Earth-centered Earth-fixed Research Articles

Global integrated navigation position correction algorithm and virtual polar region technology based on normal vector

To achieve the inherent uniformity of all-earth navigation for autonomous underwater vehicles (AUV), a global integrated navigation position correction algorithm based on the normal vector (n-vector) is proposed. First, a four-element vector comprising the non-singular n-vector and height represents the carrier’s position in the Earth-centered Earth-fixed (ECEF) frame. The integrated navigation systems are designed with the strapdown inertial navigation system (SINS), Doppler velocity log (DVL), and other equipment. Secondly, the reverse navigation algorithm in the ECEF mechanization is derived, and the results of forward and reverse navigation are fused to correct the AUV’s underwater position. Additionally, a virtual polar region technology based on the ECEF attitude, velocity, and height invariant method (E-AVHIM) is proposed to convert the actual test data obtained at low and middle latitudes into high latitudes for more convincing polar region algorithm verification. Simulations and lake trial demonstrated the excellence and efficiency of the proposed algorithm.

Spatial positioning method based on range-only measurement of multi-station radar

Aiming at the characteristics that affect the high ranging accuracy of shipborne radar, a multi station radar spatial positioning method based on ranging is proposed. This method is based on the ECEF (Earth Centered Earth Fixed) coordinate system, and adopts the method of intersecting the detection distances of multiple radars to the target, and directly calculates the spatial position of the target. This method only needs the geodetic coordinates of each radar station and the detection range of the target to calculate the geodetic coordinates of the target, which can effectively solve the coordinate conversion problem caused by the curvature of the earth, and does not involve higher-order equations and multi-value solutions, and it does not involve iterative initial value calculation. The positioning system can not only obtain high positioning accuracy, but also has a long operating distance, which can better solve the multi-radar range measurement intersection positioning problem.

An Invariant Filtering Method Based on Frame Transformed for Underwater INS/DVL/PS Navigation

Underwater vehicles heavily depend on the integration of inertial navigation with Doppler Velocity Log (DVL) for fusion-based localization. Given the constraints imposed by sensor costs, ensuring the optimization ability and robustness of fusion algorithms is of paramount importance. While filtering-based techniques such as Extended Kalman Filter (EKF) offer mature solutions to nonlinear problems, their reliance on linearization approximation may compromise final accuracy. Recently, Invariant EKF (IEKF) methods based on the concept of smooth manifolds have emerged to address this limitation. However, the optimization by matrix Lie groups must satisfy the “group affine” property to ensure state independence, which constrains the applicability of IEKF to high-precision positioning of underwater multi-sensor fusion. In this study, an alternative state-independent underwater fusion invariant filtering approach based on a two-frame group utilizing DVL, Inertial Measurement Unit (IMU), and Earth-Centered Earth-Fixed (ECEF) configuration is proposed. This methodology circumvents the necessity for group affine in the presence of biases. We account for inertial biases and DVL pole-arm effects, achieving convergence in an imperfect IEKF by either fixed observation or body observation information. Through simulations and real datasets that are time-synchronized, we demonstrate the effectiveness and robustness of the proposed algorithm.

