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• Case rotation modulation is proven useful for nuclear-spin comagnetometer. • The modulation performs well when suppressing starting random error. • The modulation has positive effect on the low frequency part of random drift. To restrain the effect of the bias error of nuclear-spin comagnetometer in space-stable Inertial Navigation System (INS) for long-endurance independent navigation, the case rotating modulation for comagnetometer was researched. The structure of comagnetometer case rotating in space-stable INS was presented and the modulation equation is derived. By comparing the modulation results of three types of rotating schemes, the four-positing rotating scheme was considered optimal. Modulation result showed that comagnetometer constant bias and partial magnetic-field related errors can be averaged out, low-frequency random errors in one rotating modulation period can be averaged out as constant errors; high-frequency random errors are affected by rotating modulation. Semi-physical simulation test results show that the accuracy of the K-Rb-21Ne comagnetometer data is effectively improved by case rotating modulation with the bias mean value decreasing from the magnitude of 0.01°/h to 10−4°/h and the bias stability improving from the magnitude of 0.01°/h to 0.001°/h. [ABSTRACT FROM AUTHOR]

Dual-axis rotational inertial navigation system (RINS) has been widely used in long-term marine navigation for recent years. With all constant biases averaged out, those gyro biases related to geomagnetic or gravitational field, which cannot be averaged out, become the main error source. In this paper, the geographic-frame-equivalent (G-F-E) gyro bias is defined by integrating the gyro biases caused by all kinds of external fields. A practicable online calibration method is proposed by deducing the error propagation rules. The calibration equation is established by observing position errors at three points, and the optimal solution of the G-F-E gyro bias is obtained using the least square method. Static and sailing experimental results show that the G-F-E gyro bias can be calibrated during the 6-h initial alignment. The proposed calibration method can further improve the position accuracy of a dual-axis RINS by 30% compared with the previous method when the G-F-E gyro bias changes. [ABSTRACT FROM AUTHOR]

According to the application characteristics of the K-Rb-21Ne comagnetometer, a space-stable navigation mechanization is designed and the requirements of the comagnetometer prototype are presented. By analysing the error propagation rule of the space-stable Inertial Navigation System (INS), the three biases, the scale factor of the z-axis, and the misalignment of the x- and y-axis non-orthogonal with the z-axis, are confirmed to be the main error source. A numerical simulation of the mathematical model for each single error verified the theoretical analysis result of the system’s error propagation rule. Thus, numerical simulation based on the semi-physical data result proves the feasibility of the navigation scheme proposed in this paper. [ABSTRACT FROM AUTHOR]

Zero velocity update (ZUPT) is widely discussed for error restriction in land vehicle Inertial Navigation Systems (INSs) and wearable pedestrian INSs to overcome the problems of Global Positioning System (GPS) unavailability in urban canyons or indoor scenarios. In this paper, an online smoothing method for ZUPT-aided INSs is presented. By introducing the Rauch–Tung–Striebel (RTS) smoothing method into the ZUPT-aided INS, position errors can be effectively restrained not only at stop points but during the whole trajectory. By integrating reverse navigation with a ZUPT smoother, the method realises forward and real-time processing. Compared with existing approaches, it can improve the position accuracy in real time without any other sensors, which is well suited for applications on high-accuracy navigation in GPS-challenging environments. Accuracy test results with different Inertial Measurement Units (IMUs) show that the developed method can significantly decrease position errors from hundreds or thousands of metres to below ten metres. During the whole trajectory, the online smoothing method ensures the maximum position errors at non-stop points can reach the same level of accuracy at stop points. A delay test result proves that the delay of the reverse online smoothing method proposed in this paper is much shorter than existing online smoothing methods. [ABSTRACT FROM AUTHOR]

