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Various systems have been developed to process agricultural land data for better management of crop production. One such system is Cropland Data Layer (CDL), produced by the National Agricultural Statistics Service of the United States Department of Agriculture (USDA). The CDL has been widely used for training deep learning (DL) segmentation models. However, it contains various errors, such as salt-and-pepper noise, and must be refined before being used in DL training. In this study, we used two approaches to refine the CDL for DL segmentation of major crops from a time series of Sentinel-2 monthly composite images. Firstly, different confidence intervals of the confidence layer were used to refine the CDL. Secondly, several image filters were employed to improve data quality. The refined CDLs were then used as the ground-truth in DL segmentation training and evaluation. The results demonstrate that the CDL with +45% and +55% confidence intervals produced the best results, improving the accuracy of DL segmentation by approximately 1% compared to non-refined data. Additionally, filtering the CDL using the majority and expand–shrink filters yielded the best performance, enhancing the evaluation metrics by about 1.5%. The findings suggest that pre-filtering the CDL and selecting an effective confidence interval can significantly improve DL segmentation performance, contributing to more accurate and reliable agricultural monitoring.

This paper introduces a current control method for permanent magnet synchronous motors (PMSMs) using a disturbance sliding mode observer (DSMO) in conjunction with a linear quadratic regulator (LQR). This approach enhances control performance, streamlines the tuning of controller parameters, and offers robust optimal control that is resistant to system disturbances. The LQR controller based on state feedback is advantageous for its simplicity in parameter adjustment and achieving an optimal control effect easily under specific performance indicators. It is suitable for the optimal control of strong linear systems that can be accurately modeled. However, most practical systems are difficult to model accurately, and the time-varying system parameters and existing nonlinearity limit the engineering application of LQR. In the PMSM current control loop, there is strong nonlinear disturbance manifesting as the nonlinearity of its dynamic model. Additionally, substantial noise and variations in system parameters within actual motor circuits hinder the linear quadratic regulator from attaining optimal performance. A disturbance sliding mode observer is proposed to enhance the LQR controller, enabling superior performance in nonlinear current loop control. Simulation and actual hardware experiments were conducted to verify the performance and robustness of the control scheme proposed in this paper. Compared with the widely used PI controller in engineering and sliding mode control (SMC) specialising in disturbance rejection, it offers the advantage of straightforward parameter tuning and can swiftly achieve the robust and optimal control performance that engineers prioritize.

The demodulation phase error will cause the quadrature error to be coupled to the rate output, resulting in performance deterioration of the MEMS gyroscope. To solve this problem, an in-run automatic demodulation phase error compensation method is proposed in this paper. This method applies square wave angular rate input to the gyroscope and automatically identifies the value of the demodulation phase error through the designed automatic identification algorithm. To realize in-run automatic compensation, the demodulation phase error corresponding to the temperature point is measured every 10 °C in the full-temperature environment (−40~60 °C). The relationship between temperature and demodulation phase error is fitted by a third-order polynomial. The temperature is obtained by the temperature sensor and encapsulated in the ceramic packages of the MEMS gyroscope, and the in-run automatic compensation is realized based on the fitting curve. The temperature hysteresis effect on the zero-rate output (ZRO) of the gyroscope is eliminated after compensation. The bias instability (BI) of the three gyroscopes at room temperature (25 °C) is reduced by four to eight times to 0.1°/h, while that at full-temperature environment (−40~60 °C) is reduced by three to four times to 0.1°/h after in-run compensation.