Phased Array Radio Navigation System on UAVs: In-Flight Calibration

Global Navigation Satellite Systems (GNSS) has been the primary positioning solution for Unmanned Aerial Vehicles (UAVs) due to their worldwide coverage, high precision and lightweight receivers. However, GNSS is prone to electromagnetic interference and malicious assaults, including jamming or spoofing because of its low signal-to-noise ratio (SNR). To ensure the continuity and protection of UAV operations, using redundant navigation systems is essential. In recent years, the phased array radio system (PARS) has established itself as a local navigation solution. PARS is robust towards malicious assaults because of an much higher SNR than GNSS regarding directed and encrypted transmission. An essential factor of PARS is that the orientation of the radio antenna at a ground station needs to be precisely determined to obtain the correct positioning of UAVs. This paper presents a method for extending a previously proposed calibration algorithm to estimate the ground antenna orientation with an inertial navigation system (INS) aided by redundant positioning sensors (GNSS, PARS or barometer) using a multiplicative extended Kalman filter (MEKF) so that the calibration can be activated during flights whenever GNSS is available. In other words, the proposed navigation system is essentially an aided-INS which switches between two modes depending on the availability of GNSS: calibration and GNSS aiding mode when GNSS is available (Mode 1) and PARS and barometer aiding mode when GNSS is unavailable (Mode 2). Considering that the navigation system needs to include the effect of Earth’s curvature for a long-distance flight, PARS horizontal measurement and the barometer measurement were treated independently, and the navigation equations were propagated in Earth Centred Earth Fixed (ECEF) frame. The independent treatment of barometer measurement, and the propagation in ECEF frame were also beneficial when using multiple ground antennas to have a common reference point and reference frame. The proposed method was validated using data (Inertial Measurement Unit (IMU), GNSS, PARS, Pixhawk autopilot (including barometer) measurements) collected during a field test. In the validation, GNSS was made available at the middle of the flight and the calibration mode was activated for 200s. The proposed navigation system successfully estimated the precise orientation of multiple ground antennas and the navigation solutions were verified using GNSS and Pixhawk autopilot solutions as ground truth.

Cavsiopy: a Python package to calculate and visualize spacecraft instrument orientation

Spacecraft attitude plays an important role in the observations of various atmospheric, planetary, and terrestrial parameters and phenomena that are of interest to the scientific community. Precise measurements from imagers, particle sensors, and antennas require accurate knowledge of instrument orientation. cavsiopy is an easy-to-install and use, light-weight open-source Python package for researchers who need to consider instrument pointing direction and observation geometry. cavsiopy contains the coordinate transformation routines and the corresponding rotation matrices from the spacecraft orbital reference frame (ORF) to any of the geocentric equatorial inertial for epoch J2000 (GEI J2K)/International Celestial Reference Frame (ICRF), Earth-centered, Earth-fixed (ECEF), International Terrestrial Reference Frame (ITRF), geodetic north-east-down, and geocentric north-east-center coordinate systems. Additionally, cavsiopy includes routines for importing Swarm-E ephemeris and generic two-line-element (TLE) data files; for the calculation of spacecraft azimuth, elevation, and orbital parameters; as well as for the 2D/3D visualization of the geometry between the instrument and the target. Functionality and utilization of cavsiopy for research problems are demonstrated with examples and visualizations for the Radio Receiver Instrument (RRI) and the Fast Auroral Imager (FAI) of e-POP/Swarm-E.

Dual-UAV Collaborative High-Precision Passive Localization Method Based on Optoelectronic Platform

Utilizing the optical characteristics of the target for detection and localization does not require actively emitting signals and has the advantage of strong concealment. Once the optoelectronic platform mounted on the unmanned aerial vehicle (UAV) detects the target, the vector pointing to the target in the camera coordinate system can estimate the angle of arrival (AOA) of the target relative to the UAV in the Earth-centered Earth-fixed (ECEF) coordinate system through a series of rotation transformations. By employing two UAVs and the corresponding AOA measurements, passive localization of an unknown target is possible. To achieve high-precision target localization, this paper investigates the following three aspects. Firstly, two error transfer models are established to estimate the noise distributions of the AOA and the UAV position in the ECEF coordinate system. Next, to reduce estimation errors, a weighted least squares (WLS) estimator is designed. Theoretical analysis proves that the mean squared error (MSE) of the target position estimation can reach the Cramér–Rao lower bound (CRLB) under the condition of small noise. Finally, we study the optimal placement problem of two coplanar UAVs relative to the target based on the D-optimality criterion and provide explicit conclusions. Simulation experiments validate the effectiveness of the localization method.

