Integrated Navigation Algorithm Research Articles

A shipboard integrated navigation algorithm based on smartphone built-in GNSS/IMU/MAG sensors

The rapid development of built-in sensors in smartphones has inspired a variety of ubiquitous public navigation applications. Nevertheless, previous works have focused on vehicle and pedestrian navigation by smartphones, with limited research on shipboard navigation. In this contribution, we designed a multi-sensors fusion navigation algorithm that integrates the global navigation satellite systems (GNSS), inertial measurement unit (IMU), and magnetometer (MAG) to achieve high-precision horizontal positioning on shipboard for smartphones. Considering the changeable motion state of a ship and the setting of non-holonomic constraint (NHC) noise, a magnetometer-based turning detection method is proposed, and a NHC model with adaptive noise is constructed based on the turning detection results. We conducted a lake experiment in Taku Forts Lake, Tianjin, using sensor data collected from a Xiaomi MI8 through our self-developed ’Sensor Logger’ app. The experimental results demonstrated a high success rate of 94.22 % for magnetometer-based turning detection which can effectively detect turning motions. Compared to the traditional algorithm without constraint information, the roll, pitch and yaw accuracy improve by approximately 34.7 %, 17.9 %, and 57.9 %, respectively. Additionally, the position and velocity accuracy in the east and north directions improve to 0.0926 m, 0.1779 m, 0.0548 m/s, and 0.0589 m/s, respectively, representing enhancements of about 10.7 %, 7.4 %, 10.5 %, and 6.4 %. Overall, the proposed algorithm efficiently improves the shipboard navigation accuracy of smartphones, especially in terms of attitude accuracy.

An Adaptive Fast Incremental Smoothing Approach to INS/GPS/VO Factor Graph Inference

In response to asynchronous and delayed sensors within multi-sensor integrated navigation systems, the computational complexity of joint optimization navigation solutions persistently rises. This paper introduces an adaptive fast integrated navigation algorithm for INS/GPS/VO based on factor graph. The factor graph model for INS/GPS/VO is developed subsequent to individual modeling of the Inertial Navigation System (INS), Global Positioning System (GPS), and Visual Odometer (VO) using the factor graph model approach. Additionally, an Adaptive Fast Incremental Smoothing (AFIS) factor graph optimization algorithm is proposed. The simulation results demonstrate that the factor-graph-based integrated navigation algorithm consistently yields high-precision navigation outcomes even amidst dynamic changes in sensor validity and the presence of asynchronous and delayed sensor measurements. Notably, the AFIS factor graph optimization algorithm significantly enhances real-time performance compared to traditional Incremental Smoothing (IF) algorithms, while maintaining comparable real-time accuracy.

A Robust and Adaptive AUV Integrated Navigation Algorithm Based on a Maximum Correntropy Criterion

A Robust and Adaptive AUV Integrated Navigation Algorithm Based on a Maximum Correntropy Criterion

An integrated navigation algorithm assisted by CNN-Informer during short-time GNSS outages

Abstract Inertial Navigation System (INS) and Global Navigation Satellite System (GNSSs) are commonly used in integrated navigation systems. The GNSS navigation system, however, is not autonomous, and its signals are susceptible to environmental influences leading to poor navigation results. In order to improve the positioning accuracy of the INS/GNSS integrated navigation system during GNSS outages, a hybrid algorithm of Convolutional Neural Network (CNN)-Informer model-assisted INS is proposed. The CNN-Informer model combines the advantages of each of the convolutional neural network and the Informer network. It utilizes CNN to rapidly extract spatial features from input data, employs the Informer network to establish relationships between inputs and outputs, and acquires pseudo-GNSS signals to compensate for position errors in the INS. Lastly, we evaluate the proposed algorithm through six sets of experiments conducted on public datasets and real road scenarios. The comparative results demonstrate that the proposed method offers a more accurate and reliable solution during GNSS outages. Specifically, CNN-Informer can improve navigation accuracy by 81.46% over MLP and by 58.91% over LSTM during 20-second GNSS outages.

