This article investigates a fast azimuth gyro drift calibration method based on low-cost single-axis rotation strapdown inertial navigation system (SINS) under mooring conditions, utilizing an adaptive robust Kalman filter (ARKF) framework. Firstly, a rotation modulation KF model based on the angular rate extended measurement equation is designed, which effectively enhances the observability of heading misalignment angle and azimuth gyro drift. The validity of the proposed method is verified through singular value decomposition. Secondly, an online estimation method for measurement noise variance based on variational Bayesian (VB) is employed to address the issue of inaccurate acquisition of the extended measurement equation under dynamic conditions. To tackle the degradation of filter performance caused by VB's iterative computations, a novel robust method employing multi-correction factors is formulated. Subsequently, a multivariate nonlinear optimization model utilizing an improved particle swarm optimization algorithm is established, enabling global optimization of correction factors while preventing local optima entrapment. This framework achieves multi-channel measurement error decoupling and selective error correction, thereby substantially improving filter stability. Experimental validation via Stewart platform testing demonstrates the method's efficacy, with azimuth gyro drift estimation accuracy reaching 0.45 degrees/h over one-hour trials.

In complex marine environments, achieving low-cost, highly reliable, and continuous navigation is crucial for the intelligent and autonomous operation of unmanned surface vehicles (USVs). Currently, the integrated Global Navigation Satellite System and Strapdown Inertial Navigation System (GNSS/SINS) serves as the primary navigation architecture for USVs. While the cost of high-performance GNSS receivers has steadily decreased, high-precision SINS remains prohibitively expensive. Consequently, micro-electromechanical system (MEMS)-based SINS has emerged as a preferred alternative due to its favorable balance of cost, power consumption, and size. However, significant inertial sensor errors make it difficult to maintain high-precision positioning during GNSS outages. To address this limitation, the single-axis rotational inertial navigation system (SRINS) has been introduced. Nevertheless, constrained by the single-axis mechanical structure and complex sea state disturbances, the system still struggles to effectively modulate random errors and azimuth gyroscope drift, rendering it insufficient for highly demanding navigation tasks. To overcome these bottlenecks, this article systematically reviews four core technologies: (1) Comprehensive denoising and temperature drift compensation techniques for MEMS gyroscopes; (2) rapid moving-base initial alignment models under high sea state disturbances; (3) fast online calibration methods for azimuth gyroscope drift; and (4) adaptive and robust GNSS/SINS integration architectures capable of accommodating high-dynamic conditions and non-Gaussian interference. Finally, this article discusses the engineering conflict between deploying high-precision algorithms and the limited onboard computational capacity of USVs. It concludes by highlighting a highly promising navigation paradigm for future research: the integration of factor graph optimization with physics-informed deep learning.

To further improve the positioning accuracy of the multiple unmanned surface vessel (USV) systems, we introduce an information fusion algorithm equipped with adaptive fuzzy logic (FZ) control. The FZ controller is designed for the filter to effectively respond to measurement noise amidst dynamic disturbances. To address the inefficient innovation updating of the measurements for the nonlinear model and the potential lack of error covariance positive definiteness, a maximum a posteriori-based iterated square-root cubature Kalman Filter (MISCKF) is employed. To fully utilize the relative information among the USVs, a local-cooperation navigation framework is proposed. The effectiveness of the proposed framework and the FZMISCKF is validated through simulations and experiments.

In order to improve the positioning accuracy and reliability of intelligent farm machinery in orchard environment, a combined GNSS(Global Navigation Satellite System)/SINS (Inertial Navigation System)navigation system for orchard in loose combination mode was built based. An improved UKF algorithm, IUKF (Improved Unscented Kalman Filter), is proposed for the problem that interference in the orchard environment causes observation coarseness in the measurement data and the standard UKF causes degradation in the filtering accuracy of the combined navigation system. Physical experiments show that compared with UKF, the average absolute error of IUKF is reduced by more than 47.16% and the root mean square error is reduced by more than 59.78%, and IUKF meets the requirements of orchard positioning accuracy.

