Design of Bayesian upper confidence bound modulation strategy with multi-scale Fibonacci extended Kalman filter

This paper proposes a novel approach to fuse the Extended Kalman Filter (EKF) with the Multiscale Fibonacci Filter (MSFibFilter) technique to develop an adaptive filter with adjustable gain characteristics, termed Fibonacci Adaptive Extended Kalman Filter (Fib-AEKF). The innovation of this work lies in enhancing the EKF’s applicability in dynamic environments characterized by high-frequency noise and multi-scale signal processing. By exploiting the multi-scale properties of the Fibonacci sequence to dynamically adjust filter weights, Fib-AEKF can be used to improve noise suppression and signal tracking capabilities. The proposed MSFibFilter uses normalized Fibonacci weights to perform weighted smoothing on the signal to effectively remove noise while retaining the basic signal characteristics. In this study, a Bayesian upper confidence bound modulation strategy is used to enhance the filter’s adaptability. These weights are dynamically adjusted based on the state predictions from the EKF, allowing the filter to adaptively respond to rapid signal changes. The design of the adaptive weights depends on the discrepancy between the predicted state and the actual input signal, enhancing the filter’s sensitivity and robustness to signal fluctuations. By modifying the exponential decay term of the weights, the Fib-AEKF significantly improves the tracking accuracy of nonlinear dynamic system states, especially facing substantial differences between predictions and measurements. Experimental results demonstrate that applying the Fib-AEKF to the processing of acceleration signals in inertial navigation systems leads to a significant improvement in positioning accuracy and stability. The Fib-AEKF outperforms both multi-layer adaptive EKF and single-layer EKF in terms of cumulative error reduction. Its superior performance in inertial navigation applications highlights its potential for practical implementation, offering a more viable and effective solution for real-world dynamic systems. This study provides a new method for handling noise and uncertainties in nonlinear systems, expanding the capabilities of traditional EKF approaches.