Abstract
This paper develops a novel nonlinear adaptive robust filter called the multiple-step randomly delayed variational Bayesian adaptive high-degree cubature Huber-based filter (MRD-VBAHCHF) for a class of nonlinear stochastic systems whose measurements are randomly delayed by multiple sampling times and corrupted by contaminated Gaussian noise with unknown covariance. First, a system with randomly delayed measurement is modeled in terms of multiple Bernoulli random variables. Then, the multiple-step randomly delayed high-degree cubature Kalman filter (MRD-HCKF) is derived by employing the fifth-degree cubature rule to compute the mean and covariance of the nonlinear equations in the system model. Next, the MRD-HCKF is modified to the MRD-VBAHCHF by incorporating the variational Bayesian theory and Huber technique for estimating the measurement noise covariance online and suppressing the influence of non-Gaussian noise. Consequently, the proposed filter is not only adaptive to unknown measurement noise statistics but also robust to random measurement delays and non-Gaussian noise. Finally, the MRD-VBAHCHF is verified for use in inertial navigation system/visual navigation system (INS/VNS) integrated navigation on asteroid missions, and the results of Monte Carlo simulations demonstrate that the MRD-VBAHCHF outperforms the high-degree cubature Kalman filter (HCKF), the MRD-HCKF and the variational Bayesian adaptive high-degree cubature Huber-based filter (VBAHCHF), thus showing the superiority of the proposed filter.
Highlights
Asteroid exploration is significant for advancing our understanding of the Solar System and monitoring potential threats to the Earth
The results suggest that the MRD-variational Bayesian adaptive high-degree cubature Huber-based filter (VBAHCHF) exhibits better performance in estimating the unknown covariance Rsen than the VBAHCHF does because the proposed filter considers the random measurement delay, and this means that the MRD-VBAHCHF has better adaptivity than the VBAHCHF
The results show that the estimation errors of the VBAHCHF and MRD-VBAHCHF are smaller than those of the high-degree cubature Kalman filter (HCKF) and MRD-HCKF, respectively, demonstrating the robustness of the VBAHCHF and MRDVBAHCHF to contaminated Gaussian noise
Summary
In [23], the multiple-step randomly delayed cubature Kalman filter (MRD-CKF), which uses the residuals and channel statistics of the received measurements to calculate tuned weighting factors, was proposed to handle nonlinear systems in the presence of multiple-step randomly delayed measurements These studies ignored the presence of contaminated Gaussian measurement noise with unknown covariance, which may cause the filter accuracy to deteriorate. The main contribution of our paper is the proposal of a high-accuracy nonlinear filter with strong adaptivity and robustness; we consider multiple-step random delays in the received measurements and account for the non-Gaussianity and covariance uncertainty of the measurement noise.
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