Differential Correction Method Research Articles

Differential Correction Method of Long-Wave Propagation Time Delay Applied to Complex Long-Distance Path

Differential Correction Method of Long-Wave Propagation Time Delay Applied to Complex Long-Distance Path

2OC: A General Automated Orientation and Orthorectification Method for Corona KH-4B Panoramic Imagery

Due to a lack of geographical reference information, complex panoramic camera models, and intricate distortions, including radiation, geometric, and land cover changes, it can be challenging to effectively apply the large number (800,000+) of high-resolution Corona KH-4B panoramic images from the 1960s and 1970s for surveying-related tasks. This limitation hampers their significant potential in the remote sensing of the environment, urban planning, and other applications. This study proposes a method called 2OC for the automatic and accurate orientation and orthorectification of Corona KH-4B images, which is based on generalized control information from reference images such as Google Earth orthophoto. (1) For the Corona KH-4B panoramic camera, we propose an adaptive focal length variation model that ensures accuracy and consistency. (2) We introduce a robust multi-source remote sensing image matching algorithm, which includes an accurate primary orientation estimation method, a multi-threshold matching enhancement strategy based on scale, orientation, and texture (MTE), and a model-guided matching strategy. These techniques are employed to extract high-accuracy generalized control information for Corona images with significant geometric distortions and numerous weak texture areas. (3) A time-iterative Corona panoramic digital differential correction method is proposed. The orientation and orthorectification results of KH-4B images from multiple regions, including the United States, Russia, Austria, Burkina Faso, Beijing, Chongqing, Gansu, and the Qinghai–Tibet Plateau in China, demonstrate that 2OC not only achieves automation but also attains a state-of-the-art level of generality and accuracy. Specifically, the standard deviation of the orientation is less than 2 pixels, the mosaic error of orthorectified images is approximately 1 pixel, and the standard deviation of ground checkpoints is better than 4 m. In addition, 2OC can provide a longer time series analysis of data from 1962 to 1972, benefiting various fields such as environmental remote sensing and archaeology.

Redesign of high-precision reference orbit for interferometric SAR satellite with injection error

A two-step optimization algorithm is proposed to redesign a precision reference repeating sun-synchronous orbit for interferometric synthetic aperture radar satellites with injection error. This purpose is to design a new reference orbit for the satellite that deviates from the original preset orbit. Manoeuvring satellites to this new orbit consumes less propellant than manoeuvring to the original orbit. In addition, the repeatability of the orbit is a guarantee for obtaining good interference images, which puts higher requirements on the revisit accuracy of the redesign reference orbit. In the first step, the initial guess for reference orbital elements is designed by considering the global coverage of the Earth and the propellant consumption, taking into account the J2 and J4 perturbations. A search table of feasible solutions in the neighbourhood of the injection orbit is established. This approach, which is based on a search table, transforms the optimization of continuous variables in infinite space into the traversal of discrete variables in finite space, thus greatly reducing the optimization time. In the second step, the revisit accuracy of the satellite’s full-dimensional state vector is optimized under the orbit propagation of a high-order gravity field. Unlike traditional methods that only optimize the revisit error of position, this paper also optimizes that of velocity. A new optimization method for full-dimensional revisit error of state vector is proposed, which combines nested differential correction with non-dominated sorting genetic algorithm-II. Compared with the traditional genetic algorithms, the proposed nested differential correction method provides the non-dominated sorting genetic algorithm-II with more accurate initial values, which reduces the iterations. Finally, the simulation results show that the total velocity change from the actual injection orbit to the redesigned reference orbit is halved compared to the original preset orbit. Moreover, the revisit errors of position and velocity are within 1m and 1m/s, respectively.

