Collision Probability Prediction and Orbit Maneuvering Probability Determination of Non-Cooperative Space Object Orbit

Probability of collision between non-cooperative space object (NCSO) and the reference spacecraft (RS) has been increased drastically over the past few decades. The traditional method is difficult to identify the maneuvering of non-cooperative space object. In the present paper, not only positions and velocities, but also accelerations of non-cooperative space object are estimated as parameters by the extended Kalman filtering based on setting up the state linear equation and measurement model of the non-cooperative space object. The algorithm for predicting collision probability is derived from position error ellipsoid, and the algorithm for determining maneuvering probability is derived from maneuvering acceleration and its error ellipsoid, which can be employed to identify whether the upcoming space object is being maneuvered. An epoch Earth-centered inertial (EECI) coordinate system is suggested to replace Earth-centered inertial (ECI) to simplify coordinate transformation. Finally, a set of simulations were conducted to validate the proposed algorithms with the simulated measurement data of the reference spacecraft space-borne millimeter-wave (MMW) radar.

The impact of non-Gaussianity on the Epoch of Reionization parameter forecast using 21-cm power-spectrum measurements

ABSTRACT Measurements of the Epoch of Reionization (EoR) 21-cm signal hold the potential to constrain models of reionization. In this paper, we consider a reionization model with three astrophysical parameters namely (1) the minimum halo mass that can host ionizing sources, Mmin, (2) the number of ionizing photons escaping into the IGM per baryon within the halo, Nion, and (3) the mean free path of the ionizing photons within the IGM, Rmfp. We predict the accuracy with which these parameters can be measured from future observations of the 21-cm power spectrum (PS) using the upcoming SKA-Low. Unlike several earlier works, we account for the non-Gaussianity of the inherent EoR 21-cm signal. Considering cosmic variance only and assuming that foregrounds are completely removed, we find that non-Gaussianity increases the volume of the 1σ error ellipsoid of the parameters by a factor of 133 relative to the Gaussian predictions, the orientation is also different. The ratio of the volume of error ellipsoids is 1.65 and 2.67 for observation times of 1024 and 10 000 h, respectively, when all the $\boldsymbol {k}$ modes within the foreground wedge are excluded. With foreground wedge excluded and for 1024 h, the 1D marginalized errors are (ΔMmin/Mmin, ΔNion/Nion, ΔRmfp/Rmfp) = (6.54, 2.71, 7.75) × 10−2 that are, respectively, $2 {{\ \rm per\ cent}}$, $5 {{\ \rm per\ cent}}$, and $23 {{\ \rm per\ cent}}$ larger than the respective Gaussian predictions. The impact of non-Gaussianity increases for longer observations, and it is particularly important for Rmfp.

An Algorithm of Reinforcement Learning for Maneuvering Parameter Self-Tuning Applying in Satellite Cluster

Satellite cluster is a type of artificial cluster, which is attracting wide attention at present. Although the traditional empirical parameter method (TEPM) has the potential to deal with the mission of satellite flocking, it is difficult to select the proper parameters. In order to improve the flight effect in the problem of satellite cluster, as well as to make the selection of flight parameters more reasonable, the traditional sensing zones are improved. A 3σ position error ellipsoid and an induction ellipsoid are applied for substituting the traditional repulsing zone and attracting zone, respectively. Besides, we propose an algorithm of reinforcement learning for parameter self-tuning (RLPST), which is based on the actor-critic framework, to automatically learn the suitable flight parameters. To obtain the parameters in the repulsing zone, orientating zone, and attracting zone of each member in the cluster, a three-channel learning framework is designed. The learning process makes the framework finally find the suitable parameters. Numerical experimental results have shown the superiorities compared to the traditional method, which include trajectory deviation and sensing rate or terminal matching rate, as well as the improvement of the flight paths under the learning framework.

A Stellar Imaging Error Correction Method Based on an Ellipsoid Model: Taking Ziyuan 3-02 Satellite Data Analysis as an Example

Stellar point image coordinates are one of the important observations needed for high-precision space attitude measurement with a star sensor. High-coupling imaging errors occur under dynamic imaging conditions. Using the results of preliminary star point extraction from star sensor imaging data combined with a superimposed time series, we analyze the relative motion and trajectory based on the star point image, establish an image error ellipsoid fitting model based on the elliptical orbit of a satellite platform, and achieve geometric error correction of a star sensors’ image star point using multi-parameter screening of the ambiguous solutions of intersection of the elliptic equations. The simulation data showed that the accuracy of the correction error of this method reached 89.8%, and every star point coordinate required 0.259 s to calculate, on average. In addition, it was applied to real data from the satellite Ziyuan 3-02 to carry out the correction of the star points. The experiment shows that the mean of attitude quaternion errors for all its components was reduced by 52.3%. Our results show that the estimation parameters of dynamic imaging errors can effectively compensate for the star point image observation value and improve the accuracy of attitude calculation.