Attitude solving aided UWB/IMU integrated algorithm with real-time NLOS suppression

In response to the challenges posed by non-line-of-sight (NLOS) errors and inadequate attitude estimation accuracy in ultra-wideband and inertial measurement unit (UWB/IMU) integrated navigation algorithms in the complex environment, a robust UWB/IMU integrated positioning scheme is proposed. On one hand, the utilization of the robust local weighted regression algorithm (RLWR) is employed to mitigate the impact of NLOS errors on UWB data. RLWR incorporates information from nodes with known pseudo-range within local time intervals into the regression model, enhancing the identification of NLOS errors and improving positioning accuracy. On the other hand, the variational Bayesian filter algorithm based on adaptive conjugate gradient descent (ACGD) is proposed to improve the accuracy of IMU attitude calculation. The algorithm leverages an ACGD approach to optimize the attitude output of the accelerometer and magnetometer. The output is then incorporated into the variational Bayesian filtering system alongside the gyroscopic attitude output compensated by integrated positioning. Compared to conventional quaternion calculation and gradient descent linear filtering methods, the approach exhibits superior precision and stability. The experimental findings demonstrate that the amalgamation of the proposed NLSO identification suppression algorithm and the enhanced attitude computation algorithm confers significant advantages in terms of both localization accuracy and attitude estimation precision in complex environments. Moreover, the robust solution presented in the paper ensures the preservation of filter performance in the event of UWB measurement failure.

An Adaptive INS/CNS/SMN Integrated Navigation Algorithm in Sea Area

In this paper, we present an innovative inertial navigation system (INS)/celestial navigation system (CNS)/scene-matching navigation (SMN) adaptive integrated navigation algorithm designed to achieve prolonged and highly precise navigation in sea areas. The algorithm establishes the structure of the INS/CNS/SMN integrated navigation system. To ensure the availability of CNS in the Nanhai Sea (South China Sea) area, a cloud and fog model is meticulously constructed. Three distinct types of sea area landmarks are defined, and an automated classification model for sea area landmarks, employing support vector machines (SVM), is developed. Corresponding matching methods and strategies for these landmarks are also delineated. Concurrently, the observable probability of each landmark is computed to generate a probability cloud, representing the usability of sea area landmarks. The proposed INS/CNS/SMN adaptive integrated navigation algorithm is simulated and validated across varied altitudes and trajectories in the sea area. The results show that CNS and SMN can dynamically assist INS in achieving prolonged and highly precise navigation.

Adaptive federated filter–combined navigation algorithm based on observability sharing factor for maritime autonomous surface ships

The integrated navigation system ensures maritime autonomous surface ships (MASSs) to safely, efficiently, and autonomously complete various operations in different complex navigation environments. Investigating robust algorithms for integrated navigation is crucial for enhancing the fault tolerance of the system and ensuring the stable and continuous output of the ship’s motion state. However, existing research primarily focused on optimising particular filtering algorithms or examining the foundations of information allocation within a predetermined integrated navigation structure. As such, strategies for enhancing the robustness of the MASS integrated navigation system and the design of subsystems for federated filters in the event of navigation sensor failures have not been sufficiently investigated for complex maritime navigation scenarios. Consequently, this research introduces an observability sharing factor accounting for both system characteristics and state estimation performance in integrated navigation systems, employing nonlinear sampling filtering. Subsequently, a robust integrated navigation framework with distributed federal filter is developed. Within this framework, an adaptive federated filtering integrated navigation algorithm is proposed based on the observability sharing factor to allocate information in federated filtering. Finally, both the theoretical correctness and effectiveness of the algorithm were verified through simulations and real-ship experiments to assist with the development of accurate and fault-tolerant maritime navigation systems.

