Robust Weighted Measurement Fusion Kalman Predictor with Uncertain Parameters and Noise Variances

For the multisensor time-invariant system with uncertainties of both the noise variances and parameters, by introducing a fictitious white noise to compensate the uncertain parameters, the uncertain system can be converted into the conservative system with known parameters and uncertain noise variances. Using the minimax robust estimation principle, and the Lyapunov equation approach, a robust weighted measurement fusion Kalman predictor is presented based on the worst-case conservative system with the conservative upper bounds of noise variances. A Monte-Carlo simulation example shows its effectiveness.

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The Design of a Robust Weighted Measurement Fusion Steady-State Kalman Filter

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.701-702.624 ◽

2014 ◽

Vol 701-702 ◽

pp. 624-629

Author(s):

Wen Qiang Liu ◽

Xue Mei Wang ◽

Zi Li Deng

Keyword(s):

Kalman Filter ◽

Steady State ◽

Lyapunov Equation ◽

Model Parameters ◽

Invariant System ◽

Parameter Uncertainties ◽

Worst Case ◽

Uncertain Model ◽

Time Invariant ◽

Time Invariant System

For the linear discrete-time multisensor time-invariant system with uncertain model parameters and measurement noise variances, by introducing fictitious noise to compensate the parameter uncertainties, using the minimax robust estimation principle, based on the worst-case conservative multisensor system with conservative upper bounds of measurement and fictitious noises variances, a robust weighted measurement fusion steady-state Kalman filter is presented. By the Lyapunov equation approach, it is proved that when the region of the parameter uncertainties is sufficient small, the corresponding actual fused filtering error variances are guaranteed to have a less-conservative upper bound. Simulation results show the effectiveness and correctness of the proposed results.

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Covariance Intersection Fusion Robust Time-Varying Kalman Filter for Two-Sensor System with Uncertain Noise Variances

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.475-476.470 ◽

2013 ◽

Vol 475-476 ◽

pp. 470-475

Author(s):

Wen Juan Qi ◽

Peng Zhang ◽

Gui Huan Nie ◽

Zi Li Deng

Keyword(s):

Kalman Filter ◽

Kalman Filters ◽

Tracking System ◽

System Simulation ◽

Lyapunov Equation ◽

Conservative System ◽

Upper Bounds ◽

Time Varying ◽

Worst Case ◽

Covariance Intersection

This paper investigates the problem of designing covariance intersection fusion robust time-varying Kalman filter for two-sensor time-varying system with uncertain noise variances. Using the minimax robust estimation principle, the local and covariance intersection (CI) fusion robust time-varying Kalman filters are presented based on the worst-case conservative system with the conservative upper bounds of noise variances. Their robustness is proved based on the proposed Lyapunov equation, and the robust accuracy of time-varying CI fuser is higher than that of each local robust time-varying Kalman filter. A two-sensor tracking system simulation verifies the robustness and robust accuracy relations.

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Covariance Intersection Fusion Robust Steady-State Kalman Smoother for Multisensor System with Uncertain Noise Variances

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.475-476.476 ◽

2013 ◽

Vol 475-476 ◽

pp. 476-481

Author(s):

Wen Juan Qi ◽

Peng Zhang ◽

Zi Li Deng

Keyword(s):

Monte Carlo Simulation ◽

Steady State ◽

Tracking System ◽

Lyapunov Equation ◽

Conservative System ◽

Upper Bounds ◽

Worst Case ◽

Multisensor System ◽

Kalman Smoother ◽

Covariance Intersection

This paper deals with the problem of designing covariance intersection fusion robust steady-state Kalman smoother for multisensor system with uncertain noise variances. Using the minimax robust estimation principle, the local and covariance intersection (CI) fusion robust steady-state Kalman smoothers are presented based on the worst-case conservative system with the conservative upper bounds of noise variances. Their robustness is proved based on the proposed Lyapunov equation, and the robust accuracy of CI fuser is higher than that of each local robust Kalman smoother. A Monte-Carlo simulation of three sensors tracking system verifies their robustness and robust accuracy relations.

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Weighted Fusion Robust Steady-State Kalman Filters for Multisensor System with Uncertain Noise Variances

Journal of Applied Mathematics ◽

10.1155/2014/369252 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11 ◽

Cited By ~ 9

Author(s):

Wen-Juan Qi ◽

Peng Zhang ◽

Zi-Li Deng

Keyword(s):

Steady State ◽

Kalman Filters ◽

Robustness Analysis ◽

Optimal Estimation ◽

Lyapunov Equation ◽

Conservative System ◽

Minimum Variance ◽

Upper Bounds ◽

Worst Case ◽

Weighted Fusion

A direct approach of designing weighted fusion robust steady-state Kalman filters with uncertain noise variances is presented. Based on the steady-state Kalman filtering theory, using the minimax robust estimation principle and the unbiased linear minimum variance (ULMV) optimal estimation rule, the six robust weighted fusion steady-state Kalman filters are designed based on the worst-case conservative system with the conservative upper bounds of noise variances. The actual filtering error variances of each fuser are guaranteed to have a minimal upper bound for all admissible uncertainties of noise variances. A Lyapunov equation method for robustness analysis is proposed. Their robust accuracy relations are proved. A simulation example verifies their robustness and accuracy relations.

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