J_2 invariant relative orbits via differential correction algorithm

This paper describes a practical method for finding the invariant orbits in Ja relative dynamics. Working with the Hamiltonian model of the relative motion including the J2 perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended to formation flying of Earth＇s orbiters. Rather than using orbital elements, the analysis is done directly in physical space, which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the ascending node period of the leader satellite, and a preliminary explanation for this phenomenon is presented. Then the compatibility between J2 invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible configuration is proposed. The influences of measure errors on the invariant orbit are also investigated by the Monte-Carlo simulation.

Differential correction method applied to measurement of the FAST reflector

The Five-hundred-meter Aperture Spherical radio Telescope （FAST） adopts an active deformable main reflector which is composed of 4450 triangular panels. During an observation, the illuminated area of the reflector is deformed into a 300-m diameter paraboloid and directed toward a source. To achieve accurate control of the reflector shape, positions of 2226 nodes distributed around the entire reflector must be measured with sufficient precision within a limited time, which is a challenging task because of the large scale. Measurement of the FAST reflector makes use of stations and node targets. However, in this case the effect of the atmosphere on measurement accuracy is a significant issue. This paper investigates a differen- tial correction method for total stations measurement of the FAST reflector. A multi-benchmark differential correction method, including a scheme for benchmark selection and weight assignment, is proposed. On- site evaluation experiments show there is an improvement of 70%-80% in measurement accuracy compared with the uncorrected measurement, verifying the effectiveness of the proposed method.

Novel adaptive Hatch filter to mitigate the effects of ionosphere and multipath on LAAS

It has been proven that carrier smoothing and differential global positioning system （DGPS） are effective to improve the accuracy of pseudorange by reducing the noise in it and eliminating almost all the common mode errors between the ground station and user. However, another issue coming with local area augmentation system （LAAS） is how to find an adaptive smoothing window width to minimize the error on account of ionosphere delay and multipath. Based on the errors analysis in carrier smoothing process, a novel algorithm is formulated to design adaptive Hatch filter whose smoothing window width flexibly varies with the characteristic of ionosphere delay and multipath in the differential carrier smoothing process. By conducting the simulation in LAAS and after compared with traditional Hatch filers, it reveals that not only the accuracy of differential correction, but also the accuracy and the robustness of positioning results are significantly improved by using the designed adaptive Hatch filter.

The J_2 invariant relative configuration of spaceborne SAR interferometer for digital elevation measurement

A 3-craft formation configuration is proposed to perform the digital elevation model （DEM） for the distributed spacebome interferometric synthetic aperture radar （InSAR）, and it is optimized by the modified ant colony algorithm to have the best compatibility with J2 invariant orbits created by differential correction algorithm. The configuration has succeeded in assigning the across-track baseline to vary periodically and with its mean value equal to the optimal baseline determined by the relative height measurement accuracy. The required relationship between crafts＇ magnitudes and phases is formulated for the general case of interferometry measure from non-orthographic and non-lateral view. The J2 invariant configurations created by differential correction algorithm are employed to investigate their compatibility with the required configuration. The colony algorithm is applied to search the optimal configuration holding the near-constant across-track baseline under the J2 perturbation, and the absolute height measurement accuracy is preferable as expected.

A Fault-tolerance Estimating Method for Ionosphere Corrections in Satellite Navigation System

Aiming to the reliable estimates of the ionosphere differential corrections for the satellite navigation system in the presence of the ionosphere anomaly, a fault-tolerance estimating method, which is based on the distributed Kalman filtering, is proposed. The method utilizes the parallel sub-filters for estimating the ionosphere differential corrections. Meanwhile, an infinite norm （IN） method is proposed for the detection of the ionosphere irregularity in the filter processing. Once the anomaly is detected, the sub-filter contaminated by the anomaly measurements will be excluded to ensure the reliability of the estimates. The simulation is conducted to validate the method and the results indicate that the anomaly can be found timely due to the novel fault detection method based on the infinite norm. Because of the parallel sub-filter architecture, the measurements are classified by the spatial distribution so that the ionosphere anomaly can be positioned and excluded more easily. Thus, the method can provide the robust and accurate ionosphere differential corrections.

A New Optimal Hatch Filter to Minimize the Effects of Ionosphere Gradients for GBAS

At present, the main problem faced by ground-based augment system （GBAS） is that though carder smoothing filter and local differential global positioning system （LDGPS） improve the accuracy of the pseudorange by reducing the noise in it and eliminating almost all the common errors between the user and the reference station, they also cause extra errors on account of the effects of the ionosphere temporal and spatial gradients. Based on the analysis of these errors as well as the smoothing noise, this article suggests a new algorithm to design the optimal Hatch filter, whose smoothing window width varies real-time with the satellite elevation, ionosphere variation, and distance from the user to the reference station. By conducting the positioning process in the GBAS emulation platform for several hours and after its comparison with the performances of traditional Hatch filters, it is found that the errors in the differential correction become smaller and the positioning accuracy gets heightened with this new method.