Performance Evaluation of Stereo Vision Aided Loosely Coupled GNSS/SINS Integration for Land Vehicle Navigation in Different Urban Environments

In urban environments, the positioning performance of global navigation satellite system (GNSS) degrades severely due to the harsh environment, which will be improved after fused with a strap-down inertial navigation system (SINS). However, due to the error accumulation, the positioning ability of GNSS/SINS integration will also decrease significantly during frequent GNSS outages. To improve the positioning accuracy, we use stereo vision to enhance the performance of GNSS/SINS integration, where GNSS and stereo vision are loosely coupled and tightly coupled with SINS under the Earth-centered Earth-fixed (ECEF) frame, respectively. To evaluate the positioning performance of the multisensor fusion system, two in-field experiments were conducted to assess the contribution of stereo vision. The results show that with the support of stereo vision and SINS, GNSS accuracy can be considerably improved by 60%–80% in complex environments, which also outperforms the GNSS/SINS integration. Besides, detailed analyses in various urban environments further demonstrate that stereo vision can significantly improve the performance of GNSS/SINS integration when a long-term GNSS anomaly occurs, but it shows no improvement for a short-term GNSS anomaly.

Adaptive Alignment for Low-Cost INS in ECEF Frame Under Large Initial Attitude Errors

<h3>Abstract</h3> A new two-stage alignment on a moving base is proposed for a low-cost inertial navigation system with the aid of a Global Positioning System (GPS) receiver in the Earth-centered, Earth-fixed (ECEF) frame under large initial attitude errors. Both the state and measurement equations are derived using the additive quaternion error model in the ECEF frame for alignment without the need for level adjustment. The nonlinear velocity error equations in both the coarse and the fine stages are linearized further. An improved strong tracking filter is proposed for the coarse stage to converge quickly with large initial attitude errors. After the attitude errors converge to smaller values in the coarse stage, a standard Kalman filter is implemented for the fine stage. Experiments demonstrate that attitude error can converge quickly with the proposed adaptive alignment method.

A New GNSS Spoofing Signal Power Control Algorithm for Receiver Sensors in Acquisition Phase and Subsequent Control.

Satellite navigation spoofing technology has become a hotspot of interference technology research because of its significant threat and high concealment. In a spoofing scenario, suppressive interference is typically used to ensure that the target receiver sensor is in the unlocked and reacquisition state, and then spoofing is implemented. This method has a high feasibility, and the power of the spoofing signal affects the concealment and efficiency of spoofing. Currently, there is limited research involving the GNSS spoofing signal power control. Moreover, there is no systematic complete power control scheme, most of which is limited to qualitative or simulation, and the actual application effect is still unclear. Therefore, a new GNSS spoofing signal power control algorithm under the power constraints of the receiver sensor in the acquisition phase and the subsequent control is proposed. The experimental platform is designed to prove that compared with the conventional spoofing signal high power control algorithm, the new GNSS spoofing signal power control algorithm shortens Doppler frequency fluctuation time by 72.2% and reduces the range by 75.9%. The carrier-to-noise ratio of the received signal is less than the threshold of the receiver sensor, and the range of three-dimensional coordinates of Earth-Centered, Earth-Fixed (ECEF) is significantly reduced during the spoofing signal taking over receiver sensor, this shows that the new design of the GNSS spoofing signal power control algorithm can make spoofing behavior more hidden, and it will make it more difficult for the target receiver sensor to detect spoofing behavior. The designed algorithm can take over the receiver sensor stealthily with the help of suppressing interference and then pull the bias positioning results, which has good feasibility and effectiveness.

High-precision attitude determination using spaceborne gravity gradiometer and gyroscope

