Orbit Determination Algorithm Research Articles

A New GNSS FDE Algorithm for Real-Time LEO Satellite Orbit Determination

A New GNSS FDE Algorithm for Real-Time LEO Satellite Orbit Determination

Relative Orbit Determination Algorithm of Space Targets with Passive Observation

Relative Orbit Determination Algorithm of Space Targets with Passive Observation

Relative Orbit Determination Algorithm of Space Targets with Passive Observation

Relative Orbit Determination Algorithm of Space Targets with Passive Observation

Distributed angle‐only orbit determination algorithm for non‐cooperative spacecraft based on factor graph

AbstractBayesian filtering provides an effective approach for the orbit determination of a non‐cooperative target using angle measurements from multiple CubeSats. However, existing methods face challenges such as low reliability and limited estimation accuracy. Two distributed filtering algorithms based on factor graphs employed in the sub‐parent and distributed cluster spacecraft architectures are proposed. Two appropriate factor graphs representing different cluster spacecraft structures are designed and implement distributed Bayesian filtering within these models. The Gaussian messages transmitted between nodes and the probability distributions of variable nodes are calculated using the derived non‐linear Gaussian belief propagation algorithm. Gaussian messages propagate from the deputy spacecraft to the chief spacecraft in the sub‐parent spacecraft architecture, demonstrating that the estimation accuracy converges to the centralised extended Kalman filter (EKF). Simulation results indicate that the algorithm enhances system robustness in observation node failures without compromising accuracy. In the distributed spacecraft architecture, neighbouring spacecraft iteratively exchanges Gaussian messages. The accuracy of the algorithm can rapidly approach the centralised EKF, benefiting from the efficient and unbiased transmission of observational information. Compared to existing distributed consensus filtering algorithms, the proposed algorithm improves estimation accuracy and reduces the number of iterations needed to achieve consensus.

An Improved Range-Searching Initial Orbit-Determination Method and Correlation of Optical Observations for Space Debris

The Changchun Observatory of the National Astronomical Observatories, Chinese Academy of Sciences, and the Shanghai Astronomical Observatory are used to generate very short arc (VSA) angle observations of objects in low Earth orbit (LEO) and geostationary orbit (GEO) with their ground-based electrical–optical telescope arrays (EA), the Changchun EA and SAO FocusGEO, respectively. These observations are used in this paper. The range-searching (RS) algorithm for initial orbit determination (IOD) is improved through the multiple combinations of observations and the dynamic range-searching step length. Two different computation modes (the normal mode and the refining mode) of the IOD computation process are proposed. The geometrical method for the association is used. The IOD and association methods are extended to the real optical observations for both LEO and GEO objects. The results show that the IOD success rate of arcs from the LEO objects is about 91%, the error of the semimajor axis (SMA) of the initial orbital elements is less than 50 km, and the correlation accuracy rate is about 89%. The IOD success rate of arcs from the GEO objects is higher than 88%, and the correlation accuracy rate is greater than 87%. The recent COSMOS 1408 antisatellite test (ASAT) generated a large amount of debris. The algorithm of this paper and the observations of Changchun EA are used to initially identify new debris, possibly from the ASAT through initial orbit determination and track association. Finally, 64 suspected new pieces of debris can be found. The results show the effectiveness of the IOD and the correlation algorithm, as well as the potential application of the optical–electrical array in studying space events.

Abort orbit determination of launch vehicles based on difference of convex programming

Existing exoatmospheric guidance laws become ineffective when a thrust loss fault (like one or more engines unexpectedly shut down) occurs in a launch vehicle, which makes the nominal orbit unreachable. This paper presents a new abort orbit determination process to determine an abort orbit which the launch vehicle is able to reach. It involves solving at most two optimization problems and the abort orbit may be circular or elliptical. We will present how to transform the nonconvex optimization problems into difference of convex (DC) programming problems which can be solved by existing methods with guaranteed convergence. The main contribution of this paper lies in proposing a relaxation technique to convexify a nonconvex control constraint and the combination of the introduction of new constraints and a relaxation technique to deal with the strict terminal constraints. Validity of the relaxation technique is ensured by theoretical analysis. A unique feature of the transformation process is that the feasible sets defined by both the control constraint and the strict terminal constraints are all enlarged. This brings a critical benefit that the resulting DC programming problems can be very efficiently solved. Thus, an abort orbit determination algorithm, which is based on DC programming, can be designed to very reliably and efficiently determine an abort orbit, which will be demonstrated by numerical examples.

