查看更多>>摘要：Given the orthogonal basis (or the projections) of no less than two subspaces in finite dimensional spaces, we propose two novel algorithms for computing the intersection of those subspaces. By constructing two matrices using cumulative multiplication and cumulative sum of those projections, respectively, we prove that the intersection equals to the null spaces of the two matrices. Based on such a mathematical fact, we show that the orthogonal basis of the intersection can be efficiently computed by performing singular value decompositions on the two matrices with much lower complexity than most state-of-the-art methods including alternate projection method. Numerical simulations are conducted to verify the correctness and the effectiveness of the proposed methods.
查看更多>>摘要：Spoofing attacks for Global navigation satellite system (GNSS) would cause the abnormal changes of receiver measurements. Monitoring the abnormal changes is the main pattern of anti-spoofing techniques. Anomalies of Doppler shifts are important for GNSS spoof-ing detection. Most researchers focus on the consistency of Doppler such as the consistency of carrier Doppler and code rate. But the method is powerless in some cases. Doppler shift measurement is proportional to change rate of pseudorange, and the relationship would be broken in the case of spoofing attack. As both Doppler measurements and pseudoranges are related to velocity of receiver, two approaches of computing velocity can be used to check the consistency of Doppler shifts and pseudoranges measurements. An efficient spoofing detection method based on the consistency check of velocities is proposed in the paper. Principle of the method is given in detail and its performance evaluations are provided as well. Simulation results demonstrate the effectiveness of the solution.
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