A Novel Tightly Coupled Solution for SINS/Polarized Navigation System/Odometer Integration Using Polarized and Installed Angle Errors Model

Precise and reliable autonomous navigation in a GPS-denied environment is critical to unmanned systems. The idea of combining SINS, the polarized navigation system (PNS), and the odometer (OD) inspired by desert ants has been proven to be effective for autonomous navigation. However, there are two major challenges for polarization navigation nowadays: inaccurate modeling and obtaining reliable heading information when some sensor channels are blocked. Aiming at these two problems, a tightly-coupled solution for SINS/PNS is proposed in this paper. To obtain a refined integrated navigation system model, the installation errors between the inertial units and PNS, and polarization angle calculation errors are analyzed and modeled for SINS/PNS. Then, to quickly gain the accurate state estimation, an improved iterative unscented filtering method is devised. In particular, the sigma-point updating step with the conditional distribution of high-dimensional Gaussian distribution random variables is developed, which employs partial states to sample in each iteration to reduce the calculation burden. Finally, a detection and elimination mechanism for the abnormal light channels is provided to enhance the reliability of the integration in the presence of a light blockage. The optical channels for navigation are chosen using this mechanism depending on the difference between the predicted and measured incident light intensities. The results in both simulations and outdoor experiments show that the proposed method provides a higher heading estimation accuracy than the traditional SINS/PNS navigation method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article is motivated by the inaccurate modeling and obtaining reliable heading in the presence of light occlusion for the polarization navigation. Various integrated navigation algorithms based on polarized skylight have been widely developed. However, the complex environment and inaccurate modeling limit the application of the polarization navigation. This article gives a novel accurate modeling method and reliable navigation algorithm. Tightly-coupled model with installation errors and the polarization angle error aims to improve the accuracy of the polarization navigation model. The improved iterative unscented Kalman filter is utilized to quickly obtain accurate state estimation. And the light detection and elimination mechanism is used to select normal light channels to navigate in the presence of light blockage. This navigation method can also extend the application of the polarization navigation.

Adaptive BDS/MEMS INS navigation algorithm for low-dynamic carrier based on motion characteristics detection and dual-antenna Position/Velocity constraints

With the rapid development of navigation technology, the application fields of unmanned technology are expanding constantly, including the low-dynamic scenarios, such as unmanned agricultural machinery. In a low-dynamics scenario, the classic dual-antenna BeiDou Navigation Satellite System (BDS)/micro-electro-mechanical system inertial navigation system (MEMS INS) integrated navigation algorithm has two limitations. First, the reliability of a priori system noise is significantly reduced because of the large number of turning and bumping maneuvers. Second, the accuracy of the dual-antenna BDS heading angle and a priori measurement noise cannot satisfy the necessary requirements in a complex environment. To solve these problems, an adaptive BDS/MEMS INS navigation algorithm based on low-dynamic carrier-motion characteristics and dual-antenna constraint information is proposed. This new method can identify turning and bumping states and appropriately adjust the MEMS INS system noise matrix. To avoid the influence of a low accuracy heading angle, the heading angle measurement information was replaced by position and velocity measurement information. Simultaneously, the velocity and distance vectors between the dual antennas are added as prior constraints that can adaptively adjust the BDS measurement noise matrix. The experimental results show that the positioning and heading angle accuracies of the proposed method are controlled within centimeters and 1°, respectively, thus significantly improving the navigation performance in the carrier turning, bumping, and occlusion environments. This research will be helpful in low-dynamic applications such as unmanned agricultural machinery.

An invariant error-based SINS/DVL/USBL tightly coupled integrated navigation algorithm and its robust state estimator

The existing strapdown inertial navigation system (SINS)/Doppler velocity log (DVL)/ultra-short baseline system (USBL) integrated navigation error models directly apply algebraic differences to define the vector error, which is not strictly accurate. Considering that the invariant error definitions derived from Lie group theory have been used in the navigation field to obtain more accurate linear error models, in this paper, a new SINS/DVL/USBL integrated navigation system is investigated based on the invariant error definition and tightly coupled structure. In order to suppress the effect of measurement outliers on navigation accuracy, a new statistical similarity measure (SSM)-based multiple adaptive outlier-robust state estimator (MAORSE) is proposed. It decomposes the noise covariance matrix into multiple sub-matrices. Through the estimation and adjustment of sub-matrices, the influence of abnormal observations on the filtering results is weakened while realizing the full utilization of normal observation information. The test results demonstrate the effectiveness and superiority of the proposed invariant error-based SINS/DVL/USBL tightly coupled integrated navigation algorithm and SSM-based MAORSE.

