Navigation Parameters Research Articles

Development of a method for predicting hazardous ship trajectories under uncertainty of navigator actions

The object of the research is the automation processes in maritime navigation to ensure the safety of ship movement by predicting their trajectories in complex aquatic areas, such as narrow passages, straits, and ports. The research applied six key stages to create a comprehensive method for clustering and predicting ship trajectories based on ECDIS data. In the first stage, ship movement trajectories were constructed according to risk categories, using the LCSS and DTW algorithms to compare planned and actual trajectories. This allowed for the accurate identification of course deviations and the determination of potentially dangerous sections of the trajectory. The second stage implemented clustering using the DBSCAN and GMM algorithms. DBSCAN was used to identify the density of points in space, and GMM provided modeling of cluster probabilities, allowing for better risk zone determination. The third stage applied the Douglas-Peucker compression algorithm to reduce the number of points in the trajectories, which preserved key characteristics and optimized data processing. In the fourth stage, ship movement stability was assessed using the Fourier transform, which allowed the detection of high-frequency oscillations that may indicate movement instability caused by changes in course or speed. The fifth stage included fuzzy clustering of trajectories using the Gaussian Mixture Model (GMM), which allowed modeling the probabilities of dangerous trajectories, considering the uncertainty of navigational parameters. At the final stage, a multilayer neural network (MLP) was used to predict future points of ship trajectories. The model accurately predicted the ship's coordinates, enabling timely trajectory adjustments. Experimental results showed that the developed method increased the accuracy of ship trajectory prediction to 72–81 % and also significantly reduced the final error, ensuring effective risk management during complex navigation.

Unstructured environment navigation and trajectory calibration technology based on multi-data fusion

In order to effectively improve the accuracy and efficiency of unstructured environment navigation and trajectory calibration, a multi data fusion based unstructured environment navigation and trajectory calibration method was studied. Described the basic principles of the Strapdown Inertial Navigation System and Doppler Log. After introducing DVL velocity information and relative position information of underwater robots into SINS, the Kalman filter fusion algorithm was used to obtain the system's state equation and measurement equation. The navigation parameter error and device error parameters of the system were selected as the state variables. The difference between SINS output speed and DVL measurement speed, as well as the difference between SINS output position and relative position, are used as the speed and position measurements of the measurement system. Error estimation is obtained through indirect filtering, and the accuracy of navigation and positioning is improved through output correction. The experimental results show that the proposed method has a good calibration effect and can effectively improve the accuracy and efficiency of trajectory calibration in unstructured environments.

Autonomous ground vehicle gravity anomaly measurement and dynamic error compensation

Abstract To address the issue that dynamic gravity anomaly measurement is overly dependent on GNSS and can’t be measured autonomously at this stage, this paper proposes an autonomous ground vehicle dynamic gravity anomaly measurement method based on a strapdown inertial navigation system (SINS), odometer (OD), barometer and platform gravimeter. The SINS/OD /barometer integrated navigation solution delivers high-precision navigation parameters, completes the calculation of correction terms, and performs the autonomous dynamic gravity anomaly measurement combined with the primary measurement results of the platform gravimeter. Numerical calculations provide the requirements for the application of the proposed method, and the cut-off frequency for extracting gravity anomalies is 0.02 Hz, as determined by power spectral density analysis. In order to further improve the measurement accuracy and account for dynamic errors caused by vehicle maneuvering, a long-short-term memory (LSTM) model of recurrent neural network (RNN) is introduced. A series of experiments under multiple circumstances with repeated lines were conducted in Tianjin, China, and the static measurements along the line were taken using CG-5 to provide true values of gravity anomalies. The results demonstrate that the autonomous measurement scheme can achieve accuracy comparable to GNSS-assisted, and that dynamic error compensation algorithm based on LSTM improves the dynamic gravity measurements accuracy significantly without sacrificing the spatial resolution of gravity anomalies.

