Dynamic information such as the position and velocity of the target detected by marine radar is frequently susceptible to external measurement white noise generated by the oscillations of an unmanned surface vehicle (USV) and target. Although the Sage–Husa adaptive Kalman filter (SHAKF) has been applied to the target tracking field, the precision and stability of SHAKF remain to be improved. In this paper, a square root Sage–Husa adaptive robust Kalman filter (SR-SHARKF) algorithm together with the constant jerk model is proposed, which can not only solve the problem of filtering divergence triggered by numerical rounding errors, inaccurate system mathematics, and noise statistical models, but also improve the filtering accuracy. First, a novel square root decomposition method is proposed in the SR-SHARKF algorithm for decomposing the covariance matrix of SHAKF to assure its non-negative definiteness. After that, a three-segment approach is adopted to balance the observed and predicted states by evaluating the adaptive scale factor. Finally, the unbiased and the biased noise estimators are integrated while the interval scope of the measurement noise is constrained to jointly evaluate the measurement and observation noise for better adaptability and reliability. Simulation and experimental results demonstrate the effectiveness of the proposed algorithm in eliminating white noise triggered by the USV and target oscillations.

The filter performance will be degraded in the measurements with time-varying and unknown noise statistics. To combat the above challenges, a modified strong tracking slide window variational adaptive Kalman filter algorithm is proposed in this article. First, the multiple fading factors are integrated into the proposed algorithm to adjust the error covariance. Next, an improved adaptive slide window method is designed for variational Bayesian (VB) Kalman filtering by adaptively adjusting the slide window size and correcting the previous state according to the later state, which improves the estimation accuracy and computational efficiency. Finally, the inverse Wishart distribution is considered for modeling process and measurement noise, and the state vector, as well as noise statistics, are inferred via the VB technique without prior noise covariance information. Simulation results demonstrate that the proposed filter algorithm is more robust than existing filters in counteracting measurement and process noise uncertainties.

To achieve autonomous navigation in complex marine environments, unmanned surface vehicles are equipped with a variety of sensors for sensing the surrounding environment and their own state. To address the issue of unsatisfactory multi-sensor information fusion in stochastic uncertain systems with unknown disturbances, an improved evidence theory multi-sensor data fusion method is proposed in this article. First, the affiliation function in fuzzy set theory is introduced as a support function to assign initial evidence for multi-sensor data, and the initial evidence is corrected according to the degree of data bias. Second, a divergence measure is employed to measure the degree of conflict and discrepancy among the evidence, and each piece of evidence is allocated proportional weight based on the conflict allocation principle. Finally, the evidence is synthesized through the evidence combination rule, and the data are weighted and summed to obtain the data fusion results. Since it is difficult to obtain dynamic information from multiple sensors carried by unmanned surface vehicles in practical applications, and considering that the proposed method has universal applicability, practical application experiments using previous research demonstrate that the proposed method has higher fusion accuracy than other existing data fusion methods.

The time-varying noise covariance matrices with respect to a linear Gaussian system are inaccurate, which may make the estimation accuracy of some filtering algorithms less than expected. To tackle the aforementioned issue, a modified variational robust filter is presented. In this algorithm, a sliding-window-based variational filter is employed, which improves the algorithm’s accuracy and efficiency via the latter state to adjust the previous state and avoids the iterations of fixed-point. The inverse Wishart distribution is considered as the observation noise covariance’s prior distribution and is capable of estimating the observation noise covariance and the system state via the variational Bayesian technique. The Sage-Husa filter is employed for estimating the state noise covariance, and a modified monitoring strategy for real-time adjustment of the state noise covariance is developed to ensure the matrix’s positive semi-definite. An adaptive factor is constructed for balancing the predicted and observation states to improve the algorithm’s robustness. Simulation and experiment results show that the proposed filtering algorithm performs better than some existing filtering algorithms with regard to convergence and accuracy.