Deep Learning (DL) has become a popular method for Remote Sensing (RS) Change Detection (CD) due to its superior performance compared to traditional methods. However, generating extensive labeled datasets for DL models is time-consuming and labor-intensive. Additionally, the imbalance between changed and unchanged areas in object CD datasets, such as buildings, poses a critical issue affecting DL model efficacy. To address this issue, this paper proposes a change detection enhancement method using artificial image generation and attention mechanism. Firstly, the content of the imbalanced CD dataset is enhanced using a data augmentation strategy that synthesizes effective building CD samples using artificial RS image generation and building label creation. The created building labels, which serve as new change maps, are fed into a generator model based on a conditional Generative Adversarial Network (c-GAN) to generate high-resolution RS images featuring building changes. The generated images with their corresponding change maps are then added to the CD dataset to create the balance between changed and unchanged samples. Secondly, a channel attention mechanism is added to the proposed Adversarial Change Detection Network (Adv-CDNet) to boost its performance when training on the imbalanced dataset. The study evaluates the Adv-CDNet using WHU-CD and LEVIR-CD datasets, with WHU-CD exhibiting a higher degree of sample imbalance compared to LEVIR-CD. Training the Adv-CDNet on the augmented dataset results in a significant 16.5% F1-Score improvement for the highly imbalanced WHU-CD. Moreover, comparative analysis showcases the superior performance of the Adv-CDNet when complemented with the attention module, achieving a 6.85% F1-Score enhancement.

Accurate and reliable speed and position estimation plays an important role in the safety and efficiency of intelligent railway vehicles. Due to the level required of safety, reliability, and strong norms in the current practical application, intelligent railway vehicle positioning heavily relies on a large number of balises laid on the track and the onboard odometer (OD), while the other position method, GNSS introduction, is relatively slow. This article proposed a digital track map-assisted onboard railway location system using strapdown inertial navigation system (SINS) and OD. The proposed method consists of two steps. First, an SINS- and OD-integrated navigation method based on OD velocity integration is in the inner circle. Then, a map-matching algorithm based on vertical projection and heading weighting was employed, and when the matching outer circle results were obtained, the positions obtained from the matching outer circles were used to replace the positions obtained from SINS/OD for the Kalman filter combination. The performance of our algorithm was verified using field tests, and SINS/OD and SINS/OD/MM comparison data processing results prove that our proposed digital track map-assisted SINS/OD algorithm can effectively suppress the accumulation of train position errors. After nearly 80 km of navigation, the position error is 24 m, and the relative mileage accuracy is less than or equal to 0.03% distance.

The inertial Navigation Systems/global navigation satellite system (SINS/GNSS) has become a research hotspot in the field of train positioning. However, during a uniform straight-line motion period, the heading misalignment angle of the SINS/GNSS is unobservable, resulting in the divergence of the heading misalignment angle and ultimately causing a divergence in the train’s speed and position estimation. To address this issue, this paper proposes an estimation and compensation method for the heading misalignment angle for train SINS/GNSS integrated navigation system based on an observability analysis. When the train enters a straight-line segment, the alignment of the train’s sideslip angle and the satellite velocity heading angle allows the achievement of velocity heading observation values that resolve the issue. In a curved segment, the heading angle becomes observable, allowing for an accurate estimation of the SINS’s heading misalignment angle using GNSS observations. The results showed that, whether the train is on a straight or curved track, the position estimation accuracy meets the simulation design criteria of 0.1 m, and the heading accuracy is better than 0.25°. In comparison to the results of pure GNSS position and velocity-assisted navigation, where heading divergence occurs during constant velocity straight-line segments, the method proposed in this paper not only converges but also achieves an accuracy comparable to the GNSS velocity-based heading alignment. The simulation results demonstrate that the proposed strategy significantly improves the accuracy of the heading misalignment angle estimation, thereby enhancing the accuracy of speed and position estimation under a GNSS-denied environment.

