Finding the position of a radiative source based on time-difference-of-arrival (TDOA) measurements from spatially separated receivers has been widely applied in sonar, radar, mobile communications and sensor networks. For the nonlinear model in the process of positioning, Taylor series and other novel methods are proposed. The idea of cone constraint provides a new way of solving this problem. However, these approaches do not always perform well and are away from the Cramer-Rao-Lower-Bound (CRLB) in the situations when the source is set at the array edge, the noise in measurement is loud, or the initial position is biased. This paper presents a weighted-least-squares (WLS) algorithm with the cone tangent plane constraint for hyperbolic positioning. The method adds the range between the source and the reference sensor as a dimension. So, the space-range frame is established. Different from other cone theories, this paper sets the reference sensor as the apex and finds the optimal source estimation on the cone. WLS is used for the optimal result from the measurement plane equations, a vertical constraint and a cone constraint. The cone constraint equation is linearized by a tangent plane. This method iterates through loops and updates the tangent plane, which approximates the truth-value on the cone. The proposed algorithm was simulated and verified under various conditions of different source positions and noises. Besides, some state-of-the-art algorithms were compared in these simulations. The results show that this algorithm is accurate and robust under poor external environment.

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.

The accumulated positioning errors are required to be eliminated after a long run-up of an underwater vehicle equipped with an Inertial Navigation System (INS). For the better position accuracy with less cost, a single-source aided passive location method is proposed, which applies acoustic positioning together with inertial navigation. The fixed sound source periodically emits the acoustic wave pulse under water. After a number of signals are received, a high-precision synthetic array is built with the positions measured by inertial instruments and clock on board. Then, the source is located by Time-Difference- of-Arrival (TDOA) positioning technology and the navigation error of the moving vehicle is reduced. Different from fully- autonomous, there is a radiation source and sound is provided as intermediary locally. It is independent of the control and the algorithm. The operation and calculation are performed on the vehicle, so it is called semi-autonomous. Multiple users are supported simultaneously. Since no radiation is sent from the vehicle, it is extremely concealed. More importantly, it is inexpensive and the accuracy has nothing to do with the amount of error before. In the simulation, the position error could be suppressed to 50m or less. The results show that the new approach for underwater positioning is effective and reliable. After a period of time, INS error can be eliminated quickly when the vehicle returns to the correction area within the range of the single-source. In this way, long-time and accurate navigation is realized underwater.

The accuracy of initial attitude calculated from initial alignment has an important influence on the performance of SINS/USBL integrated navigation system. Currently, two main problems need to be overcome for SINS to complete the in-motion coarse alignment assisted by USBL system. 1) As SINS cannot obtain accurate initial attitude during the initial alignment phase, so USBL system can only provide the relative position in acoustic frame, but not the precise absolute position in navigation frame. 2) The outliers contained in the USBL raw data will seriously affect the performance of coarse alignment. In this paper, an in-motion coarse alignment method for SINS/USBL using the relative position of USBL is creatively proposed. Firstly, after constructing the apparent displacement vector from the relative position provided by USBL system and the output of IMU, an in-motion vector observation model is constructed. Secondly, the proposed method can suppress the influence of outliers in USBL raw data based on the advantages of displacement vector. Finally, the experimental results of the simulation and field tests show that the proposed method can not only complete the in-motion coarse alignment with favorable performance, but also effectively suppress the influence of the outliers in USBL data on the coarse alignment. Note to Practitioners —This paper was motivated by the problem of rapid in-motion coarse alignment for the SINS/USBL integrated navigation system in an underwater environment. Due to the failure of GNSS signals in underwater environments, the existing in-motion coarse alignment algorithms assisted by GNSS position/velocity are no longer applicable. In this paper, an in-motion coarse alignment method assisted by USBL relative position is proposed for SINS in underwater environments. In this article, we compare and analyze the differences between the principle of USBL positioning and GNSS positioning. Based on the characteristics of USBL positioning principle, the displacement vectors are extracted from the relative position of USBL for coarse alignment in this paper. The designed method can effectively suppress the impact of noise and outliers in USBL data on coarse alignment performance. The results of the simulation and field tests indicate that the method investigated in this paper is feasible in practical engineering.

This paper addresses the state estimation of the nonlinear initial alignment of the strapdown inertial navigation system (SINS), which mainly focuses on the initial alignment on the swaying base and under the in-motion condition with the measurement uncertainties. In order to achieve a higher alignment precision, stronger numerical stability, and lower computational cost for the initial alignment of SINS on the swaying base, a new discrete large azimuth misalignment error model of SINS is established, and an improved fifth-degree cubature Kalman filter (5th-CKF) algorithm is proposed, which combines the 5th-CKF and a simplified dimensionality reduction filtering algorithm. The 5th-CKF is introduced to solve the nonlinear filtering problem, a simplified dimensionality reduction algorithm is derived to reduce the large calculation values of 5th-CKF. Furthermore, under the Bayesian framework, a novel filtering approach named the fifth-degree variational Bayesian (VB) adaptive cubature Kalman filter is deduced for the in-motion alignment with a large azimuth misalignment angle and unknown and time-varying measurement noise statistics, which combines the iterative VB approach and 5th-CKF. The 5th-CKF is exploited to handle the nonlinear initial alignment model, and the VB approach is utilized to iteratively estimate the sufficient statistics of the measurement noise. Mathematical simulation, turntable, and vehicle experiments are performed to demonstrate the effectiveness and the superiority of the proposed approaches.