The brief proposes a radial basis function (RBF) neural network (NN)-enabled adaptive filter (AF) algorithm, which consists of two stages. The first stage is a data-driven (DD) preprocessing part, and the RBF NN is to fit the probability density function (pdf) of the noise. The second stage is a model-driven filtering part, the RBF NN works as the cost function of the adaptive filtering, and an adaptive gradient ascent algorithm is obtained by maximizing the RBF NN. Since the RBF NN can fit any pdf of the noise, the proposed algorithm can work well in Gaussian, sub-Gaussian or light-tailed (uniform), and super-Gaussian or heavy-tailed (multipeak, pulse, and skewness) noises. Theoretical analysis shows the mean-value stability and mean square performance. Simulations verify the effectiveness of the proposed algorithm.

The paper proposes a new Kalman filtering (KF) algorithm called VBI-MCKF that combines the variational Bayesian inference (VBI)-based KF algorithm and the maximum correntropy KF (MCKF) for visual tracking problem. The VBI-based KF algorithm works to estimate the unknown measurement noise covariance matrix (MNCM) and process noise covariance matrix (PNCM), and the MCKF works to deal with non-Gaussian process noise and measurement noise. In order to cater for the visual tracking target scenario, where the MNCM and PNCM are unknown and non-Gaussian, we modify the VBI-based KF algorithm to work for suddenly occurring outliers and modify the MCKF work for small bandwidth. Simulations show that the proposed VBI-MCKF algorithm performs well when both covariance matrices of Gaussian process noise and non-Gaussian measurement noise are unknown or inaccurate.

This study addresses target-to-ROV relative localization in an unmanned surface platform-assisted UAV–ROV search-and-recovery system. Because the submerged ROV is not assumed to be visible from the air, the UAV observes the floating target and a GNSS-equipped ROV-associated surface buoy in the same image. The buoy position and target-to-buoy image displacement are combined to construct a world-frame target-position measurement, whose covariance accounts for buoy GNSS uncertainty and correlated image-projection errors. An upward-looking ROV imaging sonar provides range–bearing measurements. A delay-aware extended Kalman filter fuses the asynchronous observations using sea-state- and confidence-dependent covariance adaptation and normalized-innovation gating. ROV acoustic/inertial navigation uncertainty is propagated into the sonar measurement covariance and the reported relative-state covariance, avoiding duplication of the same navigation error in the aerial channel. The method is evaluated using a JONSWAP-based temporal disturbance model, Monte Carlo simulations, and single-factor and joint sea-state–occlusion–delay sensitivity tests. Under the nominal sea-state-5 condition, the proposed method achieves a mean ROV-frame relative RMSE of 0.992 m, compared with 1.083 m for ROV-only localization and 1.054 m for fixed-covariance fusion, with no run exceeding the 5 m divergence threshold. The results demonstrate improved relative-localization robustness within the simulated environment.

Accurate localization of underwater targets in shallow water is challenging because nonlinear sonar geometry, range-amplified angular errors, uncertain measurement noise, and environmental constraints jointly degrade state estimation. This paper proposes a variational Bayesian constrained extended Kalman filter (VB-C-EKF) for active-sonar-based underwater target tracking. A weak-maneuver motion model and an active-sonar range–bearing–elevation–Doppler measurement model are adopted, while bathymetric depth, speed, and reachable-region constraints are incorporated through sequential local Mahalanobis projection with a conservatively regularized covariance correction. To address unknown and time-varying measurement noise, the measurement-noise covariance is recursively estimated using a variational Bayesian scheme with an inverse-Wishart prior and a forgetting mechanism. In Monte Carlo experiments, the proposed method achieved an overall three-dimensional position RMSE of 7.57 m with a 95% confidence-interval half-width of 0.25 m, while maintaining zero depth/speed violations. Its mean normalized innovation squared and normalized estimation error squared were 4.04 and 6.79, respectively, and its average runtime was 0.225 ms per update. These results show that jointly adapting measurement uncertainty and enforcing physical constraints improves accuracy, feasibility, and covariance consistency under the simulated shallow-water conditions.