Abstract In order to establish a unified spatial reference for the whole ship, inertial matching measurement of hull deformation is widely used because of its continuity and concealment. However, the vibration‐shock signal of shipborne equipment often brings short‐time output disturbance to the user‐side fibre gyroscope unit (FGU), and the disturbance will bring great challenges to the accuracy and convergence of inertial matching measurement. To solve these problems, the authors put forward a new algorithm named as attitude quaternion matching method‐improved double factor adaptive Kalman filter‐parameter adaptive Kalman filter (AQM‐IDFAKF‐PAKF). (1) The AQM established the FGU attitude as observation to build the basic model for hull deformation inertial matching method. (2) The authors introduced IDFAKF to track the trend of dynamic hull deformation in vibration interference by using historical data. (3) After judging the anti‐vibration‐shock calculation stop node, PAKF was utilised to adaptively adjust the parameters of hull deformation matching after vibration‐shock, so as to quickly calculate the static hull deformation angle after shock interference. Numerical simulation results illustrated that the AQM‐IDFAKF‐PAKF can quickly converge the calculation of hull deformation angle with a small steady‐state error under the condition of vibration‐shock signal interference.

Inertial matching measurement method has been widely used to measure hull deformation in real time to establish a unified attitude reference for ships in previous decades, but most current methods were based on linear error model which adopted small angle approximation. Therefore, the large misalignment angle in the hull deformation will bring great challenges to the accuracy of inertial matching measurement methods. In order to solve this problem, we divided the hull deformation with large misalignment angle into two parts: large angle based on coarse registration and small angle of the residual part. Three improvements were made as the following: (1) The quaternion optimization method (Q) was utilized to get the coarse registration result; (2) Based on the result, we derived a brand-new residual small-angle measurement algorithm. (3) We introduced neural network Karman filter (NNKF) to calculate the hull deformation in real time to further reduce the nonlinear error of the system. The experiment results illustrated that the proposed method, namely, Q-NNKF, can accurately measure the hull deformation in real time and effectively suppressed the nonlinear error caused by large misalignment angle.

The current navigation systems used in many autonomous mobile robotic applications, like unmanned vehicles, are always equipped with various sensors to get accurate navigation results. The key point is to fuse the information from different sensors efficiently. However, different sensors provide asynchronous measurements, some of which even appear to be nonlinear. Moreover, some sensors are vulnerable in specific environments, e.g., GPS signal is likely to work poorly in interior space, underground, and tall buildings. We propose a multi-sensor information fusion method based on a factor graph to fuse all available asynchronous sensor information and efficiently and accurately calculate a navigation solution. Assuming the sensor measurements and navigation states in a navigation system as factor nodes and variable nodes in a factor graph, respectively, the update of the states can be implemented in the framework of the factor graph. The proposed method is experimentally validated using two different datasets. A comparison with Federated Filter, which has been widely used in integrated navigation systems, demonstrates the proposed method's effectiveness. Additionally, analyzing the navigation results with data loss verifies that the proposed method could achieve sensor plug and play in software.

Nonlinear error has become the most critical factor restricting the measurement accuracy of pendulous integrating gyroscopic accelerometers (PIGA) during their improvement. The key to nonlinear error suppression for PIGA is the precise measurement and compensation of the micro product of inertia (MPOI) of the float assembly. However, the existing equipment and procedure for product of inertia (POI) measurement and compensation do not meet the accuracy requirements for MPOI. To solve this problem, novel equipment and procedures are proposed for the measurement and compensation of MPOI. The principle of the proposed measurement method is to simulate the error produced by MPOI in PIGA by using a single-axis turntable to rotate the float assembly along the eccentric axis to generate a centrifugal moment due to MPOI. The principle of the proposed compensation method is to remove the asymmetric mass to reduce the MPOI to zero. Through experimental validation, it is concluded that: (1) the measurement and compensation accuracy of the proposed method are better than 1 × 10−10 kg·m2 and 3 × 10−10 kg·m2, respectively; (2) the proposed method is validated as the MPOI is reduced from 7.3 × 10−9 kg·m2 to 3 × 10−10 kg·m2 for a real float assembly in PIGA, and the quadratic error of PIGA is reduced from 10−5/g0 to 3 × 10−7/g0.