Weak Signal Processing Method for Moving Target of GNSS-S Radar Based on Amplitude and Phase Self-Correction

Navigation satellite signals have the advantages of all-day, all-weather, and global coverage, and the use of navigation signals for the detection of moving targets has significant application prospects. However, the GNSS signal is very weak, and the signal power is greatly attenuated after being scattered by the target. In order to detect the echo signal, a long integration time is required. However, the movement of the target will cause the echo signal to produce unpredictable range migration and a Doppler frequency shift, which will weaken the cumulative effect of long-term integration. This paper proposes a weak signal processing method with amplitude and phase self-correction for moving target detection in the GNSS-S radar. First, the phase consistency of the echoes of a single GNSS satellite is realized by the block expansion compression and phase differential correction method to improve the coherent accumulation gain; then, multi-star joint accumulation is carried out after the signal amplitudes of multiple satellites are corrected by the improved keystone method, so as to obtain a stable echo signal track. This method can effectively improve the integral gain of the scattering signal of the moving target and realize target detection. The simulation results and field tests show that this method can effectively improve the SNR of the GNSS-S signal and can realize the detection of small moving targets such as cars with GNSS-S radar.

Hybrid Ground-Space Target Visit Problem With a Coplanar Impulse

The hybrid ground–space target visit problem is solved by applying a single coplanar impulse. Considering the linear <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$J_{2}$</tex-math></inline-formula> perturbation, the ground target visit problem is transformed into the ground track adjustment problem, and it is expressed as a time constraint equation. The space target visit problem is viewed as the orbit interception (or flyby) problem, and it is expressed as time and radius constraint equations. Then, based on Gauss’s variational equations, the hybrid ground–space target visit problem is simplified into solving a single-variable equation only of maneuver position. Finally, the exact solution under the high-precision dynamic model is obtained by the differential correction method. Several numerical examples are presented to validate the efficiency of this approach, and the results show that there are a series of discrete solutions to this problem.

Small Satellite Orbit Determination Using Single Pass Doppler Measurements

The Doppler measurements of the telemetry radio signals nanosatellite CubeBel-1 for a single pass over the Belarusian State University ground station were carried out. Two methods for orbit determination of a small satellite (SS) are considered. The first method is based on the SGP4 model and requires additional information from the North American Aerospace Defense Command (NORAD) two-line elements (TLE) catalog of the satellite orbital parameters. An unknown SS is identified using the NORAD TLE catalog based on a probabilistic estimation of the elevation angle and the Doppler frequency shift of receiving telemetry signals. The first method was allowed to determine the nanosatellite CubeBel-1 unambiguously. The second method is based on processing experimental measurements of the Doppler frequency of the telemetry radio signals and the Keplerian circular motion model for SS. It does not require additional information from the NORAD database of satellite orbital parameters. The second method was allowed only to calculate the average state vector unknown satellite. Finally, the corrected state vector in the geocentric inertial coordinate system was obtained based on the differential correction method.

Differential evolution algorithm-based aberration correction method for the interference of vortex beams

Differential evolution algorithm-based aberration correction method for the interference of vortex beams

Two-target interception problem with a single impulse

This paper proposes a numerical method to solve the two-target interception problem with a single impulse. Free impulse position and free interception position are considered. Both elliptic and hyperbolic transfers are analyzed. Under the two-body model, by using the Gibbs method for orbit determination from three position vectors, the problem is transformed into solving nonlinear equations of only two independent variables. Newton-Raphson iterations associated with analytical Jacobi matrix are adopted to solve the nonlinear equations. The initial guesses are obtained by the Porkchop plot method. By using the solutions under the two-body model as the initial values, the solutions under the J2-perturbed model are obtained by combining the homotopy technique and the differential correction method. There are many solutions for the problem even for the zero-revolution case. Numerical examples are provided to verify the effectiveness of the proposed methods for the two-body model and the J2-perturbed model, respectively.

Research on Orbit Optimization of Manned Spacecraft Based on Dynamics

Based on the dynamics angle, the paper finds a suitable launch window based on the pork-chop diagram, and then uses the conic splicing method to carry out the preliminary design of the orbit. The two-body model is used to design the orbit at each stage, and finally under the precise mechanical model, using differential correction method, accurate track design based on B plane parameters.