Verification of the AIS service availability model based on dynamic data streams recorded from three receiving stations in the Polish coastal area

The reliability aspects of the operation of radio navigation systems constitute a crucial element for the safety of maritime navigation.. Technological progress in ship traffic monitoring is achieved through the design of ship systems and shore infrastructure equipped with Automatic Identification System (AIS) devices. One of the issues with AIS operation is the limited availability of the service in the form of data streams with an extended data age recorded on the receiving side. Another problem is the emission and reception by ships of incomplete positional reports without navigational parameters. Such situations render the system operationally unfit in terms of processed information. Therefore, it is essential to investigate the operational characteristics of radio navigation systems and develop tools to monitor the AIS service status on the receiving side. This article presents the development of a model for the availability of an AIS for vessels based on the determined mean time of the occurrence of incomplete navigation parameter values in AIS messages and the results of research in the domain of time and frequency using a mathematical method of the Fast Fourier Transform (FFT). The study results refer to six basic navigation parameters and show a varying service availability factor for the navigation parameters under study, i.e. the latitude (LAT), longitude (LON), speed over ground (SOG), course over ground (COG), heading (HDT), and the rate of turn (ROT). The data recorded by three receiving AIS stations on the Polish coast, i.e. PLKOL, PLSZZ, and PLSWI, were used as a key source of practical knowledge on the limitations of the AIS service availability. The experiment observed interruptions in the regular transmission of data from navigation equipment in the AIS service operational zone. As a result, the functional relationship was described based on the spectral analysis of the frequency of occurrence of times between the service repair (Time To Repair, TTR), and the model was proposed to be applied to the study of other variables. The presented model is a tool that allows for improving the monitoring of vessel traffic in terms of reliability, which directly affects the improvement of maritime traffic safety.

ВЛИЯНИЕ ПОГРЕШНОСТЕЙ ИЗМЕРЕНИЯ КООРДИНАТ СУДНА НА КАЧЕСТВО ПРОЦЕССА УПРАВЛЕНИЯ

Autopilots are an integral part of modern ships. However, at present, many tasks are emerging, including the ones in the unmanned navigation field, requiring the use of new control algorithms and new means of monitoring navigation parameters. In particular, to solve such problems as keeping a vessel on a given trajectory, automating the ships’ divergence and similar tasks, it is necessary to have means of continuous monitoring of the ship’s location. For this purpose, receivers of global navigation satellite systems can be applied. To model control processes, it is necessary to know the distribution of positioning errors of modern devices. Some works show that over long time intervals (a day or more), positioning errors can be considered a random process with a Gaussian distribution. This paper presents the experimental study results of the distribution of positioning errors of a ship navigation receiver operating in the GPS and GLONASS systems, in a combined GPS/GLONASS mode, as well as in the indicated modes with differential corrections. The paper shows that at time intervals of seconds – minutes (characteristic of ship’s control systems), positioning errors of the navigation receiver cannot be represented by a random process with a Gaussian distribution law. The paper presents the results of a mathematical modelling of the process of holding a ship on a given trajectory using experimental values of positioning sensor errors. For the research, a mathematical model of an innovative ship with a wheel-propulsion steering complex is used. An algorithm is created that makes it possible to keep a vessel on a given trajectory with an accuracy acceptable for a practical use, commensurate with deviations determined by the design features of the ship’s hull and its propulsors.

Stable solution to the problem of autonomous navigation of moving objects on analytical trajectory intervals based on the results of inertial measurements

Provision of solution of the problem of autonomous navigation on a long time interval is considered. The main problem when using inertial navigation systems is caused by the accumulation of positioning and angular orientation errors. It is shown that this problem can be solved by combining methods of nonlinear filtering in processing the results of inertial measurements of platform-free inertial navigation systems and methods of reducing the dimensionality of the vector of navigation parameters on trajectory sections described by analytical models. Orthodromic (shortest) and circular intervals, most typical for program trajectories of transport objects – highways, railroads, airlines, etc., are considered as such trajectory sections. For circular intervals, analytical dependencies of the spatial coordinates of strapdown inertial navigation systems were obtained for the first time. These dependencies make it possible to reduce the dimension of the vector of navigation parameters and, as a consequence, to build a model of an autonomous observer of navigation parameters to use equations excluded from the general system of these parameters. It is shown that using stochastic nonlinear filtering methods it is possible to solve the problem of noise-resistant autonomous navigation on trajectory intervals described by analytical models. The proposed approach to solving the problem of autonomous navigation of moving objects makes it possible to significantly reduce computational costs in the practical implementation of algorithms for nonlinear filtering of current navigation parameters in comparison with traditional models of strapdown inertial navigation systems. The effectiveness of the proposed approach is illustrated with a numerical example. The results obtained are useful in developing navigation support for various transport objects moving along program trajectories, for example, aircraft for various purposes, railway, road, river transport, etc.

