Robust cubature Kalman filter based on variational Bayesian and transformed posterior sigma points error

Area of Science:

• State estimation and filtering theory
• Robust control systems
• Signal processing

Background:

• Traditional Kalman filters struggle with time-varying noise, impacting navigation system accuracy.
• Robust Cubature Kalman Filters (RCKF) offer improved stability but lack adaptivity to changing noise conditions.
• Variational Bayesian (VB) methods show promise for adaptive noise estimation.

Purpose of the Study:

• To develop an improved robust cubature Kalman filter (RCKF) with enhanced adaptivity to time-varying noise.
• To integrate Variational Bayesian (VB) methods for accurate estimation of time-varying measurement noise.
• To reduce uncertainties in sigma point generation and accelerate noise estimation convergence.

Main Methods:

• Development of a novel sigma-point update framework using transformed posterior sigma points error for uncertainty reduction.
• Application of Variational Bayesian (VB) techniques for iterative estimation of time-varying, state-dependent measurement noise.
• Validation through integrated navigation simulations comparing the proposed VB-RCKF against VB-CKF and RCKF.

Main Results:

• The proposed VB-RCKF effectively retains the robustness of RCKF while introducing adaptivity to time-varying noise.
• The novel framework reduces uncertainty in sigma point generation and accelerates VB-based noise estimation convergence.
• Numerical simulations demonstrate superior performance of VB-RCKF compared to VB-CKF and RCKF in integrated navigation.

Conclusions:

• The VB-RCKF offers a robust and adaptive solution for state estimation in systems with time-varying noise.
• The integration of transformed posterior sigma points error and VB significantly enhances filter performance.
• The proposed filter is highly effective for challenging applications like integrated navigation.