Fifth order solution of halo orbits via Lindstedt–Poincaré technique and differential correction method

In the frame work of the perturbed restricted three-body problem, the solutions of halo orbits are developed up to fifth order approximation by using Lindstedt–Poincaré technique. The effect of oblateness of the more massive primary on the size, location and period of halo orbits around L1 and L2 are studied by considering the Earth–Moon system. Due to oblateness of the Earth, halo orbits around L1 and L2 enlarge and move towards the Moon. Also, the period of halo orbits around L1 and L2 decreases. Numerical solution for halo orbits around L1 and L2 in the Sun–Earth system is obtained by using the differential correction method for different values of radiation pressure and oblateness. The separation between the orbits obtained using fourth and fifth order Lindstedt–Poincaré method as well as differential correction method is found to be less than the separation between the orbits obtained using third and fourth order Lindstedt–Paincaré as well as differential correction method. This indicates that as the order of the solution increases the separation between consecutive solution decreases leading to more accurate solution.

Development of differential correction of coordinate-time and consumer navigation support based on trajectory data comparisons

The article deals with the use of the results of measuring the catalogued space objects coordinates by a radar station for long-range detection in the interests of differential correction of coordinate-time and navigation support for consumers. We describe the idea of comparing trajectory data that allows us to calculate the total electronic content in the direction of a catalyzed space object under the assumption of a thin layer at the height of the ionosphere maximum. The main stages of the method of differential correction of coordinates-but-time and navigation support for consumers based on the results of comparing trajectory data are described. The results of modeling are presented, which allow us to evaluate the possible positive effect when using the proposed approach.

Exploration of Low-Energy Earth-Moon Transfer Orbit Based on Crossing Orbit of Double Three-Body System

The design of low energy lunar transfer orbit and orbit optimization method based on crossing orbit is studied in this paper. The four-body problem of Sun-Earth-Moon-satellite is decoupled into two three-body problems of Sun-Earth-satellite and Earth-Moon-satellite. Low-energy lunar exploration orbit is designed by changing orbit at a certain intersection field through manifold of two Halo orbit of three-body system. A serial optimization design method for global initial value search and local gradient optimization are designed. When a motion state variable is partially modified, the differential correction method combined with adaptive regression algorithm is adopted. For the splicing points of manifolds of different systems, the velocity vector is modified to make the spacecraft get into the target berthing track, and to obtain the splicing points that can form crossing track of the two three-body systems. An example of orbit design is given to show that the Earth-Moon transfer orbit based on invariant manifold splicing has the characteristics of energy saving and long-time consumption, which can be used for the tasks with large loads and low time requirements. This research provides a method for the design of low energy lunar transfer orbit. It will benefit the energy consuming, material design of spacecraft, and so on.

Differential correction method in low-thrust orbit transfers near the collinear libration points

Differential correction method in low-thrust orbit transfers near the collinear libration points

Optimal impulsive time-fixed transfers around the libration points of the restricted three-body problem

A methodology is proposed to design optimal time-fixed impulsive transfers in the vicinity of the L2 libration point of the Earth-Moon system, taking the construction of a space station around the collinear libration points as the background. The approximate analytical expression of motions around the L2 point in the CRTBP is given, and the expression in the ERTBP is derived by linearizing the dynamical equations for the purpose of expanding the methodology from the CRTBP to the ERTBP. Thus, the approximate analytical solution of the transfer between two points is obtained by substituting the position vectors of the two points into the expression, which solves the Lambert problem in the three-body system. Furthermore, the transfer between different orbits is constructed by parameterization of the position vectors with the amplitudes and phases of the initial orbit and the final orbit. The transfers are optimized such that the total velocity increment required to implement the transfer exhibits a global minimum. The values of variables involved in the optimal transfers are determined by the unconstrained minimization of a function of one or nine variables using a multivariable search technique. To numerically ensure that the transfers are accurate and to eliminate the linearization bias, the differential correction and SQP method are employed. The optimality of the transfers is determined lastly by the primer vector theory. Simulations of point-to-point transfers, Lissajous-to-Lissajous transfers, halo-to-halo transfers and Lissajous-to-halo transfers are made. The results of this study indicate that the approximate analytical solutions, as well as the differential correction and SQP method, are valid in the design of the optimal transfers around the libration points of the restricted three-body problem.