System analysis and optimization of antennas of radio electronic systems

The methodological foundations are formulated and the problems of system substantiation of antenna requirements based on the objective characteristics of radio electronic systems (RES) are considered. The contradictions of the indicator parameters of the objective characteristics of the RES in the formation of requirements for antennas are noted. For space-based airborne radar complexes, radar systems for measuring navigation parameters, and communication systems of repeater satellites servicing areas with a complex boundary shape, analytical relations have been obtained linking the characteristics and parameters of antennas with the objective characteristics of the RES. For the considered types of RES, the main directions for optimizing the characteristics and parameters of antennas are shown.

Registration of Interferometric DEM by Deep Artificial Neural Networks Using GPS Control Points’ Coordinates as Network Target

The Shuttle Radar Topography Mission (SRTM) satellite’s digital elevation model (DEM) is an important tool for studying topographic features on a medium-spacing scale. Data were collected and processed using the satellite’s orbital and navigation parameters with selected global GPS stations for verification. Distortion may be expressed by surveying measurements, such as position, distance, area, and shape. This study focuses on this distortion and proposes a new registration method to reduce its effect. Because of generality, the purpose shapes were excluded from this study. The proposed registration method depends on precise GPS control points that act as the ground truth for describing the considered surveying measurements. The processing was carried out using deep artificial neural networks (DANN) to produce a new registered DEM. A comparison was made between the original DEM and the new one, focusing on the selected surveying measurements. Another comparison was made between the GPS coordinates and SRTM polynomials to determine the potential of the proposed system. Some statistical investigations were applied to determine the level of significance of the distortion in each surveying measurement. The study shows that the distortion is highly significant; therefore, the proposed registration method is recommended to fix the distortion.

An autonomous and high-accuracy gravity disturbance compensation scheme for rotary inertial navigation system

Abstract With the increasing demands for long-endurance and high-accuracy inertial navigation system (INS), gravity disturbance has been identified as one of the major error sources with decisive effects on the performance of INS. To address the problem, this paper proposes an autonomous and high-accuracy gravity disturbance compensation scheme for rotary INS (RINS). The high-accuracy velocity measured by the laser Doppler velocimeter is fused with the angular velocity measured by the gyroscope to obtain navigation parameters, such as velocity, position and attitude, that are not affected by gravity disturbance. The navigation parameters independent of gravity disturbance are matched with the gravity disturbance-related navigation parameters output by RINS, and a measurement model containing gravity disturbance information is obtained. Besides, the intrinsic coupling relationship between gravity disturbance, gravity disturbance rate and gravity disturbance gradient is revealed, and a state-space model is established to accurately reflect the time-varying characteristics of gravity disturbance. Furthermore, the gravity disturbance is estimated and compensated in real-time through the optimal estimation algorithm. The results of vehicle experiments indicate that the gravity disturbance estimation precision of the proposed scheme is better than 2.15 mGal (1σ), and its horizontal position accuracy is better than 50 m at a driving distance of 80 km.

ДВОКАНАЛЬНИЙ ГРАВІМЕТР АВІАЦІЙНОЇ ГРАВІМЕТРИЧНОЇ СИСТЕМИ

A two-gyro gravimeter of the aviation gravimetric system is proposed and investigated, which provides higher measurement accuracy than known gravimeters, due to the elimination of errors from the cross angular velocities of the base and the angular velocity of the Earth's rotation and the measurement of the full vector of the acceleration of gravity. To measure the acceleration of gravity, an AGS is proposed, which has greater accuracy and speed than known and consists of a three-stage gyroscope located in the inner and outer frames, equipped with interframe correction systems, which include an angle sensor (DC) located on the axis of the inner frame of the gyroscope and a torque sensor (DM) connected to its output is located on the axis of the outer frame. DM, located on the axis of the inner frame, is connected to the DC output. An additional, identical to the first, three-stage gyroscope, the rotor of which rotates in the opposite direction from the main gyroscope, is introduced in the AGS under consideration. The additional gyroscope of the AGS is also provided with similar correction systems, which consist of a DC located on the axis of the inner frame, and a DM located on the axis of the outer frame connected to its output, a DC located on the axis of the outer frame, to the output of which a DM located on the axis is connected inner frame The centers of gravity of two identical (main and additional) gyroscopes are shifted by the same distance in one direction along the axes of rotation of the rotors of the gyroscopes relative to the axes of the outer frames. The vectors of the kinetic moments of the two gyroscopes are oppositely directed. In the two-channel gravimeter, two output signals of linear acceleration are formed as the sum of signals from DC of two gyroscopes relative to one z-axis and as the sum of signals from DC of two gyroscopes relative to the second x-axis. The output signals are fed to the computer. Both gyroscopes of the system's gyrogravimeter are mounted on a platform whose angular position is controlled by a motor (DV) installed on the x-axis and a DV on the z-axis. Both motors control the angular position of the platform by signals. The computer also receives signals from the system for determining navigation parameters and from the height meter.

