The practical application of integrated gyroscopes in engineering has not yet been fully realized due to the linear correlation between the Sagnac effect and dimensions. In recent demonstrations, gyroscopes operating near exceptional points (EPs) under parity-time (PT) symmetry have shown significant potential in enhancing their response to rotational rates. However, constructing higher-order EPs with refined physical properties poses a considerable challenge. Additionally, current methods for constructing higher-order EPs with robustness primarily rely on passive cavities, with almost no reports on constructing robust EPs using PT-symmetric systems that encompass both gain and loss. Here, we propose a robust design for a scalable fabrication of higher-order EP gyroscopes with PT-symmetric structure. We investigate the influence of perturbations on the frequency splitting of the higher-order EP gyroscope and demonstrate that it is possible to achieve a resonance splitting eight orders of magnitude higher than that obtained through the classical Sagnac effect. In comparison to the previously proposed PT-symmetric gyroscope, our solution allows a tunable frequency splitting by adjusting the phase shift, making it more measurable at the output power spectrum.

Inspired by the remarkable collaborative echolocation mechanisms of dolphin pods, the paper addresses the challenge of achieving high-precision cooperative positioning for clusters of unmanned underwater vehicles (UUVs) in complex marine environments. Cooperative positioning systems for UUVs typically rely on acoustic ranging information to correct positional errors. However, the propagation characteristics of underwater acoustic signals are susceptible to environmental disturbances, often resulting in non-Gaussian, heavy-tailed distributions of ranging noise. Additionally, the strong nonlinearity of the system and the limited observability of measurement information further constrain positioning accuracy. To tackle these issues, this paper innovatively proposes a Factor Graph-based Adaptive Cooperative Positioning Algorithm (FGAWSP) suitable for heavy-tailed noise environments. The method begins by constructing a factor graph model for UUV cooperative positioning to intuitively represent the probabilistic dependencies between system states and observed variables. Subsequently, a novel factor graph estimation mechanism integrating adaptive weights with the product algorithm is designed. By conducting online assessment of residual information, this mechanism dynamically adjusts the fusion weights of different measurements, thereby achieving robust handling of anomalous range values. Experimental results demonstrate that the proposed method reduces positioning errors by 22.31% compared to the traditional algorithm, validating the effectiveness of our approach.

During ship operations at sea, the vessel’s attitude undergoes continuous changes due to various factors such as wind, waves, and its own motion. These influences are challenging to mathematically describe, and the changes in attitude are also influenced by multiple interconnected factors. Consequently, accurately predicting the ship’s attitude presents significant challenges. Previous studies have demonstrated that phenomena like wind speed and wave patterns exhibit chaotic characteristics when affecting attitude changes. However, research on predicting ship attitudes lacks an exploration of whether chaotic characteristics exist and how they can be described and applied. This paper initially identifies the chaotic characteristics of ship attitude data through phase space reconstruction analysis and provides mathematical representations for them. Based on these identified chaotic characteristics, a Transformer model incorporating feature embedding layers is employed for time series prediction. Finally, a comparison with traditional methods validates the superiority of our proposed approach.

As the core component of the fiber optic gyroscope, the fiber coil has been the focus of research. In the field of fiber coil environmental adaptability research, researchers are calculating environmental errors, such as thermally-induced errors and magnetic-induced errors. They approximated the refractive index and birefringence of the fiber coil to an average value. However, the values of birefringence changes by the different bending radius of the fibers in the different layers, which would greatly reduce the accuracy of the environment error model. Therefore, in this paper, a birefringence distribution model of the fiber coil is proposed for the first time based on the quadrupole symmetrical winding pattern. Firstly, we qualitatively analyze the birefringence of Panda-type polarization-maintaining fiber, and then the fiber coil winding law is established through detailed analysis of the standard quadrupole symmetric winding method. Secondly, we use the finite element method to analyze the force of the single-layer fiber, and obtain the change law of the refractive index of polarization-maintaining fiber. The mathematical model of the birefringence distribution is established and simulated. Finally, we use optical coherence domain polarization measurement technology to detect the distributed polarization crosstalk of the fiber coil. The data is obtained by using the white light interferometer that is consistent with the simulation. The result proves the correctness of the theory. Moreover, an experimental platform for Sagnac loop is built, and the interference optical power is measured by the optical spectrum analyzer. Compared with the equivalent radius method, the accuracy of model is improved by 91.48% at 1310nm.The method proposed in this paper will greatly promote the research on the environmental adaptability of fiber optic gyroscope.

Spacecraft is severely limited in weight and volume, resulting in a small bending radius of the fiber coil used by IFOG (Interference Fiber Optic Gyroscope). The fiber coil has such a size that the influence of bending on fiber birefringence cannot be ignored. In this paper, we research magnetic-induced errors of small-sized IFOG working in low orbit space. Firstly, we use the Jones matrix to analyze the effects of radial magnetic field and axial magnetic field on IFOG. Secondly, we establish a three-dimensional model for the radial magnetic-induced errors and magnetic-induced errors of minor radius fiber coil. Using the finite element method, we analyze the magnetic-induced error between different levels of the fiber coil. Combined with the birefringence distribution of the minor radius fiber coil, an accurate three-dimensional magnetic-induced error model is established. Thirdly, in the experiment, we design the magnetic-induced error test platform that includes the Fluke standard current source, transconductance amplifier, and Helmholtz coil. The experimental results show that, compared with the traditional calculation method, the three-dimensional magnetic-induced error model reduces the RMSE (Root Mean Square Error) of the radial magnetic field by 56.9% and the RMSE of the axial magnetic field by 35.7%, respectively.

In order to improve the positioning accuracy of the pipeline inspection gauge (PIG), a pipeline positioning method, based on weld location, is proposed. The position of the welding scar is recognized by wavelet transform modulus maxima (WTMM). Equidistant welding scars provide positioning references to the strap-down inertial navigation system (SINS)/dead reckoning (DR) navigation system, which is the positioning algorithm in PIG. The following improvements have been made in relation to prior research. First, we suggest a selection strategy for the optimal mother wavelet and decomposition level; based on the strategy, WTMM can recognize the collision response between the PIG and submerged weld in the burst noise for the inertial measurement unit (IMU) output. Then, characteristic position (CP), which is the site of the weld scar, and non-holonomic constraints are utilized to decrease the position and the attitude error. By doing such, the SINS/DR/CP algorithm is proposed. The positioning error of the modified algorithm is 0.129% in the experiment, which performs better than other algorithms.