Red de transporte de datos en formato RTCM, vía protocolo de Internet (Ntrip). Implementación en la región y proyección futura a través de SIRGAS

Las CORS (Estaciones de Referencia de Observación Continua), utilizan los GNSS (Sistemas Satelitales de Posicionamiento Global), para determinar con alta preci- sión una posición, mediante la observación de los satélites de las constelaciones disponibles (GPS, GLONNAS, próximamente Galileo y Compass/BeiDou). &#x0D; Empleando la técnica llamada de Corrección Diferencial, es posible eliminar casi totalmente la influencia de los errores inducidos voluntariamente o producidos por la señal GNSS. El método DGNSS, tanto en modo Post Proceso como en Tiempo Real, son las modalidades más utilizadas. Actualmente están disponibles tam- bién soluciones PPP (Precise Point Positioning - Posicionamiento Puntual Preciso), a partir de desarrollos generados en varias agencias de investigación. Últimamente se han presentado ciertos avances sobre PPP (Posicionamiento de Punto Preciso), particularmente en tiempo real: PPP-RTK. &#x0D; Las Correcciones Diferenciales pueden ser obtenidas directamente a partir de un receptor GNSS, de una CORS o de una red CORS, conectadas a un Servidor-Cáster a través de Internet. &#x0D; El cliente o usuario móvil utilizando tecnología de telefonía móvil (GSM, GPRS, EDGE, UMTS) y un programa Cliente, puede acceder a la dirección IP del Cáster, a través de protocolo Ntrip (Red de Transporte de datos en formato RTCM a través Protocolo de Internet), a fin de obtener los datos de corrección diferencial para el receptor GNSS que está utilizando. &#x0D; Ntrip se basa en HTTP (HyperText Transfer Protocol - Protocolo de Transferencia de Hipertexto), siendo capaz de trasmitir cualquier tipo de datos GNSS a través de mensajes RTCM (Radio Technical Commission for Maritime Services) o datos en formato propietario (raw data). El usuario puede elegir entre una serie de produc- tos, como por ejemplo correcciones de una sola CORS, o corrección de una red CORS. Existen diversas soluciones de red, como ser: VRS (Estación de Referencia Virtual), FKP (Parámetros de Corrección de Planos), MAX (Máster-Auxiliar), iMAX (individual Máster-Auxiliar&#x0D;

Nonlinear representation of the confidence region of orbits determined on short arcs

The total number of active satellites, rocket bodies, and debris larger than 10 cm is currently about 20,000. If all resident space objects larger than 1 cm are considered, this number increases to an estimate of 700,000 objects. The next generation of sensors will be able to detect small-size objects, producing millions of observations per day. However, due to observability constraints, long gaps between observations will be likely to occur, especially for small objects. As a consequence, when acquiring observations on a single arc, an accurate determination of the space object orbit and the associated uncertainty is required. This work aims to revisit the classical least squares method by studying the effect of nonlinearities in the mapping between observations and state. For this purpose, high-order Taylor expansions enabled by differential algebra are exploited. In particular, an arbitrary-order least squares solver is implemented using the high-order expansion of the residuals with respect to the state. Typical approximations of differential correction methods are then avoided. Finally, the confidence region of the solution is accurately characterized with a nonlinear approach, taking advantage of these expansions. The properties and performance of the proposed methods are assessed using optical observations of objects in LEO, HEO, and GEO.