This study investigates the application of a spaceborne gravity gradiometer to spacecraft attitude determination. Considering that the gradiometer raw measurements are influenced by angular rotation, a gyroscope is integrated to provide angular velocity information. To deal with unknown biases in both gradiometer and gyroscope measurements, a multiplicative extended Kalman filter (MEKF) is developed to estimate the attitude states and the instrument biases simultaneously. In addition, the cross-correlation between gyroscope measurements and gyroscope-compensated gradiometer measurements is analyzed. The MEKF algorithm is modified accordingly to cope with the correlation problem. Simulation scenarios with two different attitude modes are built to test the algorithm. With a gradiometer of 0.1 E (1 E = 10−9 s−2) accuracy and a navigation-grade gyroscope, attitude determination accuracy of several arcsecs is obtained. Real data from the GOCE (gravity field and steady-state ocean circulation explorer) spacecraft are also used to test the algorithm. Yaw, pitch, and roll angle errors of 2.8 arcsec, 20.9 arcsec, and 11.3 arcsec are achieved, respectively. The method can directly estimate a spacecraft's attitude relative to the Earth-centered Earth-fixed (ECEF) frame and is promising for high-precision spacecraft attitude determination in Earth-oriented missions.

Direct conversion of latitude and height from one ellipsoid to another

I suggest a method for converting geodetic height and latitude from one oblate ellipsoid of revolution to another having the same center and symmetry axis. Unlike other approaches, the method here does not obtain height and latitude from Earth-centered, Earth-fixed (ECEF) Cartesian coordinates; this feature allows height conversion with high accuracy even in cases where the data format limits the precision of the latitude data. Height and latitude conversions can be expressed as a Fourier series in even multiples of latitude, with height changes having only cosines and latitude changes having only sines. The absolute difference of the flattenings of the two ellipsoids furnishes a simple upper bound on the maximum absolute latitude change. Conversions between the TOPEX and WGS84 ellipsoids, a practical necessity for the inter-mission comparison of satellite laser and radar altimeter data, illustrate the findings. Because the differences in the flattenings and semi-major axes of these ellipsoids are small, truncating the Fourier series after the term in twice the latitude gives an approximate conversion with an error less than 9 times 10–12 radians of latitude and about 6 times 10–6 m of height.

Effect of Erroneous Observations in GPS-based LEO Satellite Orbit Determination

Performance of an EKF-based Orbit Determination (OD) algorithm using Global Positioning System (GPS) measurements is examined under erroneous observation conditions. A generalized formulation of a dynamic orbit model is designed to predict the satellite states in an Earth-Centered Earth-Fixed (ECEF) frame. A suitable orbit interpolation method is then chosen for interpolating the GPS satellite position at the measurement time tag before finding the geometric range between the GPS and the LEO satellites. Thereafter, the commonly used Extended Kalman Filter (EKF) algorithm is implemented for the nonlinear OD problem. The proposed algorithm is tested for the precision in OD of two LEO satellites, namely GRACE and Megha-Tropiques based on the available raw GPS measurements in the Receiver Independent Exchange (RINEX) observation files. For the GRACE satellite, the efficacy of the present OD algorithm is validated by comparing the estimated and publicly available precise orbit information. The Megha-Tropiques satellite, however, does not have precise orbit information. Furthermore, it is observed that the RINEX file has several erroneous observations as detected by the Fault Detection and Exclusion (FDE) algorithm in-built in the OD algorithm. A comparison of the estimated satellite position with that obtained from the standard software GNSS-Lab Tool (gLAB) shows that the accuracy of the position estimates varies proportionally with the number of erroneous observations of the Megha-Tropiques satellite.

Correction of precession-nutation and polar motion in analytical solutions of satellite equations of motion

In the analytical solutions of satellite equations of motion, the precession-nutation and polar motion (PNPM) effects are usually not considered. For the first-order orbit theory, the magnitude of these effects is small enough to be neglected; however, it might be a different case for a higher order solution, which could possibly be applied in precise orbit prediction or determination in the near future. To clarify the influence of PNPM acting on the Keplerian elements of near-Earth satellite orbits in analytical theory, this paper gives both theoretical and numerical analysis of these effects based on Gaussian equations of motion. From the analysis, the impact of PNPM can be divided into two parts. The first part is a rotational error on the perturbing force vector since the force vector is converted into a coordinate system without considering PNPM; the other part is caused by the error of the satellite coordinates computed in the Earth-Centered Earth-Fixed (ECEF) or True-of-Date (TOD) coordinate system when the PNPM effects are neglected. More importantly, an easy-to-use semi-analytical correction procedure is proposed. It can be applied to the Keplerian elements directly without having to derive again the solutions. With this method, the error caused by neglecting the PNPM can be well corrected.