Integrated navigation algorithm for deep-sea AUV based on M-estimation and heavy-tailed noise

This paper presents an integrated navigation algorithm for deep-sea Autonomous Underwater Vehicles (AUVs) based on M-estimation and heavy-tailed noise to solve the problems of inaccurate noise models in traditional navigation algorithms for deep-sea AUVs, significant delays in Ultra-Short Baseline (USBL) acoustic positioning, and the inability to estimate deep-sea ocean currents. The algorithm encompasses four techniques: ①A Strapdown Inertial Navigation Systems (SINS)/USBL integrated navigation algorithm based on M-estimation and heavy-tailed noise models. ②Estimation and compensation of USBL acoustic delay positioning errors. ③Estimation and compensation of steady or slowly varying ocean currents. ④Considering the distance between the submerged vehicle and the center of the earth and the variation of gravity acceleration with depth. The first and second techniques are the innovations of this article, which can effectively improve the USBL calibration accuracy with only a slight increase in computational complexity. The significant positioning error caused by long-term voyages of large-depth AUVs in the middle layer of the ocean can be effectively suppressed using the third and fourth technologies. The results of the semi-physical simulation and lake experiment demonstrate the ability of the proposed algorithm to significantly improve navigation accuracy and robustness in complex underwater environments compared to conventional methods.

Seamless MEMS-INS/Geomagnetic Navigation System Based on Deep-Learning Strong Tracking Square-Root Cubature Kalman Filter.

To suppress inertial navigation system drift and improve the seamless navigation capability of microelectromechanical system-inertial navigation systems/geomagnetic navigation systems (MEMS-INS/MNS) in geomagnetically unlocked environments, this paper proposes a hybrid seamless MEMS-INS/MNS strategy combining a strongly tracked square-root cubature Kalman filter with deep self-learning (DSL-STSRCKF). The proposed DSL-STSRCKF method consists of two innovative steps: (i) The relationship between the deep Kalman filter gain and the optimal estimation is established. In this paper, combining the two auxiliary methods of strong tracking filtering and square-root filtering based on singular value decomposition, the heading accuracy error of ST-SRCKF can reach 1.29°, which improves the heading accuracy by 90.10% and 9.20% compared to the traditional single INS and the traditional integrated navigation algorithm and greatly improves the robustness and computational efficiency. (ii) Providing deep self-learning capability for the ST-SRCKF by introducing a nonlinear autoregressive neural network (NARX) with exogenous inputs, which means that the heading accuracy can still reach 1.33° even during the MNS lockout period, and the heading accuracy can be improved by 89.80% compared with the single INS, realizing the continuous high-precision navigation estimation.

A SINS/DVL navigation method based on hierarchical water velocity estimation*

Aiming at the problem that Doppler velocity log (DVL) cannot measure the velocity of the vehicle in the middle water environment, a Strap-down Inertial Navigation System (SINS)/DVL integrated navigation method based on hierarchical water velocity assistance is proposed. Firstly, according to the principle of DVL water layer flow measurement, the paper gives a hierarchical water recurrence principle. On this basis, a water velocity estimation method based on average weighted recurrence is proposed. The carrier depth information is introduced in this method, and the carrier velocity information is obtained by means of average value. This method can prevent the carrier velocity anomaly caused by the large error of single-layer water velocity measurement. Secondly, in view of the problem that the DVL water velocity measurement is easily disturbed in the middle water environment, a sliding window and a Chebyshev polynomial fitting function are introduced to realize the robust treatment of the water velocity. On this basis, combined with the Huber M robust filter algorithm, a hierarchical water velocity assisted integrated navigation algorithm based on the improved Huber M robust estimation is proposed to further improve the autonomous navigation accuracy in the middle water environment. Finally, the method proposed in this paper is verified by simulation. The results show that the hierarchical water velocity estimation method proposed in this paper can effectively estimate the water flow velocity, and its robust filtering algorithm can further improve the SINS/DVL integrated navigation accuracy in the middle water environment.

