Set-Membership Based Hybrid Kalman Filter for Nonlinear State Estimation under Systematic Uncertainty
Yan Zhao1, Jing Zhang2, Gaoge Hu3
1Air and Missile Defense College, Air Force Engineering University, Xi'an 710051, China.
Sensors (Basel, Switzerland)
|January 26, 2020
Summary
A new set-membership based hybrid Kalman filter (SM-HKF) improves nonlinear state estimation by addressing both stochastic and unknown but bounded (UBB) errors. This advanced method outperforms the extended Kalman filter (EKF) in handling complex uncertainties.
Area of Science:
- Control Systems Engineering
- Signal Processing
- Estimation Theory
Background:
- Nonlinear state estimation is crucial in many dynamic systems.
- Traditional methods like the Extended Kalman Filter (EKF) struggle with systematic uncertainties.
- Stochastic and Unknown But Bounded (UBB) errors present significant challenges.
Purpose of the Study:
- To introduce a novel Set-Membership based Hybrid Kalman Filter (SM-HKF).
- To enhance nonlinear state estimation accuracy under combined stochastic and UBB errors.
- To overcome limitations of existing Kalman filtering techniques.
Main Methods:
- Linearization of nonlinear system models using Taylor series expansion.
- Introduction of a combined UBB error term via Minkowski sum.
- Derivation of an optimal Kalman gain minimizing mean squared error.
Main Results:
- The SM-HKF effectively integrates stochastic, UBB, and linearization errors.
- Simulations demonstrate the SM-HKF's superior performance compared to EKF.
- The proposed filter shows enhanced accuracy in nonlinear state estimation.
Conclusions:
- The SM-HKF provides a robust solution for state estimation with combined uncertainties.
- This method offers a significant improvement over the EKF for complex dynamic systems.
- SM-HKF is effective for nonlinear systems with systematic UBB and stochastic errors.
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