Calibration and Compensation of the Scale Factor Errors in DTG POS

Inertial navigation system (INS) is utilized in several applications such as missile guidance, space navigation, and marine navigation. An efficient calibration method for improving the inertial navigation system accuracy is presented. As the vital error sources in the inertial navigation system are associated with the deterministic errors of the inertial measurement unit (IMU), the proposed technique precisely determines the calibration parameters to reduce these errors, especially the gyro’s scale factor, and non-orthogonality error. In recently proposed calibration methods, the scale factor is determined by the output/input relationship linear fitting. Although the determined scale factor meets the requirement of various navigation systems to some extent it doesn’t fit the high accurate ones, such as guided missiles and marines. That’s because the gyro damping effect is changed with different input angular rates which causes the gyro scale factor varying. The presented calibration method tackles this phenomenon by assigning different weights to each input rate through a weighted linear regression fit. Moreover, the gyro nonorthogonal error which comes from the imperfection gyro mounting is merely determined by the lateral coupling signal. But the fact is that the lateral coupling signal is not induced from the gyro non-orthogonal error only but also comprises the gyro signal which is directly proportional to the centripetal acceleration caused by the applied angular rates. Even though this signal is tiny but it will be accumulated for the long-time navigation system and degrades its accuracy. The presented calibration method utilizes a lateral accelerometer to realize that signal and tear out it to accurately obtain the nonorthogonal error. Finally, a laboratory test for the proposed method was carried out to ensure its effectiveness. Where the actual applied rates are determined twice, once with the built error model by the presented calibration method and the other by the traditional one.

NRLI-UAV: Non-rigid registration of sequential raw laser scans and images for low-cost UAV LiDAR point cloud quality improvement

Unmanned Aircraft Systems (UASs) can collect high resolution and high quality images for local mapping. Before the UAS images can be used for accurate mapping tasks in local areas, the precise position and orientation of the UAS images should first be determined. Direct georeferencing by POS (Position and Orientation System), a combination of GPS (Global Positioning System) and IMU (Inertial Measurement Unit), is the best choice; however, most commercial UASs cannot carry highly accurate IMUs because of the limited payload. Therefore, this study will discuss the accuracy of indirect georeferencing for UAS images. One approach for indirect georeferencing is general aerial triangulation (AT) by using well-distributed ground control points (GCPs). The other one is GPS-supported AT with GPS observations as airborne controls. In this paper, the camera is calibrated by the field method, and the accuracy of these two approaches for indirect georeferencing is presented. Based on 20 horizontal check points and 29 vertical check points, this study shows the stereoscopic viewing accuracy of general AT for UAS images, collected by Canon EOS 5D Mark II camera with 24 mm F/1.4L II USM lens at a flying height of 550 m, is about 0.26 m (ca. 1.73 pixels) in planimetry and 0.27 m (ca. 1.80 pixels) in height. GPS-supported AT produced the stereoscopic viewing accuracy about 0.44 m (ca. 2.93 pixels) in planimetry and 0.55 m (ca. 3.67 pixels) in height. The test results show that the accuracy of these two indirect georeferencing approaches of fixed-wing UAS images can be used for updating local 1/5,000 topographic maps in Taiwan.

According to the urgent need of high-precision navigation system to future fighters, this paper researches on a dynamic error excitation and calibration method for high-precision IMU. The Kalman filter model including installation errors, scale factor errors and random constant errors of the inertial measurement unit (IMU) as state variables for online identification is established. The relationship between IMU errors and aircraft maneuver manner is derived, and the dynamic flight track to incite IMU errors is designed. Simulation results verify the feasibility of the proposed dynamic error parameter excitation and calibration method, which can incite and identify the IMU error effectively. With the error identification results, the IMU errors are compensated and the precision of the INS is improved significantly.

A new dynamic calibration method for IMU deterministic errors of the INS on the Hypersonic Cruise Vehicles

Position and orientation system (POS) is a key technology widely used in remote sensing applications, which integrates inertial navigation system (INS) and GPS using a Kalman filter (KF) to provide high-accuracy position, velocity, and attitude information for remote sensing motion compensation. However, when GPS signal is blocked, the POS accuracy will decrease owing to the unbounded INS error accumulation. To improve the reliability and accuracy of POS, this paper proposes a hybrid prediction method for bridging GPS outages. This method uses radial basis function (RBF) neural network coupled with time series analysis to forecast the measurement update of KF, resulting in reliable performance during GPS outages. In verifying the proposed hybrid prediction method, a flight experiment was conducted in 2011, based on a high-precision Laser POS. Experimental results show that the proposed hybrid prediction method is more effective than two other methods (KF and RBF neural network).