Earth Rotation-Aware Non-Stationary Satellite Communication Systems: Modeling and Analysis

In this paper, we propose a non-stationary satellite communication system model considering the impacts of Earth rotation by adopting the Earth-centered inertial (ECI), and the Earth-centered Earth-fixed (ECEF) coordinates. The position variations of a satellite (S) and a ground user (U) via coordinate transformations are demonstrated. Considering the variations of the distance between S and U, the instantaneous outage probability (OP) and channel capacity are calculated, as well as the system throughput within finite communication time. A simplified case is considered and analyzed while ignoring the Earth's rotation. Furthermore, the asymptotic expressions for the OP, capacity, and throughput are developed in the high signal-to-noise ratio (SNR) regime to obtain some insights. We also provide new definitions for throughput and OP within a short communication duration. The application and future research directions based on the derived results, including resource allocation, satellite handover, communication scenarios with multiple satellites and mobile users, are also discussed. Finally, some selected numerical results are provided to validate our proposed analysis models.

Stereo visual odometry with velocity constraint for ground vehicle applications

AbstractThis paper proposes a novel method of error mitigation for stereo visual odometry (VO) applied in land vehicles. A non-holonomic constraint (NHC), which imposes physical constraint to the rightward velocity of a land vehicle, is implemented as an observation in an extended Kalman filter (EKF) to reduce the drift of stereo VO. The EKF state vector includes position errors in an Earth-centred, Earth-fixed (ECEF) frame, velocity errors in the camera frame, angular rate errors and attitude errors. All the related equations are described and presented in detail. In this approach, no additional sensors are used but NHC, namely velocity constraint in the right direction , is applied as an external measurement to improve the accuracy. Tests are conducted with the Karlsruhe Institute of Technology and Toyota Technological Institute (KITTI) datasets. Results show that the relative horizontal positioning error improved from 0⋅63% to 0⋅22% on average with the application of the velocity constraints. The maximum and root mean square of the horizontal error with velocity constraints are both reduced to less than half of the error with stand-alone stereo VO.

Unified All-Earth Navigation Mechanization and Virtual Polar Region Technology

For a strap-down inertial navigation system (SINS), a traditional navigation frame switching mechanization can be used to solve the all-Earth navigation problem, however, this kind of method suffers from complex and discontinuous algorithms. On the basis of improving vertical channel damping technology, a complete and unified all-Earth navigation scheme arranged in the Earth-centered Earth-fixed (ECEF) frame is designed as an alternative for global applications, which results in a simpler continuous algorithm and lower computational complexity. We also propose a virtual polar region technology based on the grid attitude and velocity invariant method (G-AVIM), which can complete the polar navigation verification through the actual test data of nonpolar regions. In the reconstructed polar region trajectory, the vehicle attitude, velocity, and height information relative to the ground remain unchanged, so the real test environment can be completely reproduced in the polar region. Simulations and field test results verified the proposed methods.

SINS/BDS Integrated Navigation for Hypersonic Boost-Glide Vehicles in the Launch-Centered Inertial Frame

According to the trajectory specialty of hypersonic boost-glide vehicles, a strapdown inertial navigation system/BeiDou navigation satellite system (SINS/BDS) algorithm based on the launch-centered inertial (LCI) frame for hypersonic vehicles is proposed. First, the related frame system, especially the launch earth-centered inertial (LECI) frame, and the SINS mechanization in the LCI frame are introduced. Second, SINS discrete updating algorithms in the LCI frame for the compensation of coning, sculling, and scrolling effects are deduced in the attitude, velocity, and position updating algorithms, respectively. Subsequently, the Kalman filter of the SINS/BDS integrated navigation in the LCI frame is obtained. The method of converting BDS receiver position and velocity from the Earth-centered Earth-fixed (ECEF) frame to the LCI frame is deduced through the LECI frame. Finally, taking the typical hypersonic boost-glide vehicles as the object, the SINS/BDS algorithm vehicle field test and hardware-in-the-loop simulation are performed.