The error coefficients of the pendulous integrating gyroscopic accelerometer (PIGA) mainly include the bias, scale factor, and nonlinear error. Previous works have fully studied and suppressed the bias and scale factor of PIGAs. At present, the nonlinear error is the most critical factor restricting the measurement accuracy of PIGAs. To address this barrier, a study on the analysis and suppression of the nonlinear error of PIGAs at the instrument level was carried out. Firstly, the error model of a PIGA is established by kinematics and dynamics analyses. Then, nonlinear error is analyzed based on the established model. Finally, a suppression method for the nonlinear error is proposed based on the analysis results. The nonlinear error analysis found that (1) the nonlinear error includes a quadratic term error caused by unequal inertia and the inertia product, cross-coupling error is caused by lateral accelerations, and error is caused by unequal stiffness; (2) unequal inertia and the inertia product were the most critical factors resulting in nonlinear error. Based on the results in the nonlinear error analysis, the suppression method for error focuses on unequal inertia and the inertia product. The proposed method of analysis and suppression was validated experimentally as the quadratic term coefficient was reduced by an order of magnitude from 1.9 × 10−6/g0 to 1.91 × 10−7/g0.

In-motion alignment of Strapdown Inertial Navigation Systems (SINS) without any geodetic-frame observations is one of the toughest challenges for odometer aided navigation system. It is difficult to obtain an accurate attitude within a short time using coarse alignment under intense maneuvering condition, so one of the main obstacles during in-motion alignment for SINS/OD is to estimate an accurate attitude during fine alignment process under large azimuth misalignment angle. However, most current in-motion alignment methods were based on linear error model. In this paper, an OD aided in-motion alignment method based on backtracking scheme for large misalignment angles is proposed. Three improvements were made as the following: (1) A continuous nonlinear 16-dimensional (16D) SINS/OD error model is derived. (2) We proposed a backtracking-based Extended Kalman filter (EKF) and (3) a strict reverse navigation method is utilized in the backward process. Experimental results illustrated that the proposed method can autonomously improve the estimated attitude accuracy under the condition of large misalignment angle.

It is necessary to locate the precise timing of switching into non-damping mode when the ship comes across zigzag maneuver, which helps avoid overshoot errors and maintain accuracy of ship's attitudes. In this paper, we propose a novel method to make the right decision on the damping/non-damping switch timing selection. Ship's in-motion data, collected by the gyrocompass system in advance, will first be pre-processed using wavelet denoising procedure and then treat as support vector machine (SVM) training in-put. Once the model is established, strapdown fiber optic gyrocompass (FOGC) can be equipped with the ability of self-judgment on when to cut off the alignment closed loops to become invulnerable and when to let it back online to remain stable by means of SVM classification schemes for switch timing recognition. Results show our method has better performance in the time of ships maneuver compared to the whole course damping network solution. Furthermore, transverse comparisons indicate our Wavelet-SVM method has better performance than BP neural network and traditional threshold method during maneuvering navigation process.

In the field of ultra high accuracy inertial measurement unit (IMU), pendulous integrating gyroscopic accelerometer (PIGA) has become a research hot spot due to its high-end performance. However, PIGA is sensitive to angular velocity, and the calibration process of PIGA-based IMU will be very complicated, which makes online self-calibration difficult to implement. To solve the above problems, we proposed an online self-calibration method utilizing angular velocity observation. The main contributions of this study are twofold: (1) An error analysis of PIGA is conducted in this paper, and the error model has also been simplified to suit the self-calibration model. (2) An improved online self-calibration method utilizing angular observation based on a simplified PIGA error model is proposed in this study. Experimental results show that the self-calibration method proposed in this study can improve the PIGA online calibration accuracy effectively (with the accuracy within 0.02 m/s/pulse), which can improve the dynamic accuracy of the PIGA.

