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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.

Multiple-Step Randomly Delayed Adaptive Robust Filter With Application to INS/VNS Integrated Navigation on Asteroid Missions