This article investigates a novel Bluetooth odometer (BOD)-aided smartphone-based vehicular navigation system for satellite-denied environments. First, a wheel-mounted BOD is designed to measure rotational speed and send data to smartphones by Bluetooth transmission. Second, a nonlinear smartphone-based microelectromechanical system (MEMS) inertial measurement unit (IMU)/BOD error model is derived to solve the problem of azimuth divergence. Then, a position delay time model is proposed to compensate for the delay time of Bluetooth transmission. An Android app is developed to receive the BOD data from Bluetooth transmission, and the proposed BOD smartphone-based vehicular navigation algorithm provides positioning information in real time. In field tests, positioning accuracy reaches 0.38%D by using the proposed MEMS-IMU/BOD model. The designed scheme can be used as a low-cost and convenient solution for smartphone-based civilian vehicular autonomous navigation systems without changing the habits of drivers. [ABSTRACT FROM AUTHOR]

It is vital for a strapdown inertial navigation system (SINS) to be calibrated before normal use. In this paper, a new kind of norm-observed calibration method is proposed. Considering that the norm of the output of accelerometers and gyroscopes can be exactly the norm of local acceleration of gravity and Earth rotation angular velocity, respectively, optimization function about all-parameter calibration and the corresponding 24-position calibration path is established. Differential evolutionary algorithm (DE) is supposed to be the best option in parameter identification due to its strong search and fast convergence abilities. However, the high-dimensional individual vector from calibration error equations restrains the algorithm's optimum speed and accuracy. To overcome this drawback, improved DE (IDE) optimization is specially designed: First, current "DE/rand/1" and "DE/current-to-best/1" mutation strategies are combined as one with complementary advantages and overall balance during the whole optimization process. Next, with the increase of the evolutionary generation, the mutation factor can adjust itself according to the convergence situation. Multiple identification tests prove that our IDE optimization has rapid convergence and high repeatability. Besides, certain motivation of external angular velocity is added to the gyroscope calibration, and a series of dynamic observation paths is formed, further improving the optimization accuracy. The final static navigation experiment shows that SINS with calibration parameters solved by IDE has better performance over other identification methods, which further explains that our novel method is more accurate and reliable in parameter identification. [ABSTRACT FROM AUTHOR]

Rotational inertial navigation system (RINS) could improve the navigation performance by rotating the IMU around gimbals, and the structure and function of the dual-axis RINS also help realize the process of self-calibration. However, the gyro–accelerometer asynchronous time is not considered in current studies. Coupled into the navigation error, the gyro–accelerometer asynchronous time can lead to velocity accuracy decline during the process of rotation. Therefore, the modeling and calibration of the gyro–accelerometer asynchronous time would enhance the systemic reliability. In this article, in order to solve the abovementioned problem: 1) we model the gyro–accelerometer asynchronous time and perform an error analysis of gyro–accelerometer asynchronous time; 2) we propose a compensation method of the outer lever arm to improve the accuracy of the observed velocity and position; and 3) we derive a continuous linear 40-D RINS error model considering the abovementioned two error parameters compared with the traditional method, the PWCS method, and the SVD method is utilized to provide the observability degrees of the proposed state during the self-calibration process. Experimental results illustrated that the proposed method can improve the accuracy in the long-endurance navigation. [ABSTRACT FROM AUTHOR]

A significant issue of land vehicle navigation is in-motion attitude alignment of the odometer (OD)-aided strapdown inertial navigation system (SINS). The consecutive OD outliers can occur due to sudden wheel slipping and skidding while vehicle maneuvering. They seriously reduce the robustness and precision of attitude alignment. In this paper, we investigate a robust in-motion attitude alignment method for the OD-aided SINS. The method consists of in-motion coarse alignment and in-motion fine alignment. In the in-motion coarse alignment process, we developed Huber's M-estimation and integral formula based robust Kalman filter (HRKF/IF-CA), which can restrain the interference of consecutive OD outliers on reconstructed observation vectors. Thus, HRKF/IF-CA can contribute to better coarse attitude results. The next process is in-motion fine alignment. Under the popular repeated backtracking scheme, we investigate HRKF based fine alignment (HRKF-FA) with the SINS/OD summed measurement model. HRKF-FA can refine attitude alignment and restrain the interference of consecutive OD outliers simultaneously. Finally, the proposed method is evaluated by simulation and vehicle test. The attitude alignment results show that this method can achieve reasonable attitude results, and the interference of consecutive OD outliers caused by sudden wheel slipping and skidding can be greatly restrained. [ABSTRACT FROM AUTHOR]