Image misalignment during image stitching is a common issue for the mechanically stitched CCDs in the aerial cameras due to the relative image motion between CCDs. In this paper, we analyze the error in imaging stitching for the mechanically stitched CCDs and propose a compensation method based on position and orientation system (POS). First, the imaging relationship of overlapping pixels in mechanical stitching is analyzed. The imaging model of adjacent CCD is constructed according to the collinear equation. The effects of stitching staggered distance, carrier attitude change and flight speed on the image mosaic of overlapping areas are given. Monte Carlo algorithm is used to analyze the statistical value of image mosaic error in overlapping area under typical working conditions. Then, a geometric correction method based on POS recording of external orientation elements of adjacent CCD imaging is proposed. The overlapping area stitching error is reduced from 14.9 pixels to 0.4 pixels which meets the engineering requirements. The mechanical stitching mathematical model, analysis and correction method established in this paper have strong engineering and application significance for mechanical stitching of aerial cameras.

Position and orientation system (POS) is widely applied in remote sensing applications, which provide high-accuracy position, velocity, and attitude information for remote sensing motion compensation. As a multisensory system, time-delay usually occurs during signal preprocessing, transmission, integration, filtering, etc., which decrease the measurement accuracy. As the POS motion parameter varies nonlinearly, the time-delay error can’t be precisely compensated by the conventional linear method. To solve this problem, a novel time-delay error compensation method based on Support Vector Machine (SVM) is proposed, and Particle Swarm Optimization (PSO) is used to optimize the key parameters of SVM. In verifying the proposed method, a flight experiment was conducted. Experimental results show that the proposed method can effectively compensate the time-delay error of POS, and is more accurate than the conventional one.

<sec>The Taiji program is a space mission designed to detect low-frequency gravitational waves. The mission's success hinges on the precise operation of its core payloads, particularly the inertial sensors, which are responsible for measuring the residual acceleration noise of the test masses. The duration of a space-based gravitational wave detection mission is 3 to 5 years. During this period, the shift in the satellite’s center of mass due to propellant consumption and other factors, as well as the drift in the scale factors caused by electronic component aging, will gradually degrade the accuracy of inertial sensor data. Therefore, it is necessary to regularly perform in-orbit calibration of inertial sensor parameters.</sec><sec>In this work, we develop a calibration scheme, which actively applies controlled satellite oscillations and is tailored according to the installation layout of the inertial sensors in the Taiji program and the noise models. For the calibration of scale factors, high-precision star sensors are used to measure the satellite attitude signal, which is then combined with the driving voltage data from inertial sensors. By using the linear relationship between these signals, the scale factors are estimated using an extended Kalman Filter. For the calibration of center of mass (CoM) offsets, the calibrated scale factors are utilized, along with the driving voltage data from the front-end electronics of inertial sensors, to derive the test mass's angular acceleration, linear acceleration, and angular velocity. These parameters are then used to complete the CoM offset calibration according to the dynamic equation.</sec><sec>The feasibility of the proposed calibration scheme is validated through a simulation experiment. The results demonstrate that the scale factors of the three axes can be calibrated to relative accuracies of 33 ppm, 27 ppm, and 173 ppm , respectively, meeting the requirement within 300 ppm. The CoM deviation are calibrated with accuracies of <inline-formula><tex-math id="M2">\begin{document}$ {\delta }_{{\boldsymbol{r}}_{1}}= $\end{document}</tex-math></inline-formula>[15 μm, 31 μm, 34 μm], <inline-formula><tex-math id="M4">\begin{document}$ {\delta }_{{\boldsymbol{r}}_{2}}= $\end{document}</tex-math></inline-formula>[5 μm, 15 μm, 13 μm], satisfying the 75 μm threshold. These results confirm that the proposed scheme can effectively maintain the inertial sensors’ performance within the required accuracy range.</sec><sec>All in all, the calibration scheme developed in this study is crucial for maintaining the high performance of inertial sensors in the Taiji program. By achieving the precise calibration of the scale factors and deviation of center of mass within the required accuracy ranges, the scheme ensures the reliability of inertial sensor data, thereby significantly enhancing the sensitivity of space-based gravitational wave detection, which paves the way for groundbreaking discoveries in astrophysics and cosmology.</sec>