In-motion alignment of navigation-grade strapdown inertial navigation system (SINS) combined with odometer (OD) is one of the challenging issues for the land vehicle navigation, while most current in-motion alignment methods still rely on the measurements of the global positioning system or only aim at improving the attitude alignment, thus neglecting the position alignment. Thus, one of the main obstacles during the in-motion alignment for SINS/OD is to autonomously and simultaneously obtain the high-precision attitude and position within specified time. In this paper, an in-motion alignment scheme based on the backtracking scheme is presented to solve this problem. The proposed method consists of two steps. First, an improved optimization-based coarse alignment (IOBCA) is employed to obtain the attitude and position with reasonable precision, and the gravity deflexion error projection in inertial frame caused by the positioning error is diminished, which contributes to better alignment results for the subsequent process. Second, initialized with the alignment results provided by IOBCA, a backtracking-scheme-based fine alignment combined with the Kalman filter is investigated to make a further improvement in the precision of attitude and position, during which the known initial binding position and zero velocity have been utilized again. The car-mounted field experimental results illustrate that the proposed method can not only autonomously improve the precision of attitude within a short time but also simultaneously achieve the position with high precision.

This paper develops an improved hybrid calibration scheme for the strapdown inertial navigation system (SINS) that combines the advantages of an optimal rotational norm calibration method and an improved system-level calibration method. To accurately determine the scale factors and misalignment error of gyros triad, the optimal rotation norm calibration method is applied. Similarly, the improved system-level calibration method based on the 24-dimensional error state Kalman filter (ESKF) plays an important role in accelerometer calibration and gyro biases calibration. The clockwise and counterclockwise multi-cycles rotation scheme is designed to eliminate the effects of the Earth's rate and gyros biases, and then provide accurate rotational norm to completely determine the gyros triad scale factors and misalignment. In addition, the improved ESKF system-level calibration method is employed to estimate accelerometer parameters and gyros biases. Simulation test verify the validity of the proposed method, and the calibration experiences and the verification tests of the two high-precision optical gyros inertial measurement units (IMU) are carried out. For comparison, the traditional 30-dimensional system-level calibration is also performed. The attitude error of high maneuvering swing test indicate that the gyros calibration accuracy of hybrid calibration scheme is better than that of traditional system-level calibration scheme. Furthermore, the positioning error of pure inertial navigation solution in static and dynamic condition for two calibration methods indicate that the hybrid calibration scheme significantly improves the positioning accuracy, especially in the dynamic experiment, that is, the proposed scheme provides a more accurate calibration of the IMU.

This study investigated the impact of the assimilation of satellite radiance observations in a three-dimensional variational data assimilation system (3DVAR) that could improve the tracking and intensity forecasts of the Tropical Storm Dianmu in 2021, which occurred over parts of southeast mainland Asia. The weather research and forecasting (WRF) model was used to conduct the assimilation experiments of the storm. Four sets of numerical experiments were performed using the WRF. In the first, the control experiment, only conventional data in Binary Universal Form for the Representation of Meteorological Data (PREPBUFR) observations from the National Centers for Environmental Prediction (NCEP) were assimilated. The second experiment (RDA1) was performed with PREPBUFR observations and satellite radiance data from the Advanced Microwave Unit-A (AMSU-A), and the Advanced Technology Microwave Sounder (ATMS). PREPBUFR observations and the High-resolution Infrared Radiation Sounder (HIRS-4) were used in the third experiment (RDA2). The fourth experiment (ALL-OBS) used the assimilation of PREPBUFR observations and all satellite radiance data (AMSU-A, ATMS, and HIRS-4). The community radiative transfer model was used on the forward operator for the satellite radiance assimilation, along with quality control and bias correction procedures, before assimilating the radiance data. To evaluate the impact of the assimilation experiments, a forecast starting on 00 UTC 23 September 2021, was produced for 72 h. The results showed that the ALL-OBS experiment improved the short-term forecast up to ~24 h lead time, as compared to the assimilation considering only PREPBUFR observations. When all observations were assimilated into the model, the storm’s landfall position, intensity, and structure were accurately predicted. In the deterministic forecast, the tracking errors of the ALL-OBS experiment was consistently less than 40 km within 24 h. The case study of Tropical Storm Dianmu exhibited the significant positive impact of all observations in the numerical model, which could improve updates for initial conditions and storm forecasting.