Adaptive Order-Switching Kalman Filter for Orbit Determination Using Deep-Neural-Network-Based Nonlinearity Detection

This paper proposes an adaptive estimation algorithm for orbit determination, which consists of a deep-neural-network (DNN)-based nonlinearity detector combined with an adaptive order-switching procedure, to reduce the computational complexity while still maintaining the estimation accuracy. The DNN is trained to quickly evaluate the nonlinearity degree of the state equation. An adaptive order-switching strategy is designed based on the nonlinearity degree predicted by the DNN. The algorithm switches to a high-order method when the nonlinearity of the state equation is significant and uses a linear method when the nonlinearity degree is low. The proposed method is applied to estimate the orbit of a spacecraft in cislunar space. The sample forms in the inertial frame and rotating frame are investigated and compared to find the optimum one to train the DNN. Simulations show that the proposed method can deliver accurate state estimations comparable with the state estimations obtained by the second-order extended Kalman filter but with only half of the computational cost.

Robust Initial Orbit Determination for Surveillance Doppler-Only Radars

An initial orbit determination algorithm for surveillance Doppler-only radars with embedded quantification capabilities is presented. The method is based on a combination of Gauss' and Lambert's solvers formulated in the differential algebra framework, which provides the Taylor expansion of the state estimate with respect to the measurement uncertainties. This feature makes the approach particularly suited for handling data association problems. The first part of the paper describes the mathematical formulation of the method, while an extensive analysis of its performance and a comparison with a reference algorithm are carried out in the second part, using both simulated and real data. The proposed approach is shown to be accurate and robust and particularly suited for short-arc observations.

Deep-neural-network-based angles-only relative orbit determination for space non-cooperative target

Angles-only relative orbit determination for space situational awareness is subjected to a well-known range observability problem, that is, the range between two spacecraft is weakly observable or unobservable. However, in previous studies, the solutions to this problem using nonlinear relative motion dynamics have been limited by the computational complexity and long arc of observation. To this end, this study develops a simple and fast algorithm to address the angles-only relative orbit determination problem by exploiting a deep neural network (DNN), which has a significantly strong capability of capturing nonlinearity. Emphasis is placed on the construction of a nonlinear mapping model from the line-of-sight angles to the relative orbit state by training the designed DNN. First, a training dataset generator including nonlinear relative motion dynamics and a line-of-sight measurement model is established to generate the training data for the DNN. Second, the DNN frame, including the network structure, data processing, and network training algorithm for angles-only relative orbit determination, is designed. Subsequently, a digital simulation system comprising error models, reference missions and trajectories, and computation models for error estimation is established. Thus, the anti-noise and generalization performance of the nonlinear mapping model on GEO-type orbits are verified using digital simulations. The results indicate that the proposed algorithm is effective, whereby the estimation accuracy for the relative position is generally better than that for the relative velocity. In the case of a co-elliptical orbit, the estimated errors of distance and velocity in each direction are less than 9.7% and 48.2%, respectively, whereas the maximum average errors are approximately 1.1% and 4.2%, respectively, where only three sets of angle measurements with an interval of 600 s are available. However, in the case of a non-coplanar orbit, the interval between angles can be decreased to 50 s, when the corresponding estimated error of distance in each direction is less than 9.9%, and the maximum average error is approximately 1.1%. Additionally, the sensitivity of the proposed algorithm to the arc length, number, and interval of the measurements is analyzed.

A LSTM assisted orbit determination algorithm for spacecraft executing continuous maneuver

Orbit determination (OD) for spacecraft with unknown maneuver is always a challenging task. This paper proposes a novel framework for efficiently solving continuously maneuvering spacecraft OD problems by merging the Long Short-Term Memory (LSTM) neural network and the filter algorithms. A polynomial-representation fitted the unknown continuous maneuver is first proposed. Rather than directly output the estimated maneuver, the LSTM is trained to detect the unknown maneuver and then estimate the coefficients of the polynomial-representation. Then a fusion is designed to combine the prediction of the LSTM and the estimation of the filter for a more accurate estimation. The proposed LSTM-based framework is successfully applied to solve a Low-Earth-orbit OD problem and a Middle-Earth-orbit OD problem. The continuously maneuvering target is well tracked and the unknown maneuver is accurately estimated. Numerical simulations show that the LSTM trained based on one training dataset can also be applied to other scenarios that share some common features with the training dataset.