In this article, the fast and precise initial alignment of the low-cost rotary strapdown inertial navigation system under mooring conditions is investigated. The unscented Kalman filter (UKF) is used to address model nonlinearity and to achieve fast alignment for large misalignment angles. A generalized multifading strong tracking UKF (GSTUKF) is proposed to effectively compensate for the kinematic model errors caused by mooring and rotary motions. The performance of the standard strong tracking UKF cannot be optimal because only a portion of the fading factors associated with the directly observable state variables can be obtained approximately using the analytical method. By contrast, using the iteration method to calculate the full-dimensional fading factors precisely, the GSTUKF has greater robustness and adaptability. To find out the optimal fading factors in real time, the multivariate nonlinear optimization model is first designed, and then the iteration approach based on a hybrid algorithm consisting of particle swarm optimization and beetle antennae search is developed, which has no risk of falling into a local minimum. Simulations and experiments are conducted to validate the GSTUKF's effectiveness. The experiments demonstrate that the proposed method reduces the yaw error by 47.2% compared with the standard strong tracking UKF.

The conventional SINS/CNS integrated navigation system equipped on ballistic missiles is typically equipped with attitude measurement, which can only estimate the gyro drift and has no effect on accelerometer bias. To address the issue, an improved multi-source information fusion method containing a new nonlinear framework called SINS/RKCNS with the indirect horizon reference and kinematic constraint is proposed, and a MAP-based modified iterated CKF is involved to increase positioning accuracy and system robustness. Furthermore, to reduce the influence of correlated noise, state augmentation is employed in the iterative process. Eventually, experiments are conducted, and the results confirm the effectiveness of the proposed approach.

The large misalignment angle errors generated by coarse alignment and the uncertainty time-varying calibration errors generated by the inertial measurement unit reduce the alignment accuracy, increase the alignment time, and ultimately limit the application of backtracking Kalman filters into In-motion fine alignment scene. This paper proposes a robust backtracking cubature Kalman filter (CKF) approach based on Krein space theory to overcome these issues. Specifically, considering the effect of dynamic model uncertainties of the alignment process, a linear robust filter and the existence conditions of optimal estimation are constructed to restrain the uncertainty interference according to Krein space theory. Meanwhile, an adaptive window adjustment algorithm is designed to intelligently determine the backtracking interval in different backtracking filtering stages and cross-scene motion environments, which is founded on the innovation variance gradient detection. Furthermore, using the statistical linearization scheme, the quasi-linear CKF model is derived to assist in resolving the nonlinear large misalignment angle within the Krein linear space framework for In-motion alignment. Experimental verification results from a vehicle In-motion alignment test illustrate that the proposed Krein backtracking CKF approach is effective in improving the alignment accuracy and shortening the alignment time simultaneously.

In order to compensate for the disadvantages of the large computational scale and high requirements for chip arithmetic of the traditional extended Kalman filter, reduce the computational volume of the extended Kalman filter, improve the stability of the motor controller, and reduce the dependence of the algorithm on chip arithmetic while ensuring the control accuracy. An extended Kalman filter motor control system based on weighted average fusion is designed. A weighted average fusion extended Kalman filter without position sensor control algorithm is also designed, which can complete the control of the motor with significantly reduced arithmetic load on the main controller chip, and the algorithm has high robustness and high anti-interference capability. Finally, the effectiveness and feasibility of this motor control system is further verified by simulink simulation analysis and physical platform experiments.

The large misalignment errors of horizontal and azimuthal angle cannot be converged rapidly on the sea surface due to extra disturbance of linear and angular motions caused by wind and waves, which increases the time cost of marine vehicles alignment process and ultimately limits the SINS quick working capability. In order to solve the above problem, an adaptive multiple backtracking UKF method based on Krein space theory is proposed in this paper. Firstly, considering time-varying calibration errors of inertial sensors, a novel robust posterior filtering equation in Krein space is designed to improve the matching degree between the physical process and the mathematical model. Moreover, combined with the multiple forward and reverse navigation processes, an adaptive calculation times control method in backtracking UKF based on the innovation is constructed to solve the nonlinear fast alignment problem in the case of large misalignment angle errors with the purpose of further intelligently shortening the alignment time and ensuring alignment accuracy simultaneously in different periods and working environments. The physical experiment results demonstrate that the horizontal and azimuthal alignment accuracy of the proposed algorithm are improved compared with standard CKF alignment algorithm.

