Short-range clutter suppression method combining oblique projection and interpolation in airborne CFA radar

The airborne conformal array(CFA)radar's clutter ridges are range-modulated,which result in a bias in the estimation of the clutter covariance matrix(CCM)of the cell under test(CUT),further,reducing the clutter suppression performance of the airborne CFA radar.The clutter ridges can be effectively compensated by the space-time separation interpolation(STSINT)method,which costs less computation than the space-time interpolation(STINT)method,but the performance of interpolation algorithms is seriously affected by the short-range clutter,especially near the platform height.Location distributions of CFA are free,which yields serious impact that range spaces of steering vector matrices are non-orthogonal complement and even no longer disjoint.Further,a new method is proposed that the shortrange clutter is pre-processed by oblique projection with the intersected range spaces(OPIRS),and then clutter data after being pre-processed are compensated to the desired range bin through the STSINT method.The OPIRS also has good compatibility and can be used in combination with many existing methods.At the same time,oblique projectors of OPIRS can be obtained in advance,so the proposed method has almost the same computational load as the traditional compensation method.In addition,the proposed method can perform well when the channel error exists.Computer simulation results verify the effectiveness of the proposed method.

The use of laser ranging to measure space debris

Space debris is a major problem for all the nations that are currently active in space. Adopting high-precision measuring techniques will help produce a reliable and accurate catalog for space debris and collision avoidance. Laser ranging is a kind of real-time measuring technology with high precision for space debris observation. The first space-debris laser-ranging experiment in China was performed at the Shanghai Observatory in July 2008 with a ranging precision of about 60-80 cm. The experi- mental results showed that the return signals from the targets with a range of 900 km were quite strong, with a power of 40W （2J at 20 Hz） using a 10ns pulse width laser at 532 nm wavelength. The performance of the preliminary laser ranging system and the observed results in 2008 and 2010 are also introduced.

Analysis of Galileo signal-in-space range error and positioning performance during 2015-2018

A long-term analysis of signal-in-space range error (SISRE) is presented for all healthy Galileo satellites, and the first pair of full operational capability satellites in wrong elliptical orbits. Both orbit and clock errors for Galileo show an obvious convergence trend over time. The annual statistical analyses show that the average root mean squares (RMSs) of SISRE for the Galileo constellation are 0.58 m (2015), 0.29 m (2016), 0.23 m (2017), and 0.22 m (2018). Currently, the accuracy of the Galileo signal-in-space is superior to that of the global positioning system (GPS) Block IIF (0.35 m). In addition, the orbit error accounts for the majority of Galileo SISRE, while the clock error accounts for approximately one-third of SISRE due to the high stability of the onboard atomic clock. Single point positioning results show that Galileo achieves an accuracy of 2-3 m, which is comparable to that of GPS despite the smaller number of satellites and worse geometry. Interestingly, the vertical accuracy of Galileo, which uses the NeQuick ionospheric model, is higher than that of GPS. Positioning with single frequency E1 and E5 show a higher precision than E5a and E5b signals. Regarding precise point positioning (PPP), the results indicate that a comparable positioning accuracy can be achieved among different stations with the current Galileo constellation. For static PPP, the RMS values of Galileo-only solutions are within 1 cm horizontally, and the vertical RMSs are mostly within 2 cm horizontally. For kinematic PPP, the RMSs of Galileo-only solutions are mostly within 4 cm horizontally and 6 cm vertically.

Equivalence and Strong Equivalence Between the Sparsest and Least l1-Norm Nonnegative Solutions of Linear Systems and Their Applications

Many practical problems can be formulated as l0-minimization problems with nonnegativity constraints,which seek the sparsest nonnegative solutions to underdetermined linear systems.Recent study indicates that l1-minimization is efficient for solving l0-minimization problems.From a mathematical point of view,however,the understanding of the relationship between l0-and l1-minimization remains incomplete.In this paper,we further address several theoretical questions associated with these two problems.We prove that the fundamental strict complementarity theorem of linear programming can yield a necessary and sufficient condition for a linear system to admit a unique least l1-norm nonnegative solution.This condition leads naturally to the so-called range space property(RSP)and the “full-column-rank”property,which altogether provide a new and broad understanding of the equivalence and the strong equivalence between l0-and l1-minimization.Motivated by these results,we introduce the concept of “RSP of order K”that turns out to be a full characterization of uniform recovery of all K-sparse nonnegative vectors.This concept also enables us to develop a nonuniform recovery theory for sparse nonnegative vectors via the so-called weak range space property.

Weighted Moore-Penrose inverses and fundamental theorem of even-order tensors with Einstein product

We treat even-order tensors with Einstein product as linear operators from tensor space to tensor space, define the mill spaces and the ranges of tensors, and study their relationship. We extend the fundamental theorem of linear algebra for matrix spaces to tensor spaces. Using the new relationship, we characterize the least-squares （M） solutions to a multilineax system and establish the relationship between the minimum-norm （N） leastsquares （M）solution of a multilinear system and the weighted Moore-Penrose inverse of its coefficient tensor. We also investigate a class of even-order tensors induced by matrices and obtain some interesting properties.