Identification of trace amounts of detergent powder in raw milk using a customized low-cost artificial olfactory system: A novel method

One of the common concerns in quality assurance of raw milk is the use of antimicrobial agents for reducing the microbial population. For this purpose, different kinds of agents may be added to raw milk like detergents. This illegal practice is harmful to human health and has ethical and serious sanitary consequences. In this study, an artificial olfactory machine (electronic nose) was developed based on eight metal oxide semiconductor sensors (MOS) and its ability to detect the presence of detergent powder in raw milk was investigated. Three features (area under the curve, relative response, and slope) were extracted from each sensor response and three baseline manipulation techniques (differential, relative and fractional) were used to correct the sensor responses. The multivariate analysis of variance (MANOVA) was employed to optimize the data matrix. MANOVA showed that the feature of “area under the curve” along with differential baseline correction method is the best combination for distinguishing different levels of the adulteration in milk. Based on the results, principal component analysis (PCA) with the first two PCs explains 91% of the variations. Linear discriminant analysis (LDA), support vector machine (SVM) and adaptive neuro-fuzzy inference system (ANFIS) method were employed for further qualitative classification. The result showed that the best performance (90%) was achieved by using the nu-SVM with Radial Basis Function (RBF) kernel function when the data collected from independent experiments were used for validation. The study demonstrated the potential of an electronic nose as a fast, effective and feasible method to detect detergent powder in raw milk.

Computation of three-dimensional periodic orbits in the sun-earth system

In this paper, a third-order analytic approximation is described for computing the three-dimensional periodic halo orbits near the collinear L1 and L2 Lagrangian points for the photo gravitational circular restricted three-body problem in the Sun-Earth system. The constructed third-order approximation is chosen as a starting initial guess for the numerical computation using the differential correction method. The effect of the solar radiation pressure on the location of two collinear Lagrangian points and on the shape of the halo orbits is discussed. It is found that the time period of the halo orbit increases whereas the Jacobi constant decreases around both the collinear points taking into account the solar radiation pressure of the Sun for the fixed out-of-plane amplitude.

Periodic orbits of solar sail equipped with reflectance control device in Earth–Moon system

In this paper, families of Lyapunov and halo orbits are presented with a solar sail equipped with a reflectance control device in the Earth–Moon system. System dynamical model is established considering solar sail acceleration, and four solar sail steering laws and two initial Sun-sail configurations are introduced. The initial natural periodic orbits with suitable periods are firstly identified. Subsequently, families of solar sail Lyapunov and halo orbits around the $L_{1}$ and $L_{2}$ points are designed with fixed solar sail characteristic acceleration and varying reflectivity rate and pitching angle by the combination of the modified differential correction method and continuation approach. The linear stabilities of solar sail periodic orbits are investigated, and a nonlinear sliding model controller is designed for station keeping. In addition, orbit transfer between the same family of solar sail orbits is investigated preliminarily to showcase reflectance control device solar sail maneuver capability.

Effect of orbital shadow at an Earth-Moon Lagrange point on relay communication mission

The shadow effect is an important constraint to be considered during the implementation of exploration missions. In this paper, for the Earth-Moon Lagrange point L2 relay communication mission, shadow effect issues on a periodic orbit about L2 are investigated. A systematic analysis based on the time domain and phase space is performed including the distribution, duration, and frequency of shadows. First, the Lindstedt-Poincare and second-order differential correction methods are used in conjunction with the DE421 planetary ephemeris to achieve a mission trajectory family in a high-precision ephemeris model. Next, on the basis of a conical shadow model, the influence of different orbital phases and amplitudes on the shadow is analyzed. The distribution of the shadow is investigated as well. Finally, the configuration of the shadow and its characteristics are studied. This study provides an important reference and basis for mission orbit design and shadow avoidance for relay satellites at an Earth-Moon Lagrange point.