In this work,we address the frequency estimation problem of a complex single-tone embedded in the heavy-tailed noise.With the use of the linear prediction(LP)property and l_(1)-norm minimization,a robust frequency est...In this work,we address the frequency estimation problem of a complex single-tone embedded in the heavy-tailed noise.With the use of the linear prediction(LP)property and l_(1)-norm minimization,a robust frequency estimator is developed.Since the proposed method employs the weighted l_(1)-norm on the LP errors,it can be regarded as an extension of the l_(1)-generalized weighted linear predictor.Computer simulations are conducted in the environment of α-stable noise,indicating the superiority of the proposed algorithm,in terms of its robust to outliers and nearly optimal estimation performance.展开更多
Based on the range space property （RSP）, the equivalent conditions between nonnegative solutions to the partial sparse and the corresponding weighted l1-norm minimization problem are studied in this paper. Different...Based on the range space property （RSP）, the equivalent conditions between nonnegative solutions to the partial sparse and the corresponding weighted l1-norm minimization problem are studied in this paper. Different from other conditions based on the spark property, the mutual coherence, the null space property （NSP） and the restricted isometry property （RIP）, the RSP- based conditions are easier to be verified. Moreover, the proposed conditions guarantee not only the strong equivalence, but also the equivalence between the two problems. First, according to the foundation of the strict complemenrarity theorem of linear programming, a sufficient and necessary condition, satisfying the RSP of the sensing matrix and the full column rank property of the corresponding sub-matrix, is presented for the unique nonnegative solution to the weighted l1-norm minimization problem. Then, based on this condition, the equivalence conditions between the two problems are proposed. Finally, this paper shows that the matrix with the RSP of order k can guarantee the strong equivalence of the two problems.展开更多
In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong ...In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong efficiency of the random weighting method is shown. Asimulation study is conducted to compare the L_1-norm estimator with the least square estimator interm of approximate accuracy, and simulation results are given for comparison between the randomweighting method and normal approximation method.展开更多
The orthogonal signals of multi-carrier-frequency emission and multiple antennas receipt module are used in SIAR radar.The corresponding received echo is equivalent to non-uniform spatial sampling after the frequency ...The orthogonal signals of multi-carrier-frequency emission and multiple antennas receipt module are used in SIAR radar.The corresponding received echo is equivalent to non-uniform spatial sampling after the frequency diversity process.As using the traditional Fourier transform will result in the target spectral with large sidelobe,the method presented in this paper firstly makes the preordering treatment for the position of the received antenna.Then,the Bayesian maximum posteriori estimation with l2-norm weighted constraint is utilized to achieve the equivalent uniform array echo.The simulations present the spectrum estimation in angle precision estimation of multiple targets under different SNRs,different virtual antenna numbers and different elevations.The estimation results confirm the advantage of SIAR radar both in array expansion and angle estimation.展开更多
文摘In this work,we address the frequency estimation problem of a complex single-tone embedded in the heavy-tailed noise.With the use of the linear prediction(LP)property and l_(1)-norm minimization,a robust frequency estimator is developed.Since the proposed method employs the weighted l_(1)-norm on the LP errors,it can be regarded as an extension of the l_(1)-generalized weighted linear predictor.Computer simulations are conducted in the environment of α-stable noise,indicating the superiority of the proposed algorithm,in terms of its robust to outliers and nearly optimal estimation performance.
基金Research supported by the National Natural Science Foundation of China under Grant 61672005
文摘Based on the range space property （RSP）, the equivalent conditions between nonnegative solutions to the partial sparse and the corresponding weighted l1-norm minimization problem are studied in this paper. Different from other conditions based on the spark property, the mutual coherence, the null space property （NSP） and the restricted isometry property （RIP）, the RSP- based conditions are easier to be verified. Moreover, the proposed conditions guarantee not only the strong equivalence, but also the equivalence between the two problems. First, according to the foundation of the strict complemenrarity theorem of linear programming, a sufficient and necessary condition, satisfying the RSP of the sensing matrix and the full column rank property of the corresponding sub-matrix, is presented for the unique nonnegative solution to the weighted l1-norm minimization problem. Then, based on this condition, the equivalence conditions between the two problems are proposed. Finally, this paper shows that the matrix with the RSP of order k can guarantee the strong equivalence of the two problems.
基金Supported by the Natural Science Foundation of Beijing City of China (1042002)the Science and Technology Development Foundation of Education Committee of Beijing Citythe Special Expenditure of Excellent Person Education of Beijing(20041D0501515)
文摘In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong efficiency of the random weighting method is shown. Asimulation study is conducted to compare the L_1-norm estimator with the least square estimator interm of approximate accuracy, and simulation results are given for comparison between the randomweighting method and normal approximation method.
基金supported by the Specialized Research Fund for the Doc-toral Program of Higher Education (Grant No. 200807010004)the National Natural Science Foundation of China (Grant Nos. 60776795, 60902079, 60902031), the Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT) (Grant No. IRT0645)
文摘The orthogonal signals of multi-carrier-frequency emission and multiple antennas receipt module are used in SIAR radar.The corresponding received echo is equivalent to non-uniform spatial sampling after the frequency diversity process.As using the traditional Fourier transform will result in the target spectral with large sidelobe,the method presented in this paper firstly makes the preordering treatment for the position of the received antenna.Then,the Bayesian maximum posteriori estimation with l2-norm weighted constraint is utilized to achieve the equivalent uniform array echo.The simulations present the spectrum estimation in angle precision estimation of multiple targets under different SNRs,different virtual antenna numbers and different elevations.The estimation results confirm the advantage of SIAR radar both in array expansion and angle estimation.