GNSS/MEMS IMU vehicle integrated navigation algorithm constrained by displacement vectors in urban environment

Abstract The global navigation satellite system (GNSS) and a micro-electro-mechanical system inertial measurement unit (MEMS IMU) can be integrated to form a robust navigation system, providing continuous and accurate location information on dynamic vehicles. However, the performance of a GNSS/MEMS IMU integrated navigation system is easily affected by the accuracy of measurement noise matrix, which is significantly reduced in the urban environment. The adaptive Kalman filter can improve the measurement noise matrix reliability by constructing robust equivalent weight factors; however, GNSS observations are easily misjudged as exception sources that can deteriorate the filter stability. To address these problems, a novel integrated algorithm with a displacement vector constraint is proposed based on the kinematic characteristics of vehicles, which are considered as judgment factors. In this case, the measurement noise can be adjusted accordingly only when the GNSS observations are judged as abnormal. In this study, two types of vehicle navigation experiments were conducted: a low-speed wheeled robot in a campus environment and a dynamic vehicle in an actual urban environment. The experimental results showed that the three-dimensional navigation accuracy was improved by 47% and 55% compared with the conventional algorithm under the two different environments, respectively.

A Bioinspired Navigation System for Multirotor UAV by Integrating Polarization Compass/Magnetometer/INS/GNSS

Stable and accurate heading angle estimation is challenging for low-cost small UAV navigation, especially in the presence of geomagnetic anomaly. In this paper, a bio-inspired integrated navigation system (BINS) is designed such that the environmental adaptability of the navigation system can be enhanced. A bio-inspired integrated navigation algorithm is presented to fuse the information of polarized skylight, geomagnetic field, inertia, and global navigation satellite system (GNSS). The relationship among ambient light intensity, degree of polarization, and accuracy of polarization compass is revealed. Thus, the integrated polarization compass can be adapted to more complex weather conditions. A tightly coupled integrated navigation model is developed for BINS to fuse the information of polarization compass and magnetometer. Within the developed scheme, the polarization compass can not only correct the heading error of the system, but also help the magnetometer reconstruct the actual local geomagnetic field distribution. The problem of inaccurate geomagnetic field model in the magnetic anomaly environment is addressed. Moreover, the Chi-Square test is used to detect polarization compass outliers such that the navigation modes can be switched promptly. Finally, the ground static experiments and UAV flight tests are carried out. In comparison of traditional polarization navigation and geomagnetic navigation, the proposed system effectively improves the heading accuracy.

Backward smoothing adaptive SVDCKF integrated navigation algorithm

Aiming at the problem that the Cubature Kalman filter (CKF) algorithm has a non-positive definite of the covariance matrix in GNSS/SINS integrated navigation, which leads to the failure of Cholesky decomposition and the inability to estimate GNSS measurement noise, a backward smoothing adaptive CKF integrated navigation algorithm based on Singular Value Decomposition (SVD) is proposed. Backward smoothing adaptive CKF based on Singular Value Decomposition (BS-A-SVDCKF) algorithm replaces the Cholesky decomposition in standard CKF with SVD, constructs the test threshold for backward smoothing by using the relatively stable noise of the SINS system, and adaptively estimates based on different measurement characteristics when the GNSS measurement noise changes abruptly. Experimental results show that compared with adaptive SVDCKF (A-SVDCKF), backward smoothing SVDCKF (BS-SVDCKF) and SVDCKF, the average positioning accuracy of the proposed algorithm is improved by 32.12%, 57.07% and 68.66%, the average operating efficiency is reduced by 2.19% compared with SVDCKF, and 0.57% and 3.60% higher than that of BS-SVDCKF and A-SVDCKF, which improves the positioning accuracy of the integrated navigation system and ensures real-time.

