Stochastic stability of sigma-point Unscented Predictive Filter
Lu Cao1, Yu Tang2, Xiaoqian Chen2
1The State Key Laboratory of Astronautic Dynamics, China Xi׳an Satellite Control Center, Xi׳an 710043, China.
ISA Transactions
|March 7, 2015
Summary
The Unscented Predictive Filter (UPF) offers improved nonlinear estimation accuracy over conventional particle filters. This novel approach ensures bounded estimation errors and stable covariance for nonlinear systems under specific conditions.
Area of Science:
- Control Theory
- Nonlinear Estimation
- Stochastic Systems
Background:
- Conventional sigma-point filters are limited in their scope.
- Kalman filter applications in nonlinear estimation are well-established.
Purpose of the Study:
- To derive and present the Unscented Predictive Filter (UPF) for nonlinear estimation.
- To analyze the theoretical performance and stability of the UPF.
Main Methods:
- Derivation of the Unscented Predictive Filter (UPF) using unscented transformation.
- Algorithmic flow presentation for the UPF.
- Theoretical analysis of estimate accuracy, stochastic boundedness, and error behavior.
Main Results:
- The UPF demonstrates higher accuracy in estimating model and system errors compared to conventional Particle Filters (PF).
- Theoretical analysis confirms that estimation error remains bounded and covariance is stable under conditions of small initial errors and noise.
Conclusions:
- The Unscented Predictive Filter (UPF) provides a robust advancement in nonlinear estimation.
- The UPF's stability and accuracy are theoretically validated and demonstrated through simulations.
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