Target location method of intelligent deicing robot based on nonlinear auto disturbance rejection neural network

A visual navigation scheme for intermittent walking deicing robots was designed to address the issues of multiple iterations, long computation time, and poor real-time performance in the nonlinear optimization of the original SLAM system. A computer image acquisition unit, a computer image processing module, and a visual navigation parameter extraction algorithm were also designed. Implemented a visual navigation system for deicing robots based on image processing. It can meet the navigation requirements of the deicing robot. Simulation and experiments have shown that the method proposed in this paper can quickly and accurately identify abnormal point clouds. The visual servo control scheme constructed in this paper is aimed at robot task operations with unknown system calibration and target depth information. By calibrating the robot vision system, the conversion between camera pixel coordinates and robot base coordinates is achieved, with a transmission frame rate of 53.65 per second; The maximum error in positioning accuracy in space is 10.6 mm. The feature trajectory of visual space is smooth and stable within the camera's field of view, and the end movement of Cartesian space robots is stable without rebound, resulting in high grasping and positioning accuracy.

Testing and Analysis of Selected Navigation Parameters of the GNSS/INS System for USV Path Localization during Inland Hydrographic Surveys.

One of the main methods of the path localization of moving objects is positioning using Global Navigation Satellite Systems (GNSSs) in cooperation with Inertial Navigation Systems (INSs). Its basic task is to provide high availability, in particular in areas with limited access to satellite signals such as forests, tunnels or urban areas. The aim of the article is to carry out the testing and analysis of selected navigation parameters (3D position coordinates (Northing, Easting, and height) and Euler angles (pitch and roll)) of the GNSS/INS system for Unmanned Surface Vehicle (USV) path localization during inland hydrographic surveys. The research used the Ellipse-D GNSS/INS system working in the Real Time Kinematic (RTK) mode in order to determine the position of the "HydroDron" Autonomous Surface Vehicle (ASV). Measurements were conducted on four representative routes with a parallel and spiral arrangement of sounding profiles on Lake Kłodno (Poland). Based on the obtained research results, position accuracy measures of the "HydroDron" USV were determined using the Ellipse-D GNSS/INS system. Additionally, it was determined whether USV path localization using a GNSS/INS system working in the RTK mode meets the positioning requirements for inland hydrographic surveys. Research has shown that the Ellipse-D system operating in the RTK mode can be successfully used to position vessels when carrying out inland hydrographic surveys in all International Hydrographic Organization (IHO) Orders (Exclusive, Special, 1a/1b and 2) even when it does not work 100% correctly, e.g., loss of RTK corrections for an extended period of time. In an area with limited coverage of the mobile network operator (30-40% of the time the receiver operated in the differential mode), the positioning accuracy of the "HydroDron" USV using the Ellipse-D GNSS/INS system working in the RTK mode was from 0.877 m to 0.941 m for the R95(2D) measure, depending on the route travelled. Moreover, research has shown that if the Ellipse-D system performed GNSS/INS measurements using the RTK method, the pitch and roll error values amounted to approx. 0.06°, which is almost identical to that recommended by the device manufacturer. However, when working in the differential mode, the pitch and roll error values increased from 0.06° to just over 0.2°.

Application of Object Contrast for Forming Images Used in Technical Vision Systems for Navigation of Mobile Robots

The purpose of the article is to substantiate the feasibility of using object contrast as an informative feature for the formation of images used in technical vision systems. This goal is achieved by studying the dependence of the contrast of objects in images on the viewing geometry and determining the conditions under which the greatest similarity of the compared images is ensured. The solution to the first problem is based on the presentation of reference information about sighted objects, taking into account the navigation parameters of mobile robots. By modeling in the MATLAB software environment for typical viewing conditions, selective images were obtained using randomly selected fragments from Google Earth Pro, the distribution of contrast values and the cross-correlation function of the original and selective images. The influence of viewing angles on the distribution of contrasts and the formation of the decisive function was determined. The studies were performed for viewing angles of -60˚, -80˚ and -90˚ for altitudes in the range from 500 to 600 meters. The most significant result is a model of a set of reference images, taking into account the influence of navigation parameters on the contrast of objects, as well as experimentally established dependences of the distribution of contrasts for typical viewing conditions. The novelty of the work lies in the fact that the procedure for generating images and the decision function using the contrast of objects has been further developed. This will significantly increase the efficiency of selection of objects with insignificant brightness characteristics.

