Linear Discrete Time-invariant Stochastic Systems Research Articles

Covariance Intersection Fusion Kalman Estimator for Multi-Sensor System with Measurements Delays

To handle the state estimation fusion problem between local estimation errors for the system with unknown cross-covariances and to avoid a large computation complexity of cross-covariances, for a multi-sensor linear discrete time-invariant stochastic system with time-delayed measurements, by the measurement transformation method, an equivalent system without measurement delays is obtained, and then using the covariance intersection (CI) fusion method, the covariance intersection fusion steady-state Kalman estimator is presented. It is proved that its accuracy is higher than that of each local estimator, and is lower than that of optimal Kalman fuser weighted by matrices with known cross-covariances. A Monte-Carlo simulation example shows the above accuracy relations, hence it has good performances.

Covariance Intersection Kalman Fuser for Two-Sensor System with Time-Delayed Measurements

To handle the estimation fusion problem between local estimation errors for the system with unknown cross-covariances and to avoid a large computed burden and computational complexity of cross-covariances, for a two-sensor linear discrete time-invariant stochastic system with time-delayed measurements, by the measurement transformation method, an equivalent system without measurement delays is obtained and then using the Covariance Intersection (CI) fusion method, the covariance intersection steady-state Kalman fuser is presented. It is proved that its accuracy is higher than that of each local estimator and is lower than that of optimal Kalman fuser weighted by matrices with known cross-covariances. A Monte-Carlo simulation example shows the above accuracy relation and indicates that its actual accuracy is close to that of the Kalman fuser weighted by matrices, hence it has good performances.

Covariance Intersection Kalman Fuser for Two-sensor System with Time-delayed Measurements

For a two-sensor linear discrete time-invariant stochastic system with time-delayed measurements, by the measurement transformation method, an equivalent system without measurement delays is obtained and then using the Covariance Intersection (CI) fusion method, the covariance intersection steady-state Kalman fuser is presented. It can handle the estimation fusion problem between local estimation errors for the system with unknown cross-covariances and avoid a large computed burden and computational complexity of cross-covariances. It is proved that its accuracy is higher than that of each local estimator and is lower than that of optimal Kalman fuser weighted by matrices with known cross-covariances. A Monte-Carlo simulation example shows the above accuracy relation and indicates that its actual accuracy is close to that of the Kalman fuser weighted by matrices, hence it has good performances.

Self-tuning weighted measurement fusion white noise deconvolution estimator and its convergence analysis

White noise deconvolution or input white noise estimation has a wide range of applications including oil seismic exploration, communication, signal processing, and state estimation. For the multisensor linear discrete time-invariant stochastic systems with correlated measurement noises, and with unknown ARMA model parameters and noise statistics, the on-line AR model parameter estimator based on the Recursive Instrumental Variable (RIV) algorithm, the on-line MA model parameter estimator based on Gevers-Wouters algorithm and the on-line noise statistic estimator by using the correlation method are presented. Using the Kalman filtering method, a self-tuning weighted measurement fusion white noise deconvolution estimator is presented based on the self-tuning Riccati equation. It is proved that the self-tuning fusion white noise deconvolution estimator converges to the optimal fusion steady-state white noise deconvolution estimator in a realization by using the dynamic error system analysis (DESA) method, so that it has the asymptotic global optimality. The simulation example for a 3-sensor system with the Bernoulli-Gaussian input white noise shows its effectiveness.

Convergence of self-tuning Riccati equation with correlated noises

For the linear discrete time-invariant stochastic system with correlated noises, and with unknown model parameters and noise statistics, substituting the online consistent estimators of the model parameters and noise statistics into the optimal time-varying Riccati equation, a self-tuning Riccati equation is presented. By the dynamic variance error system analysis (DVESA) method, it is rigorously proved that the self-tuning Riccati equation converges to the optimal time-varying Riccati equation. Based on this, by the dynamic error system analysis (DESA) method, it is proved that the corresponding self-tuning Kalman filter converges to the optimal time-varying Kalman filter in a realization, so that it has asymptotic optimality. As an application to adaptive signal processing, a self-tuning Kalman signal filter with the self-tuning Riccati equation is presented. A simulation example shows the effectiveness.

Optimal and self‐tuning weighted measurement fusion Kalman filters and their asymptotic global optimality

AbstractFor 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.

Self-tuning measurement fusion white noise deconvolution estimator with correlated noises

For the multisensor linear discrete time-invariant stochastic systems with correlated noises and unknown noise statistics, an on-line noise statistics estimator is presented by using the correlation method. Substituting it into the steady-state Riccati equation, the self-tuning Riccati equation is obtained. Using the Kalman filtering method, based on the self-tuning Riccati equation, a self-tuning weighted measurement fusion white noise deconvolution estimator is presented. By the dynamic error system analysis (DESA) method, it is proved that the self-tuning fusion white noise deconvolution estimator converges to the optimal fusion steady-state white noise deconvolution estimator in a realization, so that it has the asymptotic global optimality. A simulation example for Bernoulli-Gaussian input white noise shows its effectiveness.

Self-tuning weighted measurement fusion white noise deconvolution estimator

For the multi-sensor linear discrete time-invariant stochastic systems with correlated measurement noises and unknown noise statistics, an on-line noise statistics estimator is obtained using the correlation method. Substituting it into the optimal weighted fusion steady-state white noise deconvolution estimator based on the Kalman filtering, a self-tuning weighted measurement fusion white noise deconvolution estimator is presented. By the Dynamic Error System Analysis (DESA) method, it proved that the self-tuning fusion white noise deconvolution estimator converges to the steady-state optimal fusion white noise deconvolution estimator in a realization. Therefore, it has the asymptotically global optimality. A simulation example for the tracking system with 3 sensors and the Bernoulli-Gaussian input white noise shows its effectiveness.

Convergence analysis of self-tuning Riccati equation for systems with correlation noises

For linear discrete time-invariant stochastic system with correlated noises, and with unknown state transition matrix and unknown noise statistics, substituting the online consistent estimators of the state transition matrix and noise statistics into steady-state optimal Riccati equation, a new self-tuning Riccati equation is presented. A dynamic variance error system analysis (DVESA) method is presented, which transforms the convergence problem of self-tuning Riccati equation into the stability problem of a time-varying Lyapunov equation. Two decision criterions of the stability for the Lyapunov equation are presented. Using the DVESA method and Kalman filtering stability theory, it proves that with probability 1, the solution of self-tuning Riccati equation converges to the solution of the steady-state optimal Riccati equation or time-varying optimal Riccati equation. The proposed method can be applied to design a new selftuning information fusion Kalman filter and will provide the theoretical basis for solving the convergence problem of self-tuning filters. A numerical simulation example shows the effectiveness of the proposed method.