Estimating scene depth, predicting camera motion and localizing dynamic objects from monocular videos are fundamental but challenging research topics in computer vision. Deep learning has demonstrated an amazing performance for these tasks recently. This article presents a novel unsupervised deep learning framework for scene depth estimation, camera motion prediction and dynamic object localization from videos. Consecutive stereo image pairs are used to train the system while only monocular images are needed for inference. The supervisory signals for the training stage come from various forms of image synthesis. Due to the use of consecutive stereo video, both spatial and temporal photometric errors are used to synthesize the images. Furthermore, to relieve the impacts of occlusions, adaptive left-right consistency and forward-backward consistency losses are added to the objective function. Experimental results on the KITTI and Cityscapes datasets demonstrate that our method is more effective in depth estimation, camera motion prediction and dynamic object localization compared to previous models.

At present, the design and manufacturing technology of mechanically dithered ring laser gyroscope (MDRLG) have matured, the strapdown inertial navigation systems (SINS) with MDRLG have been widely used in military and business scope. When the MDRLG is working, high-frequency dithering is introduced, which will cause the size effect error of the accelerometer. The accelerometer signal has a time delay relative to the system, which will cause the accelerometer time delay error. In this article, in order to solve the above-mentioned problem: (1) we model the size effect error of the mechanically dithering of the MDRLG and perform an error analysis for the size effect error of the mechanically dithering of the MDRLG; (2) we model the time delay error of accelerometer and perform an error analysis for the time delay error of accelerometer; (3) we derive a continuous linear 43-D SINS error model considering the above-mentioned two error parameters and expand the temperature coefficients of accelerometers, inner lever arm error, outer lever arm error parameters to achieve high-precision calibration of SINS. We use the piecewise linear constant system (PWCS) method during the calibration process to prove that all calibration parameters are observable. Finally, the SINS with MDRLG is used in laboratory conditions to test the validity of the calibration method.

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.

Data assimilation with a Numerical Weather Prediction (NWP) model using an observation system in a regional area is becoming more prevalent for local weather forecasting activities to reduce the risk of disasters. In this study, we evaluated the predictive capabilities of multi-platform observation assimilation based on a WRFDA (Weather Research and Forecasting model data assimilation) system with 9 km grid spacing over the Kong-Chi basin (KCB), where tropical storms and heavy rainfall occur frequently. Data assimilation experiments were carried out with two assimilation schemes: (1) assimilating the combined multi-platform observations of PREPBUFR data from the National Centers for Environmental Prediction (NCEP) and Automatic Weather Stations (AWS) data from the National Hydroinformatics Data Center in Thailand, and (2) assimilating the AWS data only, which are referred to as DAALL and DAAWS, respectively. Assimilation experiments skill scores with lead times of 48 h and 72 h were evaluated by comparing their accumulated rainfall and mean temperatures every three hours in the AWS for heavy rainfall events that occurred on 28 July 2017 and 30 August 2019. The results show that the DAALL improved the statistical skill scores by improving the pattern and intensity of heavy rainfall events, and DAAWS also improved the model results of near-surface location forecasts. The accuracy of the two assimilations for 3 h of accumulated rainfall with a 5 mm threshold, was only above 70%, but the threat score was acceptable. Temperature observations and assimilation experiments fitted a significant correlation with a coefficient greater than 0.85, while the mean absolute errors, even at the 48 h lead times remained below 1.75 °C of the mean temperature. The variables of the AWS observations in real-time after combining them with the weather forecasting model were evaluated for unprecedented rain events in the KCB. The scores suggested that the assimilation of the multi-platform observations at the 48 h lead times has an impact on heavy rainfall prediction in terms of the threat score, compared to the assimilation of AWS data only. The reason for this could be that fewer observations of the AWS data affected the WRFDA model.