The accuracy and robustness of tightly coupled global navigation satellite system (GNSS)/strapdown inertial navigation system (SINS) integrated navigation parameter estimation are hindered by outliers caused by GNSS measurements under multipath interference and nonline-of-sight (NLOS) conditions. To address the limitations of robust estimation and the mismatch of state posterior probability density function (pdf) approximation, a novel M-estimation-based robust iterated cubature Kalman filter (ICKF) is developed to minimize the impact of GNSS outliers while improving the correction effect of high-quality line-of-sight (LOS) GNSS measurement in this article. The nonlinear weighted least squares regression model and objective function are established for outlier mitigation, including a sigma-point iterative filtering framework and an M-estimation method of down-weighting GNSS measurements. Specifically, the maximum a posteriori (MAP) estimation idea is used to design the sigma-point iterated filtering framework, which makes the posteriori pdf constantly close to the high likelihood confidence interval to obtain excellent nonlinear approximation effects. Furthermore, to avoid the inherent nonconvexity of the traditional M-estimation method, the relaxation compensation scheme based on the adaptive control factor is introduced into the robust loss function to accelerate the convergence of the penalty weight of GNSS outliers. The availability of the proposed method for GNSS outlier mitigation is proved by vehicle field tests under multipath interference and NLOS conditions.

Integrated navigation systems are prone to faults in complex environments, necessitating the isolation or mitigation of their effects on the system. This paper introduces a federated Kalman filter (FKF) structure based on the kernel multivariate exponentially weighted moving-average (KMEWMA) control chart, which incorporates statistical process control techniques to detect and mitigate faults effectively in integrated navigation systems. The proposed method demonstrates outstanding fault detection capability, successfully addressing both gradual and sudden-varying faults. Compared with chi-square test, the KMEWMA control chart could detect faults more precisely. Furthermore, instead of solely isolating faults, the system adaptively adjusts them to enhance positioning accuracy and stability. The simulation results validate the effectiveness and superiority of the proposed method.

This paper considers a robust integrated navigation system that copes with the time-varying measurement noise in a hostile environment. The Chi-square test is used to get rid of the disturbance of measurement outlier. And the estimation of measurement noise is provided by the variational Bayesian method to perform an accuracy state estimation within a challenged navigation environment. With regard to a practical system, the computation burden of the proposed algorithm is vital for the embedded system resource. The detailed numerical simulations demonstrate that the proposed filter has an advantage over the traditional filter in global performance.

In challenging circumstances, the estimation performance of integrated navigation parameters for tightly coupled GNSS/SINS is impacted by outlier measurements. An effective solution that employs a novel iterative sigma-point structure with a modified robustness optimization approach for enhancing the error compensation effectiveness and robustness of filters utilized in GNSS challenge conditions is proposed in this paper. The proposed method modifies the CKF scheme by incorporating nonlinear regression and numerous iteration processes for ameliorating error compensation. Subsequently, a loss function and penalty mechanism are implemented to enhance the filter's robustness to outlier measurements. Furthermore, to fully incorporate valid information of the innovation and speed up the operation of the proposed method, the outlier measurement detection criteria are established to bypass the penalty mechanism against measurement weights in the absence of outliers in GNSS measurements. Field experiments demonstrate that the proposed method outperforms traditional methods in mitigating navigation errors, particularly when multipath errors and non-line-of-sight (NLOS) reception are increased.

This article considers the unknown measurement noise covariance problem in the nonlinear situation of a navigation system. Aiming at the contaminated global position system (GPS) signals and the outlier environment, there are many variational Bayesian (VB)-based Gaussian approximation methods in the integrated navigation system (INS). However, the integrated navigation is nonlinear, especially for the inaccurate initial state provided by the initial alignment stage. The VB method is first incorporated into cubature particle filter (PF), of which the proposal distribution is set as cubature Kalman filter (CKF) to provide the accuracy and stable estimation for the application of navigation system. Then, the Kullback–Leibler distance (KLD) resampling method is merged into the VB-based cubature PF to supply sufficient particles that enhance the stability of the proposed filter. The numerical simulation demonstrates that the proposed filter does better at presenting accurate and stable estimation than the VB-based CKF, and the experiments verify the effectiveness of the proposed filter for the application of INS.