Highlights • A 3-D Voigt model for rubber damper is proposed. • A 6-DOF dynamic model of mechanically dithered RLG dual-axis RINS is built based on the proposed 3-D Voigt model. • An experimental verification method based on the IMU and turntable's angle encoders is proposed to measure the actual deviation angles. Abstract Deviation angles between inertial measurement unit (IMU) and turntable in dual-axis rotational inertial navigation system (RINS) degrade the navigation attitude precision seriously. And rubber dampers deformation is an unavoidable and crucial factor in deviation angles when turntable rotates for high precision mechanically dithered ring laser gyroscope (RLG) dual-axis RINS. In this paper, in order to accurately analyze the deviation angles caused by rubber dampers deformation, a novel dynamic analysis and experimental verification method for these deviation angles in dual-axis RINS is proposed. Firstly, a 3-D Voigt model for rubber damper was proposed, and then a 6-DOF dynamic model of mechanically dithered RLG dual-axis RINS was built based on the proposed 3-D Voigt model. Secondly, dynamic equations were derived based on the proposed model for inner gimbal rotation and outer gimbal rotation respectively. Then dynamic equations were solved analytically by decoupling method and the decoupling method was validated by comparing analytic solutions against numerical solutions got by Runge-Kutta method. Afterwards, rotation experiments for turntable were conducted to obtain actual deviation angles caused by rubber dampers deformation. Finally the proposed model and dynamic analysis method were validated by comparing it against the real deviation angles measured by rotation experiments for turntable. [ABSTRACT FROM AUTHOR]

An autonomous smartphone embedded inertial sensors aided vehicular navigation method is proposed in this study to solve the low accuracy of the embedded sensors and the indefinite installation angle between a smartphone and a vehicle in a smartphone-based vehicular navigation. First, the nonlinear MEMS-IMU model and nonlinear NHC model are derived, and analysis of the error generated by the traditional model under this case is conducted, proving the necessity of the nonlinear modeling in theory. Second, we establish the nonlinear integrated navigation scheme, the app is also implemented with the scheme on the Android platform. The satellite-denied simulation experiment verifies the accuracy of the proposed method is higher than that of the traditional method. The app performs well in the smartphone-based platform in the actual tunnel and underground parking lot tests. • A nonlinear autonomous integrated navigation scheme utilizing smartphone embedded MEMS-IMU is proposed. • Results show that the proposed smartphone-based navigation system can effectively improve the accuracy of positioning in satellite-denied areas. [ABSTRACT FROM AUTHOR]

The strap-down inertial navigation system (SINS) is a standard and crucial approach for attitude determination of a ship. To protect the SINS from vibration and shock, we design a Stewart platform based bumper considering the high restoration accuracy requirement of the bumper. However, reset errors of buffer bars and wear of spherical hinges will change structure parameters of the bumper and degrade the restoration accuracy. In this paper, we propose an optimal design methodology for SINS's Stewart platform bumper to improve the restoration accuracy. First, the equation of restoration accuracy was derived using total differential method. Then, based on the equation, objective function, design variables and constraints are designated, so the structural optimization problem was transferred to a numerical optimization question. Later, genetic algorithm (GA) was employed to solve the numerical optimization matter. Afterwards, comparison results among GA, sequence quadratic programming (SQP) method and interior point method indicate that the proposed method can provide optimized structural parameters of SINS's Stewart platform bumper for restoration accuracy, which is 31.81″ at the lever of current mechanical manufacturing lever. Finally, a real shock experiment for optimal designed bumper validates the proposed method. [ABSTRACT FROM AUTHOR]