To solve the problem that the ship’s strapdown inertial navigation system (SINS) alignment accuracy decreases with the increase of the nonlinear filtering state dimension under mooring conditions, a method based on Kalman filter (KF) and Adaptive scale mini-skewness single line sampling Unscented Kalman Filter (ASMUKF) hybrid filtering algorithm is proposed in this paper. Three improvements are made as the following: (1) adopt a new sampling strategy. To obtain the ASMUKF filtering algorithm, scale mini-skewness single line sampling is used to replaced the traditional symmetrical sampling method and an adaptive scale factor is adapted into the Unscented Kalman Filter (UKF) to correct the real-time transformation sampling process; (2) the improved ASMUKF algorithm is combined with KF to form KF-ASMUKF hybrid filtering model; (3) the hybrid filtering model is divided into linear and nonlinear parts. The linear filtering part adopts the KF filtering model and the nonlinear filtering part adopts the ASMUKF model. Then, the calculation steps of the hybrid filtering algorithm is designed in this paper. The simulation and experimental results show that the hybrid filtering algorithm proposed has certain advantages over the traditional algorithm, and it can reduce the ship’s SINS calculation amount and improve alignment accuracy under mooring conditions.

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.

An improved double-factor adaptive Kalman filter called AMA-RWE-DFAKF is proposed to denoise fiber optic gyroscope (FOG) drift signal in both static and dynamic conditions. The first factor is Kalman gain updated by random weighting estimation (RWE) of the covariance matrix of innovation sequence at any time to ensure the lowest noise level of output, but the inertia of KF response increases in dynamic condition. To decrease the inertia, the second factor is the covariance matrix of predicted state vector adjusted by RWE only when discontinuities are detected by adaptive moving average (AMA).The AMA-RWE-DFAKF is applied for denoising FOG static and dynamic signals, its performance is compared with conventional KF (CKF), RWE-based adaptive KF with gain correction (RWE-AKFG), AMA- and RWE- based dual mode adaptive KF (AMA-RWE-DMAKF). Results of Allan variance on static signal and root mean square error (RMSE) on dynamic signal show that this proposed algorithm outperforms all the considered methods in denoising FOG signal.

The initial geographic latitude information is the key to the self-alignment of the strapdown inertial navigation system (SINS), but how to determine the latitude when the latitude cannot be obtained directly or in a short time? The latitude determination (LD) methods are introduced, including magnitude method, geometric method, and analytical methods 1 and 2, to solve this situation only by the output of the SINS itself. Simulation and experimental test results validate the efficiency of these LD methods. In order to improve the accuracy of the LD, the error of the LD method is derived through comparative analysis. Based on the relationship between LD error and inertial measurement unit (IMU) bias. Partial bias estimation method is introduced and executed during latitude determination. After compensating the estimated IMU bias, the accuracy of the LD will be further improved. Latitude errors are also affected by the latitude where SINS is located. Comprehensive simulation and experimental tests verify the effectiveness of the method. The IMU determined latitude can not only be used to achieve the self-alignment of the SINS, but also to correct the navigation latitude of the long-term SINS, thereby improving the autonomy and positioning accuracy of the navigation system.

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.