Underwater Doppler Velocity Log (DVL) measurement is susceptible to slow changes owing to interference from forced maneuvers, ditches and fish shoals under uncharted ocean environments, where mismatched measurement model may affect navigation performance of SINS/DVL navigation applications. To solve such problems, an enhanced Kalman filtering method based on adaptive measurement noise estimation technique is proposed in this paper. By designing a centripetal acceleration errors-reinforced holonomic velocity constraint (HVC) and the adaptive Sage-Husa approach, the parameters of the Kalman filter are adjusted online to maintain the system stability and filtering accuracy, which contributes to the measurement outlier mitigation in SINS/DVL navigation applications. The sea trial of autonomous underwater glider (AUG) reveals the proposed method is resistant to external disturbances and maintains the filter convergence in uncharted ocean environments while providing more accurate position estimates than existing methods.

In order to improve the positioning accuracy and reliability of intelligent farm machinery in orchard environment, a combined GNSS(Global Navigation Satellite System)/SINS (Inertial Navigation System)navigation system for orchard in loose combination mode was built based. An improved UKF algorithm, IUKF (Improved Unscented Kalman Filter), is proposed for the problem that interference in the orchard environment causes observation coarseness in the measurement data and the standard UKF causes degradation in the filtering accuracy of the combined navigation system. Physical experiments show that compared with UKF, the average absolute error of IUKF is reduced by more than 47.16% and the root mean square error is reduced by more than 59.78%, and IUKF meets the requirements of orchard positioning accuracy.

Strapdown inertial navigation system/celestial navigation system (SINS/CNS) is commonly used to high-precision missile navigation. Conventional SINS/CNS based on attitude measurement estimates the gyro drifts effectively. However, it does nothing about the accelerometer bias, which affect the positioning accuracy. Aiming at this problem, an improved SINS/Refraction and Kinematic-CNS (SINS/RK-CNS) method is proposed based on the indirect horizon reference measurement of star refraction. In this method, the relationship between refraction apparent height and missile position is deduced, and a new nonlinear integrated navigation model is established with the kinematic constraint of missile. Furthermore, corresponding observation noise model is developed to improve the positioning accuracy and the system robustness. Finally, simulations are conducted to test the performance with ballistic missile. Systematic position errors are calculated by traditional SINS/CNS method and SINS/RK-CNS based on EKF and UKF under different initial misalignment errors. The results confirm that the proposed SINS/RK-CNS has a significant effect on estimating the accelerometer bias. Compared to the traditional approach, three-axis position errors are decreased by 84.27%, 89.53% and 85.02%, respectively.

The outlier measurement affects the accurate estimation effect of tightly coupled global navigation satellite system (GNSS) and strapdown inertial navigation system (SINS) integrated navigation parameters under GNSS-challenged environment. To improve the convergence speed and robustness of nonlinear filter used in tightly coupled GNSS/INS under GNSS-challenged environment, an iterated cubature Kalman filter (CKF) based on the improved robust estimation method is proposed. Firstly, the mind of nonlinear least squares regression is included into CKF framework, and multiple iterations are used to improve the convergence speed of the filter and the error compensation effect. Then, a simplified iterated update structure is developed to reduce the computational cost for integrated navigation system. Moreover, the Geman McClure (GM) loss function is introduced to reduce the weight of outlier measurement, which improves the robust estimation ability of the filter. The field experiment indicates that the proposed method has better compensation effect than traditional methods on navigation errors in the case of frequent signal outages.

This paper proposes an adaptively robust unscented Kalman filter (ARUKF) for the rotation micro-electro-mechanical system based strapdown inertial navigation system (MINS) to achieve fast in-motion initial alignment in the presence of large misalignment angles. First, UKF is utilized to address nonlinearity issues resulting from large misalignment angles. Second, the strong tracking strategy is implemented to robustly compensate for dynamic model errors during the transition phase. The variational Bayesian is then applied in the steady state to adaptively estimate the time-varying measurement noises. The proposed method speeds up convergence during the transition phase and improves convergence precision during the steady phase. In conclusion, the turntable experiments verify the validity of the proposed method.

A novel strong tracking unscented Kalman filter (NSTUKF) is proposed in this study for fast initial alignment of the single-axis rotation inertial navigation system (SRINS) in dynamic conditions. To begin, the NSTUKF model is created, the UKF is utilized to achieve fast alignment under large misalignment angles, and strong tracking is employed to increase the robustness of the UKF against dynamic model errors. Second, the optimal fading factors of all channels are calculated using a heuristic technique based on the gravitational search algorithm (GSA) to improve the performance of strong tracking. Finally, the turntable experiment is implemented, and the results reveal that the NSTUKF outperforms existing approaches in terms of convergence and accuracy.