Metalenses composed of a large number of subwavelength nanostructures provide the possibility for the miniaturization and integration of the optical system. Broadband polarization-insensitive achromatic metalenses in the visible light spectrum have attracted researchers because of their wide applications in optical integrated imaging. This paper proposes a polarization-insensitive achromatic metalens operating over a continuous bandwidth from 470 nm to 700 nm. The silicon nitride nanopillars of 488 nm and 632.8 nm are interleaved by Fresnel zone spatial multiplexing method, and the particle swarm algorithm is used to optimize the phase compensation. The maximum time-bandwidth product in the phase library is 17.63. The designed focal length can be maintained in the visible light range from 470 nm to 700 nm. The average focusing efficiency reaches 31.71%. The metalens can achieve broadband achromatization using only one shape of nanopillar, which is simple in design and easy to fabricate. The proposed metalens is expected to play an important role in microscopic imaging, cameras, and other fields. [ABSTRACT FROM AUTHOR]

We disclose a method to obtain the transverse light-shift along the probe light of a single-axis alkali metal-noble gas co-magnetometer. The relationship between transverse compensating field and light-shift is deduced through the steady-state solution of Bloch equations. The variety of probe light intensity is used to obtain the residual magnetic field, and step modulation tests are applied to acquire the total spin-relaxation rate of electron spins and self-compensation point. The transverse light-shift can be calculated by these parameters, and it is reduced from − 0.115 to − 0.039 nT by optimizing the probe light wavelength. Finally, long-term static test for a K-Rb-21Ne co-magnetometer has been performed. The bias instability of about 0.009 deg/h and rate ramp coefficient of 0.096 (deg/h)/h have been achieved to prove the improvement of stability. [ABSTRACT FROM AUTHOR]

Pedestrian Navigation System (PNS) is one of the research focuses of indoor positioning in GNSS-denied environments based on the MEMS Inertial Measurement Unit (MIMU). However, in the foot-mounted pedestrian navigation system with MIMU or mobile phone as the main carrier, it is difficult to make the sampling time of gyros and accelerometers completely synchronous. The gyro-accelerometer asynchronous time affects the positioning of PNS. To solve this problem, a new error model of gyro-accelerometer asynchronous time is built. The effect of gyro-accelerometer asynchronous time on pedestrian navigation is analyzed. A filtering model is designed to calibrate the gyro-accelerometer asynchronous time, and a zero-velocity detection method based on the rate of attitude change is proposed. The indoor experiment shows that the gyro-accelerometer asynchronous time is estimated effectively, and the positioning accuracy of PNS is improved by the proposed method after compensating for the errors caused by gyro-accelerometer asynchronous time. [ABSTRACT FROM AUTHOR]

In the field of high accuracy strapdown inertial navigation system (SINS), the inertial measurement unit (IMU) biases can severely affect the navigation accuracy. Traditionally we use Kalman filter (KF) to estimate those biases. However, KF is an unbiased estimation method based on the assumption of Gaussian white noise (GWN) while IMU sensors noise is irregular. Kalman filtering will no longer be accurate when the sensor's noise is irregular. In order to obtain the optimal solution of the IMU biases, this paper proposes a novel method for the calibration of IMU biases utilizing the KF-based AdaGrad algorithm to solve this problem. Three improvements were made as the following: (1) The adaptive subgradient method (AdaGrad) is proposed to overcome the difficulty of setting step size. (2) A KF-based AdaGrad numerical function is derived and (3) a KF-based AdaGrad calibration algorithm is proposed in this paper. Experimental results show that the method proposed in this paper can effectively improve the accuracy of IMU biases in both static tests and car-mounted field tests. [ABSTRACT FROM AUTHOR]

Recently, methods based on Artificial Intelligence (AI) have been widely used to improve positioning accuracy for land vehicle navigation by integrating the Global Positioning System (GPS) with the Strapdown Inertial Navigation System (SINS). In this paper, we propose the ensemble learning algorithm instead of traditional single neural network to overcome the limitations of complex and dynamic data cased by vehicle irregular movement. The ensemble learning algorithm (LSBoost or Bagging), similar to the neural network, can build the SINS/GPS position model based on current and some past samples of SINS velocity, attitude and IMU output information. The performance of the proposed algorithm has been experimentally verified using GPS and SINS data of different trajectories collected in some land vehicle navigation tests. The comparison results between the proposed model and traditional algorithms indicate that the proposed algorithm can improve the positioning accuracy for cases of SINS and specific GPS outages. [ABSTRACT FROM AUTHOR]