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

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.

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

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.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
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.

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

2014 ◽  
Vol 701-702 ◽  
pp. 538-543
Author(s):  
Chuan Shan Yang ◽  
Xue Mei Wang ◽  
Wen Juan Qi ◽  
Zi Li Deng
Keyword(s):  
Uncertain System ◽  
Lyapunov Equation ◽  
Conservative System ◽  
Upper Bounds ◽  
Uncertain Parameters ◽  
Invariant System ◽  
Worst Case ◽  
Kalman Predictor ◽  
Time Invariant ◽  
Time Invariant System

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.

Robust integrated covariance intersection fusion Kalman estimators for networked mixed uncertain time-varying systems

2020 ◽  
Author(s):  
Yuan Gao ◽  
Zili Deng
Keyword(s):  
Kalman Filtering ◽  
Estimation Error ◽  
Original System ◽  
Lyapunov Equation ◽  
Upper Bounds ◽  
Time Varying ◽  
Worst Case ◽  
Covariance Intersection ◽  
Integrated Covariance ◽  
White Noises

Abstract For the multisensor time-varying networked mixed uncertain systems with random one-step sensor delays and uncertain-variance multiplicative and linearly dependent additive white noises, a new augmented state method with fictitious noises is presented, by which the original system is transformed into a standard system without delays and with uncertain-variance fictitious white noises. According to the minimax robust estimation principle and the Kalman filtering theory, based on the worst-case system with the conservative upper bounds of uncertain noise variances, the local and integrated covariance intersection (ICI) fused robust time-varying Kalman estimators (filter, predictor and smoother) are presented respectively in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Their robustness is proved by the extended Lyapunov equation method, and their accuracy relations are compared based on the traces of the variance matrices and the covariance ellipsoids, respectively. Specially, a universal ICI fusion robust Kalman filtering method of integrating the local robust estimators and their conservative cross-covariances is presented. It overcomes the drawbacks of the original covariance intersection (CI) fusion method and improves robust accuracy of the original CI fuser. A simulation example applied to two-mass spring system shows the effectiveness of the proposed methods and results.

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

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.

Multi-Channel ARMA Signal Covariance Intersection Fusion Kalman Smoother

2013 ◽  
Vol 655-657 ◽  
pp. 701-704
Author(s):  
Peng Zhang
Keyword(s):  
Steady State ◽  
Kalman Filtering ◽  
Geometric Interpretation ◽  
Fusion Method ◽  
Filtering Method ◽  
Kalman Smoother ◽  
Cross Covariance ◽  
Covariance Intersection ◽  
Optimal Signal

For the multi-channel ARMA signal with two sensors, by the classical Kalman filtering method and the covariance intersection (CI) fusion method, a covariance intersection fusion steady-state Kalman signal smoother is presented, which is independent of the unknown cross-covariance. It is proved that its accuracy is higher than that of each local Kalman signal smoother, and is lower than that of the optimal signal fuser weighted by matrices. The geometric interpretation of the above accuracy relations are presented based on the covariance ellipses. A simulation example result shows its effectiveness and correctness.

scholarly journals Interregional Transfers for Pandemic Surges

2020 ◽  
Author(s):  
Kenneth A Michelson ◽  
Chris A Rees ◽  
Jayshree Sarathy ◽  
Paige VonAchen ◽  
Michael Wornow ◽  
...  
Keyword(s):  
The United States ◽  
Upper Bounds ◽  
Hospital Inpatient ◽  
Worst Case ◽  
Icu Patients ◽  
Interregional Transfers ◽  
Number Of Patients ◽  
Bed Capacity ◽  
Model Scenarios ◽  
Do So

Abstract Background Hospital inpatient and intensive care unit (ICU) bed shortfalls may arise due to regional surges in volume. We sought to determine how interregional transfers could alleviate bed shortfalls during a pandemic. Methods We used estimates of past and projected inpatient and ICU cases of coronavirus disease 2019 (COVID-19) from 4 February 2020 to 1 October 2020. For regions with bed shortfalls (where the number of patients exceeded bed capacity), transfers to the nearest region with unused beds were simulated using an algorithm that minimized total interregional transfer distances across the United States. Model scenarios used a range of predicted COVID-19 volumes (lower, mean, and upper bounds) and non–COVID-19 volumes (20%, 50%, or 80% of baseline hospital volumes). Scenarios were created for each day of data, and worst-case scenarios were created treating all regions’ peak volumes as simultaneous. Mean per-patient transfer distances were calculated by scenario. Results For the worst-case scenarios, national bed shortfalls ranged from 669 to 58 562 inpatient beds and 3208 to 31 190 ICU beds, depending on model volume parameters. Mean transfer distances to alleviate daily bed shortfalls ranged from 23 to 352 miles for inpatient and 28 to 423 miles for ICU patients, depending on volume. Under all worst-case scenarios except the highest-volume ICU scenario, interregional transfers could fully resolve bed shortfalls. To do so, mean transfer distances would be 24 to 405 miles for inpatients and 73 to 476 miles for ICU patients. Conclusions Interregional transfers could mitigate regional bed shortfalls during pandemic hospital surges.

Dynamic Absorption by Passive and Active Control1

2000 ◽  
Vol 122 (4) ◽  
pp. 429-433 ◽  
Author(s):  
Kumar Vikram Singh ◽  
Yitshak M. Ram
Keyword(s):  
Steady State ◽  
Active Control ◽  
Conservative System ◽  
Degree Of Freedom ◽  
Loss Of Stability ◽  
Steady State Motion ◽  
Damped System ◽  
Single Sensor ◽  
Dynamic Absorber

The motion of a particular degree-of-freedom in a harmonically excited conservative system can be vanished by attaching an appropriate dynamic absorber to it. It is shown here that under certain conditions, which are characterized in the paper, the steady state motion of a damped system may be completely absorbed, without loss of stability, by active control implementing a single sensor and an actuator. The results are established theoretically and they are demonstrated by means of analytical examples. [S0739-3717(00)02104-8]

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