Real-time marine PPP-B2b/SINS integrated navigation based on BDS-3

The BeiDou-3 global navigation satellite system was operated successfully in July 2020. It broadcasts precise point positioning (PPP)-B2b signals and provides real-time PPP services free of charge, which greatly meets the navigation needs of real-time users, especially warship navigation. This paper first introduces the PPP-B2b real-time positioning model, and then expounds the two-velocity measurement algorithm of Doppler and carrier phase time difference. Next, it combs the extended Kalman filter (EKF) and factor graph optimization (FGO) integrated navigation algorithm in detail, and finally comprehensively evaluates the real-time integrated navigation performance of PPP-B2b/strapdown inertial navigation system (SINS) through the measured data at sea. The experimental results show that the real-time dynamic positioning accuracy of PPP-B2b can reach the decimeter level, and the positioning accuracy is not significantly improved when integrated with SINS. Furthermore, dynamic alignment experiments results show after adding time-differenced carrier phase and Doppler velocimetry information, the convergence accuracy of yaw misalignment angle has been greatly improved. The accuracy of the EKF algorithm is 16.7% higher than that of the FGO algorithm after the convergence of the yaw angle error.

An GNSS/INS Integrated Navigation Algorithm Based on PSO-LSTM in Satellite Rejection

When the satellite signal is lost or interfered with, the traditional GNSS (Global Navigation Satellite System)/INS (Inertial Navigation System) integrated navigation will degenerate into INS, which results in the decrease in navigation accuracy. To solve these problems, this paper mainly established the PSO (particle swarm optimization) -LSTM (Long Short-Term Memory) neural network model to predict the increment of GNSS position under the condition of satellite rejection and accumulation to obtain the pseudo-GNSS signal. The signal is used to compensate for the observed value in the integrated system. The model takes the advantages of LSTM, which is good at processing time series, and uses PSO to obtain the optimal value of important hyperparameters efficiently. Meanwhile, the improved threshold function is used to denoise the IMU (inertial measurement unit) data, which improves the SNR (signal-to-noise ratio) of IMU outputs effectively. Finally, the performance of the algorithm is proved by actual road test. Compared with INS, the method can reduce the maximum errors of latitude and longitude by at least 98.78% and 99.10% while the satellite is lost for 60 s, effectively improving the accuracy of the GNSS/INS system in satellite rejection.

Architecture of integrated navigation systems with enhanced coordinate accuracy and fault detection

The integration of GNSS/INS is becoming increasingly pivotal for the precise operation of uncrewed aerial vehicles, especially in agriculture. This integration is underscored by two primary necessities: the assurance that after prolonged operation, the accuracy of the navigation parameters remains uncompromised and the implementation of an integrated navigation algorithm that is both straightforward and dependable, demanding minimal processing power from the onboard chips. This article first introduces the centralized Kalman filter approach, employed to merge GPS and INS systems, based on a loosely coupled framework. This amalgamation is streamlined, significantly curtailing the computational demands of the system, and reducing its intricacy. Subsequently, the discrepancies in the INS system's navigation parameters, as gauged by the discrete Kalman filter algorithm, are rectified using a feedback amendment method. This strategy effectively counters the degradation in navigational accuracy that typically ensues from extended operational periods.

Improved Adaptive Federated Kalman Filtering for INS/GNSS/VNS Integrated Navigation Algorithm

To address the issue of low positioning accuracy in unmanned vehicles navigating in obstructed spaces due to easily contaminated navigation measurement information, an improved adaptive federated Kalman filtering INS/GNSS/VNS integrated navigation algorithm is proposed. In this algorithm, an inertial navigation system (INS) serves as the common reference system, and, together with the global navigation satellite system (GNSS) and visual navigation system (VNS), they form the subsystems that together make up the main system. In the event of faulty measurement values in the subsystems, a combination of the residual chi-square and sliding-window averaging methods are used for fault detection to improve the fault tolerance of the integrated navigation algorithm. Additionally, an adaptive sharing factor is proposed to adjust the accuracy of the integrated navigation algorithm based on the accuracy of the sub-filters. Simulation experiments demonstrated that, compared with classic federated Kalman filtering, the proposed algorithm reduced the root mean square errors (RMSEs) of the three-dimensional position by 56.4%, 54.8%, and 43.4% and the root mean square errors of the three-dimensional velocity by 71.0%, 72.1%, and 28.4% in the event of sub-filter faults, effectively solving the problem of low positioning accuracy for unmanned vehicles in obstructed spaces while ensuring the real-time performance of the system.