This paper addresses the source location problem by using time-difference-of-arrival (TDOA) measurements. The two-stage weighted least squares (TWLS) algorithm has been widely used in the TDOA location. However, the estimation accuracy of the source location is poor and the bias is significant when the measurement noise is large. Owing to the nonlinear nature of the system model, we reformulate the localization problem as a constrained weighted least squares problem and derive the theoretical bias of the source location estimate from the maximum-likelihood (ML) estimation. To reduce the location bias and improve location accuracy, a novel bias-reduced method is developed based on an iterative constrained weighted least squares algorithm. The new method imposes a set of linear equality constraints instead of the quadratic constraints to suppress the bias. Numerical simulations demonstrate the significant performance improvement of the proposed method over the traditional methods. The bias is reduced significantly and the Cramér–Rao lower bound accuracy can also be achieved.

In order to suppress the impact of some error factors of the existing strap-down inertial navigation system and ultra-short base line (SINS/USBL) position matching loosely integration approach on positioning accuracy, a tightly integration strategy is creatively proposed and designed relying on the derived state error equation and measurement equation, the relative measurement information are directly used as the observation information. The error factors such as attitude error and installation error are considered in the filtering model to avoid the influences on the matching position, and the filter algorithm can be also effectively designed according to the sensor parameters of USBL, which can improve the integration positioning accuracy. Meanwhile, in order to address the decreased positioning performance caused by the measurement uncertainty, a Student's t-based Kalman filter with adaptiveness and robustness is reorganized and derived for the proposed SINS/USBL tightly integration strategy, the adaptiveness can be obtained by estimating the unknown measurement noise statistics using variational Bayesian (VB) approximation, and the robustness can be achieved by dealing with the measurement outliers based on the Student's t distribution. Finally, the feasibility and the superiority of the proposed strategy are evidenced both through the simulations and the field tests in the river.

This article addresses the underwater acoustical localization problem by using the time-difference-of-arrival (TDOA) and bearing-angle-of-arrival (BAOA) measurements. For the underwater acoustic equipment, such as the ultrashort baseline system (USBL), whose bearing measurements are different from the traditional angle-of-arrival (AOA) model, a closed-form solution for the hybrid TDOA/BAOA-based source localization problem is developed. However, the solution suffers from the measurement noise and cannot achieve the Cramer–Rao lower bound (CRLB) performance in the case of large measurement noise. Thus, an iterative constrained weighted least-squares method is presented to further minimize the error in the case of large noise. The CRLB for hybrid TDOA/BAOA source localization is analyzed, and the solution is proved to achieve the CRLB performance. Numerical simulations and field tests demonstrate that the proposed method outperforms the traditional methods in terms of estimation bias and accuracy. It can achieve the CRLB performance better.

Factor graph optimization (FGO) is a well-known approach in the robotics field. Due to multiple iterations and application of large amounts of data, it usually could superior performance than the Kalman Filter (KF) under complex scenarios. However, it is rarely used in the underwater environment, especially for applications based on fiber-optic inertial navigation. Taking the ultra-short baseline system (USBL) as the application background, a novel inertial navigation system (INS)/USBL integrated navigation scheme based on FGO is presented in this paper. The traditional pre-integration factor simplifies the earth rotation and coordinate system, which limits its application in high-precision sensors. This paper proposed an improved pre-integration model using the high precision measurements of fiber optics gyroscope in FGO. Simulation and field tests proved that, with the FGO method, improved accuracy of INS/USBL integration was obtained compared to the traditional KF method. It confirms the potential of FGO in the applications of underwater navigation and positioning.

Dynamic statistical process monitoring methods have been widely studied and applied in modern industrial processes. These methods aim to extract the most predictable temporal information and develop the corresponding dynamic monitoring schemes. However, measurement noise is widespread in real-world industrial processes, and ignoring its effect will lead to suboptimal modeling and monitoring performance. In this article, a probabilistic predictable feature analysis (PPFA) is proposed for multivariate time series modeling, and a multistep dynamic predictive monitoring scheme is developed. The model parameters are estimated with an efficient expectation–maximization algorithm, where the genetic algorithm and the Kalman filter are designed and incorporated. Furthermore, a novel dynamic statistical monitoring index, the dynamic index, is proposed as an important supplement of T2 and SPE to detect dynamic anomalies. The effectiveness of the proposed algorithm is demonstrated via its application on the three-phase flow facility and a medium-speed coal mill.

The Ultra-short baseline (USBL) positioning system has important application in the positioning of underwater vehicles. The installation error angle of the USBL positioning system has an important influence on the positioning accuracy of USBL system. The traditional calibration methods have limited estimation accuracy for installation error angles and have high route requirements. To solve the above problems, a calibration method of installation error angle based on attitude determination is proposed in this paper. When strapdown inertial navigation system (SINS) and USBL are fixed together in the application process, the installation error angle of USBL is fixed and unchanged. Then the calibration of installation error angle can be accomplished with the idea of attitude determination. The vector observation model based on the installation error angle matrix is established first. Observation vectors are obtained by the relative position of transponders in the USBL coordinate frame. The reference vector is calculated by position of transponder, position and attitude of SINS and lever arm between SINS and USBL. By constructing the observation vectors and the reference vectors, the proposed method can calibrate the installation error angle of SINS and USBL in real time. The advantages of the proposed method are that it has no specific requirements for the calibration route and can calibrate the installation error angle in real time with high accuracy. In order to verify the performance of the proposed algorithm, simulation experiment and field experiment are carried out in this paper. The results of simulation experiment and field experiment show that the proposed method can give the estimated installation error angle of USBL in real time, and the estimated result is the best among several methods. The proposed method can not only achieve the calibration of the installation error angle in circular trajectory, but also in straight trajectory.