INS/GNSS integration is a well known technique in navigation and, in general, in time-Position-Velocity-Attitude (tPVA) trajectory determination. It is also known, that INS and GNSS are complementary and that the key to their integration is the correct calibration of the Inertial Measurement Unit (IMU) sensors, of the IMU's Inertial Sensor Assembly (ISA) system parameters (axes misalignments and center of navigation), and of the IMU-to-GNSS system parameters (eccentricity vectors). Calibration is performed both at the manufacturer's facilities prior to shipping and "on-the-job," i.e., together with navigation. Classical INS calibration has two parts: INS error modeling and actual INS calibration once an INS error model is available (also called INS calibration model) either at the manufaturer's or on-the-job. INS error modeling is about understanding the error features - systematic and random - of an IMU and its result uses to be dynamic models - Stochastic Differential Equations (SDE) and white noise amplitude - of the main error sources like biases, scale factors and misalignment angles. INS calibration is about solving for the unknowns (states) of the SDE calibration model together with the unknown states of the SDE of motion. The quality of INS calibration is dependent on the mission dynamics. In classical INS/GNSS navigation, the INS calibration model is dynamics independent; i.e., SDEs formulas and white noise figures are derived following a number of established procedures and then kept fixed. However, it can be shown, that the error features and the INS error calibration model of an IMU change from mission to mission or, more to the point, from one to another type of dynamics. It is therefore natural, to investigate the relationship between IMU errors and motion dynamics and, once this is understood, use this knowledge to improve the performance of INS/GNSS tPVA trajectory determination. In this paper we present a method for IMU error analysis and its first results. It consists of using a reference IMU (REF) together with the IMU under test (IUT) for the simultaneous measurement of REF and ITU signals. First, we show how the sensor random behavior changes with dynamics for tactical and low-cost grade IMUs with respect a navigation grade one. Second, we introduce a procedure to analyze the error of the dynamic dat. The procedure is based on inertial data analysis tools as the Allan Variance applied to the errors of the target IMU with respect to the reference IMU.

An integrated compact airborne multispectral imaging system using embedded computer based control system was developed for small aircraft multispectral imaging application. The multispectral imaging system integrates CMOS camera, filter wheel with eight filters, two-axis stabilized platform, miniature POS (position and orientation system) and embedded computer. The embedded computer has excellent universality and expansibility, and has advantages in volume and weight for airborne platform, so it can meet the requirements of control system of the integrated airborne multispectral imaging system. The embedded computer controls the camera parameters setting, filter wheel and stabilized platform working, image and POS data acquisition, and stores the image and data. The airborne multispectral imaging system can connect peripheral device use the ports of the embedded computer, so the system operation and the stored image data management are easy. This airborne multispectral imaging system has advantages of small volume, multi-function, and good expansibility. The imaging experiment results show that this system has potential for multispectral remote sensing in applications such as resource investigation and environmental monitoring. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

The position and attitude information obtained by the position and orientation system (POS) are defined by using the navigation coordinate system, but the actual production application is generally carried out under the map projection frame. Therefore, it is necessary to transform POS data into the map projection frame before it is applied in practice. Considering the complexity of the existing algorithms, and the geocentric coordinate systems that are currently widely used, such as WGS84 and CGCS2000, this letter proposes a simplified transformation method (ST-method) for the POS attitude transformation. It is obviously different from the classical Legat's method which is widely used at present. The algorithm in this letter can be called one-step transformation method, in which the geocentric coordinate system and the local tangent plane coordinate system are not involved. The conversion process has been deeply analyzed and the conversion formula is deduced, directly from navigation coordinate system to projection coordinate system. Compared with the classical methods, the most important contribution of this letter is to simplify the conversion process, and the experimental results show that the proposed method can achieve the same effect as the existing methods with no loss of accuracy.

Nowadays, multi-sensor fusion technology is a fundamental prerequisite to achieve highly autonomous robots and robustness. Many studies have been conducted, such as visual–inertial odometry (VIO), integrated navigation, and LiDAR–inertial odometry. Typically, for VIO, gratifying results have been achieved, ascribing to the complementary sensing capabilities of inertial measurement units (IMUs) and cameras. However, this work mainly focuses on the fusion of visual and inertial data, while the IMU error is less considered, especially for low-cost or poorly calibrated microelectromechanical system (MEMS) IMU. Such errors may have a significant effect on the VIO performance. In this study, we compensated for the IMU using camera assistance. The key characteristic of the method is that we optimize the compensation parameters (scale factor) from coarse to fine by combining the time domain with the frequency domain. The proposed method is to use the time-domain and frequency-domain optimization to suppress large noise in the dynamic calibration process of the extremely low-cost sensor platform. The effectiveness of this method is validated through experiments and simulations. The minimal calibration error (0.46%) is commensurate with the advanced work. By feeding the compensated IMU into the VIO algorithm, the localization accuracy is improved by 9% to 15%. This method improves the performance in the VIO algorithm, which is equipped with the low-cost or poorly calibrated MEMS IMU and reduces the hardware and deployment costs of the system.

According to a small, lightweight, low-cost high performance inertial Measurement Units(IMU), an effective calibration method is implemented to evaluate the performance of Micro-Electro-Mechanical Systems(MEMS) sensors suffering from various errors to get acceptable navigation results. A prototype development board based on FPGA, dual core processor's configuration for INS/GPS integrated navigation system is designed for experimental testing. The significant error sources of IMU such as bias, scale factor, and misalignment are estimated in virtue of static tests, rate tests, thermal tests. Moreover, an effective intelligent calibration method combining with Kalman Filter is proposed to estimate parameters and compensate errors. The proposed approach has been developed and its efficiency is demonstrated by various experimental scenarios with real MEMS data.

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.