Sensitivity analysis of profile navigation command of underwater gliders to the initial heading error for improving trajectory accuracy

With the widespread application of underwater gliders (UGs) in marine research, there is an increasing demand for improved trajectory control accuracy. However, the initial heading error is unavoidable in internally actuated UGs, making it challenging to rectify the trajectory error generated in the heading error correction process. To effectively mitigate the impact of this error on trajectory accuracy, this study analyzes the sensitivity of profile navigation command parameters to the initial heading error through dynamic modeling of Petrel-L UG. Firstly, a simulator is developed to model the behaviors of Petrel-L, mainly involving dynamic modeling, underwater navigation, low-level control, and environment model. Subsequently, the sensitivity of profile navigation parameters in various commands to the initial heading error is analyzed. Surrogate model and Monte Carlo simulation are integrated to improve the computational speed of the analysis while preserving calculation precision. The average maximum single-profile horizontal error is 661 m, and the average maximum single-profile course error is 6.47°. Among profile navigation parameters, the target pitch during diving is proved to be the primary factor affecting the maximum trajectory error, and the increase of this parameter can enhance trajectory accuracy. This research also provides valuable reference for path following and station-keeping control of other UGs.

Effect of underwater vehicle wake on sound propagation characteristics in stratified medium

Due to the uneven distribution of seawater temperature and salinity, the density distribution at different depths is different, thus forming a density step layer with a certain gradient. Acquiring the wake internal wave field generated by underwater vehicles passing through this layered structure and mastering its modulation characteristics for the sound field can provide new technical support for the tracking and identification of underwater vehicles. In this paper, the real size model of a certain type of underwater vehicle is taken as the research object to explore the characteristics of its wake internal wave field, and the influence of navigation parameters on the wake field and the change of winning characteristics under the influence of internal waves are simulated and analyzed. The results show that the navigation parameters of underwater vehicles have obvious influence on the wake field, and then have specific influence on the sound field structure in a certain range, especially on the sound signal of the sound field.

Devising an approach for the automated restoration of shipmaster’s navigational qualification parameters under risk conditions

The object of this study is the safety control system of ship management, by identifying and restoring the qualification parameters of shipmasters in critical situations. The task solved in the study is the timely determination of an insufficient level of qualification for the performance of certain operations in controlling the movement of the ship, by applying a formal-logical model of detecting the intuitive actions of the operator-shipmaster and gradually restoring his/her qualification parameters using the devised method. The stages of development and the formal-logical structure of the model and method in terms of cognitive automation were described in detail as the study results. It was possible to ensure early detection of risks when controlling the movement of the ship in 56 % of cases, during a laboratory experiment on simulators, which in 24 % of cases turned out to be particularly dangerous. The interpretation of the results involved algorithmizing complex and formalized data on the actions of operators and the application of the method of restoring their qualification parameters, which allowed a comprehensive approach to safety management. The distinguishing features of the findings were to predict the level of danger by simulating maritime operations with input navigational and individual conditions. This made it possible to improve the effectiveness of operations to 89 %, reduce the phenomenon of loss of control over the course to 32 %, reduce critical situations to 7 % and the cost of resources. The scope and conditions of practical use involve a comprehensive assessment of external and internal influences on the level of danger, delay in decision-making by operators, as well as sailing conditions. The simulation results could be used to devise strategies for planning maneuvers, predicting risks, and developing maritime security systems

Cooperative navigation of unmanned aerial vehicle formation with delayed measurement

Abstract This paper focused on the problem of positioning accuracy degradation caused by delayed measurement information in Unmanned Aerial Vehicle (UAV) formation cooperative navigation under complex environments such as cities and hills, and presented a non-synchronous compensation algorithm based on kinematic constraints and constructed a distributed cooperative navigation filter based on the analysis of the basic operating characteristics of inertial devices, satellite receivers, and ranging sensors. In the UAV formation, the leader-UAV is equipped with Real-Time Kinematic (RTK) differential equipment and airborne data link to construct the airborne reference beacons and provide cooperative navigation services for the wingmen-UAV. Firstly, the navigation filtering framework with inertial sensors as the core is established. Secondly, the non-synchronous compensation filter is constructed by using the kinematic constraint model, which compensates and corrects the non-synchronous air-based position of the leader-UAV, and reduces the effect of delayed measurement on the positioning error of the system. Then the fault diagnosis algorithm is utilized to complete the identification and rejection of abnormal range values in the case of Non-Line-of-Sight (NOLS). Finally, the navigation parameters are solved by the Kalman filter. Simulation results show that the non-synchronous compensated filtering proposed in this paper can improve the absolute positioning accuracy by 55%, which effectively improves the cooperative navigation performance and robustness under the presence of random time delay in the measurement information.