Emerging errors in the orientation of the constellation in GNSS autonomous orbit determination based on inter-satellite link measurements

The emergence of inter-satellite link (ISL) technology, which realizes the high-precision measurement of the inter-satellite distances and forms a spatial geometric constraint within the constellation, enables the high-precision autonomous orbit determination of the GNSS satellites. Firstly, according to the fact that ISL adjustment is singular to the satellite orbit state vector, a distributed autonomous orbit determination algorithm employing the long-term forecast ephemeris to constrain the constellation orientation is designed in this paper. Then, the autonomous orbit determination using 60-day onboard ISL observations of the whole constellation is carried out. Then, the resulting orbits accuracy is evaluated by comparing them with a precise orbit determination using a global reference network with an accuracy of 0.10 m. The results show that the mean root mean square (RMS) of the user range error (URE) over a 60-day period of the 24 BDS-3 satellites in the constellation is 3.22 m. The characteristics of orbit errors for individual satellite are very similar, which is mainly caused by the overall orientation errors of the constellation. After eliminating these orientation errors, the corresponding mean RMS of URE is reduced to 0.68 m. The prediction errors of the Earth rotation parameters and the determination errors of the parameters of the state vectors, which compose the orientation errors, are further investigated. The Earth rotation parameter prediction errors mainly cause errors in the estimates of the longitude of ascending node, of which the 60-day error can reach 2.5e-5°. The determination errors of the parameters of the state vectors -- the inclination and the right ascension of ascending node, can reach 2.4e-5° and 5.1e-5° rad, respectively.

Real-time carrier observation quality control algorithm for precision orbit determination of LEO satellites

Real-time carrier observation quality control algorithm for precision orbit determination of LEO satellites

Сучасні низькоорбітальні угруповання космічних апаратів дистанційного зондування землі з використанням радарів із синтезованою апертурою

The purpose of this work is to determine the current trends in the development of low-orbit constellations of spacecraft with synthetic aperture radar (SAR), which have a number of significant advantages in Earth remote sensing. It is shown that the demand for Earth remote sensing data and products and services based thereon continues to grow worldwide. The applicability of SAR to Earth remote sensing is considered. The main differences and advantages of image acquisition using SAR spacecraft in comparison with optical spacecraft are shown. The main directions of using low-orbit SAR spacecraft in Earth remote sensing are identified. Land and water surface observation using SAR spacecraft is shown to be one of the most effective remote sensing methods. In particular, it is shown that low-orbit spacecraft constellations can be used to advantage in solving many tasks in the socio-economic sector and tasks aimed at continuous real-time monitoring of various objects. The characteristics of the various Earth remote sensing spacecraft constellations, in particular low-orbit commercial ones, launched into orbit during the past decade are considered. Problems in and prospects for the development of low-orbit SAR spacecraft constellations are elucidated. Existing and planned SAR spacecraft constellations with traditional and mini-satellite platform technologies are overviewed. It is shown that the performance characteristics continue to improve, thus allowing one to get data from any area of the Earth at any time. It is shown that small spacecraft in low and ultralow orbits have significant benefits over traditional spacecraft in power characteristics, but are outperformed by them in the duration of communication sessions and active life. The results obtained make it possible to work out recommendations on the designing of low-orbit constellations of domestic Earth remote sensing spacecraft, in particular on the development of orbit determination models and algorithms and spacecraft dynamics models.

Establishing the Capabilities of the Murchison Widefield Array as a Passive Radar for the Surveillance of Space

This paper describes the use of the Murchison Widefield Array, a low-frequency radio telescope at a radio-quiet Western Australian site, as a radar receiver forming part of a continent-spanning multistatic radar network for the surveillance of space. This paper details the system geometry employed, the orbit-specific radar signal processing, and the orbit determination algorithms necessary to ensure resident space objects are detected, tracked, and propagated. Finally, the paper includes the results processed after a short collection campaign utilising several FM radio transmitters across the country, up to a maximum baseline distance of over 2500 km. The results demonstrate the Murchison Widefield Array is able to provide widefield and persistent coverage of objects in low Earth orbit.

Onboard Orbit Determination for Deep-Space CubeSats

In this work, an orbit determination algorithm suitable for CubeSats onboard implementation is developed, which simulates optical autonomous navigation accomplished by a stand-alone platform. An extended Kalman filter featuring line-of-sight acquisitions of planets is selected as the state estimator, and its performances are tested on a Raspberry Pi, whose characteristics are comparable to a miniaturized onboard computer. An improvement of the solution accuracy is performed by correcting the planetary light-time and aberration effects as well as by exploiting the optimal beacons selection strategy to acquire the external observations. Moreover, the numerical precision of the estimator is improved through the implementation of factorization techniques and nondimensionalization strategies. The results are presented for a sample Earth–Mars transfer, where the time slot for the navigation campaign involves 2 h every 10 days. At final time, the probe position and velocity are estimated with a accuracy of 360 km and 0.04 m/s, respectively.