Aerial Forest Fire Detection and Monitoring Using a Small UAV

In recent years, large patches of forest have been destroyed by fires, bringing tragic consequences for the environment and small settlements established around these regions. In this context, it is essential that fire fighting teams possess an increased situational awareness about the fire propagation, in order to promptly act in the extinguishing process. Recent advances in UAV technology allied with remote sensing and computer vision techniques show very promising UAVs applicability in forest fires detection and monitoring. Besides presenting lower operational costs, these vehicles are able to reach regions that are inaccessible or considered too dangerous for fire fighting crews operations. This paper describes the application of a real-time forest fire detection algorithm using aerial images captured by a video camera onboard an Unmanned Aerial Vehicle (UAV). The forest fire detection algorithm consists of a rule-based colour model that uses both RGB and YCbCr colour spaces to identify fire pixels. An intuitive targeting system was also developed, allowing the detection of multiple fires at the same time. Additionally, a fire geolocation algorithm was developed in order to estimate the fire location in terms of latitude (φ), longitude (λ) and altitude (h). The geolocation algorithm consists of applying two coordinates systems transformations between the body-fixed frame, North-East-Down frame (NED) and Earth-Centered, Earth Fixed (ECEF) frame. Flight tests were performed during a controlled burn in order to assess the fire detection algorithm performance. The algorithm was able to detect the fire with few false positive detections.&#x0D; Keywords: Aerial fire detection algorithm, Aerial fire monitoring, Forest fire, UAV, Remote sensing

Improved Kalman Filter Variants for UAV Tracking with Radar Motion Models

Unmanned aerial vehicles (UAV) have made a huge influence on our everyday life with maturity of technology and more extensive applications. Tracking UAVs has become more and more significant because of not only their beneficial location-based service, but also their potential threats. UAVs are low-altitude, slow-speed, and small targets, which makes it possible to track them with mobile radars, such as vehicle radars and UAVs with radars. Kalman filter and its variant algorithms are widely used to extract useful trajectory information from data mixed with noise. Applying those filter algorithms in east-north-up (ENU) coordinates with mobile radars causes filter performance degradation. To improve this, we made a derivation on the motion-model consistency of mobile radar with constant velocity. Then, extending common filter algorithms into earth-centered earth-fixed (ECEF) coordinates to filter out random errors is proposed. The theory analysis and simulation shows that the improved algorithms provide more efficiency and compatibility in mobile radar scenes.

Sequential unbiased converted measurement non‐linear filter with range rate in ECEF coordinates

Air-to-air target tracking is a challenging task for practical military and civilian applications. In this study, an unbiased converted measurement Kalman filter in Earth-centred Earth-fixed (ECEF) coordinates (E-UCMKF) is proposed for air-to-air target tracking, which takes account for noisy measurements from the airborne radar and the inertial navigation system/global navigation satellite system. The unbiased measurement conversion approach from spherical coordinates to ECEF coordinates is presented, and the Kalman filter is implemented for target state estimation with the unbiased converted measurements and the corresponding measurement error covariances. Besides, when range-rate measurements are available to the processor, a sequential unbiased converted measurement non-linear filter in ECEF coordinates with range-rate measurements (E-SUCMNFwR) is developed, which constructs a pseudo measurement to decorrelate the range-rate measurement noise from the unbiased converted measurement noise, and estimates the state sequentially by the E-UCMKF and a modified cubature Kalman filter. Target tracking scenarios with different sensor accuracies are presented to demonstrate the validity of the proposed algorithms. Simulation results validate the consistency of the proposed unbiased measurement conversion. The results also show that the proposed E-UCMKF and E-SUCMNFwR outperform the conventional algorithms in terms of the position and velocity root-mean-square error, demonstrating their effectiveness and practicality.