The Influence of Orbital Element Error on Satellite Coverage Calculation

This paper studies the influence of orbital element error on coverage calculation of a satellite. In order to present the influence, an analysis method based on the position uncertainty of the satellite shown by an error ellipsoid is proposed. In this error ellipsoid, positions surrounding the center of the error ellipsoid mean different positioning possibilities which present three-dimensional normal distribution. The possible subastral points of the satellite are obtained by sampling enough points on the surface of the error ellipsoid and projecting them on Earth. Then, analysis cases are implemented based on these projected subastral points. Finally, a comparison report of coverage calculation between considering and not considering the error of orbital elements is given in the case results.

STOCHASTIC SURFACE MESH RECONSTRUCTION

A generic and practical methodology is presented for 3D surface mesh reconstruction from the terrestrial laser scanner (TLS) derived point clouds. It has two main steps. The first step deals with developing an anisotropic point error model, which is capable of computing the theoretical precisions of 3D coordinates of each individual point in the point cloud. The magnitude and direction of the errors are represented in the form of error ellipsoids. The following second step is focused on the stochastic surface mesh reconstruction. It exploits the previously determined error ellipsoids by computing a point-wise quality measure, which takes into account the semi-diagonal axis length of the error ellipsoid. The points only with the least errors are used in the surface triangulation. The remaining ones are automatically discarded.

Three-dimensional relative reachable domain with initial state uncertainty in Gaussian distribution

A probability threshold is a confidence level defining a bound outside which the occurrence of a random variable is considered as a rare event. Upon providing such a probability threshold on the initial state uncertainty, relative reachable domain is defined as the minimum positional volume enclosing all the possible relative trajectories resulting from the initial state uncertainty. In this study, the conventional coplanar relative reachable domain with initial state uncertainty in isotropic Gaussian distribution is extended to the three-dimensional case with uncertainty in arbitrary Gaussian distribution. Positional errors in Gaussian distribution are thought to be confined within an error ellipsoid depending on the given probability threshold. Such an error ellipsoid will evolve with time and consequently sweep out a volume, which is the relative reachable domain to be determined. This paper proposed an algorithm of solving the envelope surface of the relative reachable domain for close range relative motion based on the linearized dynamical model and the mathematical definition of an envelope. Moreover, the algorithm is modified to improve the accuracy for long range relative motion. Comparisons between the solved relative reachable domain and the result of 10,000 Monte Carlo runs, which can be regarded as the true result, for different scenarios on circular reference orbits demonstrated the feasibility of the proposed method.

Recursive of Least Square Based Online Calibration Method in Geomagnetic Detection

With the problem of attitude measurement accuracy is susceptible to various errors of geomagnetic survey, this paper establishes geomagnetic measurement error ellipsoid model by analysis of on the environment and own errors, uses the maximum likelihood algorithm for solving the static error correction coefficient. The experimental results show that, the maximum of attitude angle errors is less than 5° near blind direction, online combination correction can ensure the accuracy of attitude detection system under different shooting conditions.

A NEW METHOD FOR DETERMINING THE DEFORMATION MONITORABLE INDICATOR OF POINT CLOUD

With the continuous development of the terrestrial laser scanning (TLS) technique, the precision of the laser scanning has been improved which makes it possible that TLS could be used for high-precision deformation monitoring. A deformation monitorable indicator (DMI) should be determined to distinguish the deformation from the error of point cloud and plays an important role in the deformation monitoring using TLS. After the DMI determined, a scheme of the deformation monitoring case could be planned to choose a suitable instrument, set up a suitable distance and sampling interval. In this paper, the point error space and the point cloud error space are modelled firstly based on the point error ellipsoid. Secondly, the actual point error is derived by the relationship between the actual point cloud error space and the point error space. Then, the DMI is determined using the actual point error. Finally, two sets of experiments is carried out and the feasibility of the DMI is proved.

A NEW METHOD FOR DETERMINING THE DEFORMATION MONITORABLE INDICATOR OF POINT CLOUD

With the continuous development of the terrestrial laser scanning (TLS) technique, the precision of the laser scanning has been improved which makes it possible that TLS could be used for high-precision deformation monitoring. A deformation monitorable indicator (DMI) should be determined to distinguish the deformation from the error of point cloud and plays an important role in the deformation monitoring using TLS. After the DMI determined, a scheme of the deformation monitoring case could be planned to choose a suitable instrument, set up a suitable distance and sampling interval. In this paper, the point error space and the point cloud error space are modelled firstly based on the point error ellipsoid. Secondly, the actual point error is derived by the relationship between the actual point cloud error space and the point error space. Then, the DMI is determined using the actual point error. Finally, two sets of experiments is carried out and the feasibility of the DMI is proved.