In the dual-axis rotation inertial navigation system (INS), besides the gyro error, accelerometer error, rolling misalignment angle error, and the gimbal angle error, the shaft swing angle and the axis non-orthogonal angle also affect the attitude accuracy. Through the analysis of the structure, we can see that the shaft swing angle and axis non-orthogonal angle will produce coning errors which cause the fluctuation of the attitude. According to the analysis of the rotation vector, it can be seen that the coning error will generate additional drift velocity along the rotating shaft, which can reduce the navigation precision of the system. In this paper, based on the establishment of the modulation average frame, the vector projection is carried out, and then the attitude conversion matrix and the attitude error matrix mainly including the shaft swing angle and axis non-orthogonal are obtained. Because the attitude angles are given under the static condition, the shaft swing angle and the axis non-orthogonal angle are estimated by the static Kalman filter (KF). This kind of KF method has been widely recognized as the standard optimal estimation tool for estimating the parameters such as coning angles (α1 , α2), initial phase angles (ϕ1,ϕ2), and the non-perpendicular angle (η). In order to carry out the system level verification, a dual axis rotation INS is designed. Through simulation and experiments, the results show that the amplitudes of the attitude angles’ variation are reduced by about 20%–30% when the shaft rotates. The attitude error equation is reasonably simplified and the calibration method is accurate enough. The attitude accuracy is further improved.

In recent years, with the emergency of high precision inertial sensors (accelerometers and gyros), gravity compensation has become a major source influencing the navigation accuracy in inertial navigation systems (INS), especially for high-precision INS. This paper presents preliminary results concerning the effect of gravity disturbance on INS. Meanwhile, this paper proposes a novel gravity compensation method for high-precision INS, which estimates the gravity disturbance on the track using the extreme learning machine (ELM) method based on measured gravity data on the geoid and processes the gravity disturbance to the height where INS has an upward continuation, then compensates the obtained gravity disturbance into the error equations of INS to restrain the INS error propagation. The estimation accuracy of the gravity disturbance data is verified by numerical tests. The root mean square error (RMSE) of the ELM estimation method can be improved by 23% and 44% compared with the bilinear interpolation method in plain and mountain areas, respectively. To further validate the proposed gravity compensation method, field experiments with an experimental vehicle were carried out in two regions. Test 1 was carried out in a plain area and Test 2 in a mountain area. The field experiment results also prove that the proposed gravity compensation method can significantly improve the positioning accuracy. During the 2-h field experiments, the positioning accuracy can be improved by 13% and 29% respectively, in Tests 1 and 2, when the navigation scheme is compensated by the proposed gravity compensation method.

For real-time solution of inertial navigation system (INS), the high-degree spherical harmonic gravity model (SHM) is not applicable because of its time and space complexity, in which traditional normal gravity model (NGM) has been the dominant technique for gravity compensation. In this paper, a two-dimensional second-order polynomial model is derived from SHM according to the approximate linear characteristic of regional disturbing potential. Firstly, deflections of vertical (DOVs) on dense grids are calculated with SHM in an external computer. And then, the polynomial coefficients are obtained using these DOVs. To achieve global navigation, the coefficients and applicable region of polynomial model are both updated synchronously in above computer. Compared with high-degree SHM, the polynomial model takes less storage and computational time at the expense of minor precision. Meanwhile, the model is more accurate than NGM. Finally, numerical test and INS experiment show that the proposed method outperforms traditional gravity models applied for high precision free-INS.

An inertial navigation system (INS) has been widely used in challenging GPS environments. With the rapid development of modern physics, an atomic gyroscope will come into use in the near future with a predicted accuracy of 5 × 10−6°/h or better. However, existing calibration methods and devices can not satisfy the accuracy requirements of future ultra-high accuracy inertial sensors. In this paper, an improved calibration model is established by introducing gyro g-sensitivity errors, accelerometer cross-coupling errors and lever arm errors. A systematic calibration method is proposed based on a 51-state Kalman filter and smoother. Simulation results show that the proposed calibration method can realize the estimation of all the parameters using a common dual-axis turntable. Laboratory and sailing tests prove that the position accuracy in a five-day inertial navigation can be improved about 8% by the proposed calibration method. The accuracy can be improved at least 20% when the position accuracy of the atomic gyro INS can reach a level of 0.1 nautical miles/5 d. Compared with the existing calibration methods, the proposed method, with more error sources and high order small error parameters calibrated for ultra-high accuracy inertial measurement units (IMUs) using common turntables, has a great application potential in future atomic gyro INSs.