This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers i...This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers is not countably infinite. Likewise, countably infinite tree structures could represent all real numbers, and all points in any number of dimensions in multi-dimensional spaces. The objective of this paper is not to overturn previous research based on Cantor’s argument, but to suggest that this situation may be treated as a definitional or axiomatic choice. This paper proposes a “non-Cantorian” branch of cardinality theory, representing all these infinities with countably infinite tree structures. This approach would be consistent with the Continuum Hypothesis.展开更多
In view of the low performance of adaptive asymmetric joint diagonalization（AAJD）, especially its failure in tracking high maneuvering targets, an adaptive asymmetric joint diagonalization with deflation（AAJDd） al...In view of the low performance of adaptive asymmetric joint diagonalization（AAJD）, especially its failure in tracking high maneuvering targets, an adaptive asymmetric joint diagonalization with deflation（AAJDd） algorithm is proposed. The AAJDd algorithm improves performance by estimating the direction of departure（DOD） and direction of arrival（DOA） directly, avoiding the reuse of the previous moment information in the AAJD algorithm.On this basis, the idea of sequential estimation of the principal component is introduced to turn the matrix operation into a constant operation, reducing the amount of computation and speeding up the convergence. Meanwhile, the eigenvalue is obtained, which can be used to estimate the number of targets. Then, the estimation of signal parameters via rotational invariance technique（ESPRIT） algorithm is improved to realize the automatic matching and association of DOD and DOA. The simulation results show that the AAJDd algorithm has higher tracking performance than the AAJD algorithm, especially when the high maneuvering target is tracked. The efficiency of the proposed method is verified.展开更多
A novel joint diagonalization fractional lower-order spatio-temporal （ST） moments DOA matrix method is proposed to estimate the 2-D DOAs of uncorrelated narrowband signals in the presence of impulsive noise. The new...A novel joint diagonalization fractional lower-order spatio-temporal （ST） moments DOA matrix method is proposed to estimate the 2-D DOAs of uncorrelated narrowband signals in the presence of impulsive noise. The new method retains the advantage of the original ST-DOA matrix method which can estimate 2-D DOAs with neither peak searching nor pair matching. Moreover, it can handle sources with common 1-D angles. Simulation results show that the proposed method yields to better performance to restrain the strong impulsive noise than ST-DOA matrix method, especially for low signal-to-noise ratio case.展开更多
文摘This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers is not countably infinite. Likewise, countably infinite tree structures could represent all real numbers, and all points in any number of dimensions in multi-dimensional spaces. The objective of this paper is not to overturn previous research based on Cantor’s argument, but to suggest that this situation may be treated as a definitional or axiomatic choice. This paper proposes a “non-Cantorian” branch of cardinality theory, representing all these infinities with countably infinite tree structures. This approach would be consistent with the Continuum Hypothesis.
基金supported by the National Natural Science Foundation of China(6167145361201379)Anhui Natural Science Foundation of China(1608085MF123)
文摘In view of the low performance of adaptive asymmetric joint diagonalization（AAJD）, especially its failure in tracking high maneuvering targets, an adaptive asymmetric joint diagonalization with deflation（AAJDd） algorithm is proposed. The AAJDd algorithm improves performance by estimating the direction of departure（DOD） and direction of arrival（DOA） directly, avoiding the reuse of the previous moment information in the AAJD algorithm.On this basis, the idea of sequential estimation of the principal component is introduced to turn the matrix operation into a constant operation, reducing the amount of computation and speeding up the convergence. Meanwhile, the eigenvalue is obtained, which can be used to estimate the number of targets. Then, the estimation of signal parameters via rotational invariance technique（ESPRIT） algorithm is improved to realize the automatic matching and association of DOD and DOA. The simulation results show that the AAJDd algorithm has higher tracking performance than the AAJD algorithm, especially when the high maneuvering target is tracked. The efficiency of the proposed method is verified.
基金the National Natural Science Foundation of China (Grant No.60372022)Program for New Century Excellent Talents in University (Grant No.NCET-05-0806)
文摘A novel joint diagonalization fractional lower-order spatio-temporal （ST） moments DOA matrix method is proposed to estimate the 2-D DOAs of uncorrelated narrowband signals in the presence of impulsive noise. The new method retains the advantage of the original ST-DOA matrix method which can estimate 2-D DOAs with neither peak searching nor pair matching. Moreover, it can handle sources with common 1-D angles. Simulation results show that the proposed method yields to better performance to restrain the strong impulsive noise than ST-DOA matrix method, especially for low signal-to-noise ratio case.