Echo-Level SAR Imaging Simulation of Wakes Excited by a Submerged Body.

The paper introduces a numerical simulation method for Synthetic Aperture Radar (SAR) imaging of submerged body wakes by integrating hydrodynamics, electromagnetic scattering, and SAR imaging simulation. This work is helpful for better understanding SAR images of submerged body wakes. Among these, the hydrodynamic model consists of two sets of ocean dynamics closely related to SAR imaging, namely the wake of the submerged body and wind waves. For the wake, we simulated it using computational fluid dynamics (CFD) numerical methods. Furthermore, we compared and computed the electromagnetic scattering characteristics of wakes under various navigation parameters and sea surface conditions. Following that, based on the operational principles and imaging theory of synthetic aperture radar (SAR), we established the SAR raw echo signal of the wake. Employing a Range-Doppler (RD) algorithm, we generated simulated SAR images of the wake. The results indicate that utilizing Computational Fluid Dynamics (CFD) numerical methods enables the simulation of wake characteristics generated by the motion of a submerged body with different velocities. The backscattering features of wakes are closely associated with the relative orientation between the wake and the radar line of sight. Under specific wind speeds, the wake gets masked within the sea surface background, resulting in less discernible characteristics of the wake in SAR images. This suggests that at lower speeds of submerged body or under specific wind conditions, the detectability of the wake in SAR images significantly diminishes.

The bearings and distances isolines combinations of the navigational landmarks pair for the vessel fixed position determination

The issues of applying basic navigation parameters (bearing and distance), and their isolines traditionally used in navigation practice in coastal waters are studied in the paper. A new distinctive feature is the use of isolines combinations (three distance arcs, two isoazimuths, a hyperbola and an ellipse) based on measured bearings and distances to the pair of landmarks to obtain the vessel fixed positions with high precision. The traditional navigation methods (the theory of isolines, the generalized method of lines position, the method of least squares) are involved as a mathematical framework. The mathematical argumentation and the isolines characteristics of bearings and distances, their combinations (difference and sum of distances, difference of bearings) are given. The solutions of the surplus equations of the lines position under random error influence by the least squares method and the accuracy assessment of the vessel fix position by the radial error including the reduced variant to compensate the systematic errors are suggested. The principal points of the research are supported by the graphic interpretation, and the given expressions are adjusted to the practical application and navigation systems software development. The computer simulation that shows the radial error of the fixed position by seven position lines is at least two times less than by any pair of position lines has been carried out. The formalization of the proposed methods in the automatic navigation systems or in autonomous ship control systems will enable the navigator on board or at operating the vessel remotely to solve the problems of the navigation information processing in coastal and congested waters on a new level.

A Fast Self-Calibration Method for Dual-Axis Rotational Inertial Navigation Systems Based on Invariant Errors.

In order to ensure that dual-axis rotational inertial navigation systems (RINSs) maintain a high level of accuracy over the long term, there is a demand for periodic calibration during their service life. Traditional calibration methods for inertial measurement units (IMUs) involve removing the IMU from the equipment, which is a laborious and time-consuming process. Reinstalling the IMU after calibration may introduce new installation errors. This paper focuses on dual-axis rotational inertial navigation systems and presents a system-level self-calibration method based on invariant errors, enabling high-precision automated calibration without the need for equipment disassembly. First, navigation parameter errors in the inertial frame are expressed as invariant errors. This allows the corresponding error models to estimate initial attitude even more rapidly and accurately in cases of extreme misalignment, eliminating the need for coarse alignment. Next, by utilizing the output of a gimbal mechanism, angular velocity constraint equations are established, and the backtracking navigation is introduced to reuse sensor data, thereby reducing the calibration time. Finally, a rotation scheme for the IMU is designed to ensure that all errors are observable. The observability of the system is analyzed based on a piecewise constant system method and singular value decomposition (SVD) observability analysis. The simulation and experimental results demonstrate that this method can effectively estimate IMU errors and installation errors related to the rotation axis within 12 min, and the estimated error is less than 4%. After using this method to compensate for the calibration error, the velocity and position accuracies of a RINS are significantly improved.