-layer fusion structure with a fault tolerant property. The first and the second fusion layers both have netted parallel structrues to determine cross-covariance matrices between any two faultless sensors. The third fusion layer is the fusion centre to determine the optimal weights and obtain the optimal fusion smoother. The fusion smoother has higher precision than that of any local smoother. Its effectiveness is shown by applying it to a double-channel signal system with three sensors.