Analysis and improvement of the Bancroft algorithm for GNSS satellite orbit determination

Satellite orbit information is crucial for ensuring that global navigation satellite systems (GNSSs) provide appropriate positioning, navigation and timing services. Typically, users can obtain access to orbit information of a specific accuracy level from navigation messages or precise ephemeris products. Without this information, a system will not be able to provide normal service. In response to this problem, initial orbit information of a certain level of precision must be obtained to support subsequent applications, such as broadcasting or precise ephemeris calculations, thereby ensuring the successful subsequent operation of the navigation system. One of two ways to calculate the initial orbit of a GNSS satellite is to utilize ground tracking stations to observe satellite vector information in the geocentric inertial system; the second way is to utilize GNSS range observations and known orbit information from other satellites. For the second approach, some researchers use the Bancroft algorithm combined with receiver clock offset to determine the initial orbit of GNSS satellites. Because this method requires an additional known receiver clock offset, we study the dependence of the Bancroft algorithm on clock offset in GNSS orbit determination. By assessing the impact of errors of different magnitude on the accuracy of the orbit results, we obtain experimental conclusions. After comprehensively analyzing various errors, we determine the accuracy level that the Bancroft algorithm can achieve for orbit determination without considering receiver clock correction. Dual-frequency and single-frequency pseudorange data from International GNSS Service stations are used in orbit determination experiments. When a small receiver clock offset is considered and no correction is made, the deviations in the calculated satellite positions in three dimensions are approximately 979.3 and 1118.1 m (dual and single frequency); with a satellite clock offset, these values are approximately 928.8 and 1062.7 m (dual and single frequency).

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.

Non-cooperative LEO Satellite Orbit Determination Based on Single Pass Doppler Measurements

Precise orbit information is the premise of the wide application of low-Earth-orbit (LEO) satellites. Traditional orbit determination (OD) methods have disadvantages of poor reliability, high hardware cost, and long orbit determination time. To account for these issues, we propose an OD framework, using several distributed facilities to acquire Doppler shift values of signals of opportunity (SOPs) during the same pass.Firstly, we propose a search-least squares (LS) algorithm for initial orbit determination (IOD), providing a reliable accurate initial value for precise orbit determination (POD). Moreover, a non-recursive cubature batch filter (NR-CBF) is proposed for POD to reduce linearization errors, avoid tuning parameters, and save the calculation time. Besides, we modify the measurement model by considering signal propagation delays and provide the corresponding theoretical basis. Finally, the real experiment result verifies the feasibility of the proposed method, whose velocity accuracy is at m/s grade.

Estimation of the thermospheric density using ephemerides of the CYGNSS and Swarm constellations

Modeling the neutral density in the upper atmosphere is a major challenge as it involves a comprehensive understanding of the complex coupling between the thermosphere and its environment. In addition, this system is strongly driven by solar activity, which is hardly predictable. This complexity limits the ability of thermospheric models to accurately estimate thermospheric characteristics, such as the neutral density. With the rapidly increasing number of satellites in orbit and the recent progress in tracking their trajectories, new techniques are being implemented to derive density estimates based on trajectory perturbations. However, most of these methods require the integration of complex and costly orbit determination algorithms, which greatly limit their applicability at a public level. The approach presented here provides density estimates along a spacecraft trajectory and only requires the implementation of an orbit propagator. More specifically, it corrects density predictions made by the NRLMSIS00e thermosphere model by optimizing the orbit fitting of modeled trajectories with observations under different thermospheric density conditions. The algorithm is applied to the Cyclone Global Navigation Satellite System and Swarm-B spacecraft trajectories during a period of varying geomagnetic activity. The study puts in evidence a bias in NRLMSIS00e estimates during moderate solar activity, corrected by the algorithm. In addition, the approach provides a better characterization of the rapid density enhancement resulting from a geomagnetic storm. Overall, the correlation with the Level 2 data is improved by 15% and the normalized root mean square error decreased by a factor ~2.3, compared to the estimations with NRLMSIS00e.

Improvement of orbit determination using laser altimeter crossovers: JUICE mission case study

This work evaluates the added benefit of using laser altimeter measurements for orbit reconstruction. As a spacecraft orbits a celestial body, its altimetry swaths progressively cross previous swaths. These locations, known as crossover points, yield valuable information about the orbited body and the spacecraft trajectory. The mathematical expressions for the inclusion of crossover measurements into orbit determination algorithms are presented and evaluated. It is shown that a first-order approximation of these expressions is insufficient and a more detailed expression is developed. To evaluate the impact of altimetry crossover measurements on orbit determination, the planetary mission Jupiter Icy moons Explorer (JUICE) by the European Space Agency (ESA) is used as a case study by means of a covariance analysis. In this initial analysis, the assumption is made that all altimetry measurements are obtained with nadir pointing which limits the direct applicability of our method until pointing is accounted for.