The fast convergence without initial value dependence is the key to solving large angle relative orientation.Therefore,a hybrid conjugate gradient algorithm is proposed in this paper.The concrete process is:①stochast...The fast convergence without initial value dependence is the key to solving large angle relative orientation.Therefore,a hybrid conjugate gradient algorithm is proposed in this paper.The concrete process is:①stochastic hill climbing(SHC)algorithm is used to make a random disturbance to the given initial value of the relative orientation element,and the new value to guarantee the optimization direction is generated.②In local optimization,a super-linear convergent conjugate gradient method is used to replace the steepest descent method in relative orientation to improve its convergence rate.③The global convergence condition is that the calculation error is less than the prescribed limit error.The comparison experiment shows that the method proposed in this paper is independent of the initial value,and has higher accuracy and fewer iterations.展开更多
Stochastic gradient descent(SGD)methods have gained widespread popularity for solving large-scale optimization problems.However,the inherent variance in SGD often leads to slow convergence rates.We introduce a family ...Stochastic gradient descent(SGD)methods have gained widespread popularity for solving large-scale optimization problems.However,the inherent variance in SGD often leads to slow convergence rates.We introduce a family of unbiased stochastic gradient estimators that encompasses existing estimators from the literature and identify a gradient estimator that not only maintains unbiasedness but also achieves minimal variance.Compared with the existing estimator used in SGD algorithms,the proposed estimator demonstrates a significant reduction in variance.By utilizing this stochastic gradient estimator to approximate the full gradient,we propose two mini-batch stochastic conjugate gradient algorithms with minimal variance.Under the assumptions of strong convexity and smoothness on the objective function,we prove that the two algorithms achieve linear convergence rates.Numerical experiments validate the effectiveness of the proposed gradient estimator in reducing variance and demonstrate that the two stochastic conjugate gradient algorithms exhibit accelerated convergence rates and enhanced stability.展开更多
Main lobe jamming seriously affects the detection performance of airborne early warning radar.The joint processing of polarization-space has become an effective way to suppress the main lobe jamming.To avoid the main ...Main lobe jamming seriously affects the detection performance of airborne early warning radar.The joint processing of polarization-space has become an effective way to suppress the main lobe jamming.To avoid the main beam distortion and wave crest migration caused by the main lobe jamming in adaptive beamforming,a joint optimization algorithm based on adaptive polarization canceller(APC)and stochastic variance reduction gradient descent(SVRGD)is proposed.First,the polarization plane array structure and receiving signal model based on primary and auxiliary array cancellation are established,and an APC iterative algorithm model is constructed to calculate the optimal weight vector of the auxiliary channel.Second,based on the stochastic gradient descent principle,the variance reduction method is introduced to modify the gradient through internal and external iteration to reduce the variance of the stochastic gradient estimation,the airspace optimal weight vector is calculated and the equivalent weight vector is introduced to measure the beamforming effect.Third,by setting up a planar polarization array simulation scene,the performance of the algorithm against the interference of the main lobe and the side lobe is analyzed,and the effectiveness of the algorithm is verified under the condition of short snapshot number and certain signal to interference plus noise ratio.展开更多
自适应波束形成是机载预警雷达数字信号处理的一个关键环节。针对传统最小均方误差(least mean square,LMS)算法在短快拍数条件下的波束形成性能下降以及因迭代震荡易收敛于局部最优值的问题,提出了一种基于机器学习的随机方差减小梯度...自适应波束形成是机载预警雷达数字信号处理的一个关键环节。针对传统最小均方误差(least mean square,LMS)算法在短快拍数条件下的波束形成性能下降以及因迭代震荡易收敛于局部最优值的问题,提出了一种基于机器学习的随机方差减小梯度下降(stochastic variance reduction gradient descent,SVRGD)自适应波束形成方法。首先,建立面阵列接收信号数据模型。其次,基于随机梯度下降原理,引入方差缩减法通过内外循环迭代方式进行梯度修正,以减小随机梯度估计的方差,建立算法模型与实现流程。最后,通过设置平面阵列仿真场景,分析SVRGD自适应波束形成算法在波束形成、抗干扰、收敛速度等方面的性能,验证了该算法在低快拍数、强干扰和强噪声背景下具有的优良能力。展开更多
基金National Natural Science Foundation of China(Nos.4156108241161061)。
文摘The fast convergence without initial value dependence is the key to solving large angle relative orientation.Therefore,a hybrid conjugate gradient algorithm is proposed in this paper.The concrete process is:①stochastic hill climbing(SHC)algorithm is used to make a random disturbance to the given initial value of the relative orientation element,and the new value to guarantee the optimization direction is generated.②In local optimization,a super-linear convergent conjugate gradient method is used to replace the steepest descent method in relative orientation to improve its convergence rate.③The global convergence condition is that the calculation error is less than the prescribed limit error.The comparison experiment shows that the method proposed in this paper is independent of the initial value,and has higher accuracy and fewer iterations.
基金supported by the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA27010101)the Beijing Natural Science Foundation(Grant No.Z220004)+1 种基金the Chinese NSF(Grant No.12021001)the Fundamental Research Funds for the Central Universities(Grant No.2023ZCJH02)。
文摘Stochastic gradient descent(SGD)methods have gained widespread popularity for solving large-scale optimization problems.However,the inherent variance in SGD often leads to slow convergence rates.We introduce a family of unbiased stochastic gradient estimators that encompasses existing estimators from the literature and identify a gradient estimator that not only maintains unbiasedness but also achieves minimal variance.Compared with the existing estimator used in SGD algorithms,the proposed estimator demonstrates a significant reduction in variance.By utilizing this stochastic gradient estimator to approximate the full gradient,we propose two mini-batch stochastic conjugate gradient algorithms with minimal variance.Under the assumptions of strong convexity and smoothness on the objective function,we prove that the two algorithms achieve linear convergence rates.Numerical experiments validate the effectiveness of the proposed gradient estimator in reducing variance and demonstrate that the two stochastic conjugate gradient algorithms exhibit accelerated convergence rates and enhanced stability.
基金supported by the Aviation Science Foundation of China(20175596020)。
文摘Main lobe jamming seriously affects the detection performance of airborne early warning radar.The joint processing of polarization-space has become an effective way to suppress the main lobe jamming.To avoid the main beam distortion and wave crest migration caused by the main lobe jamming in adaptive beamforming,a joint optimization algorithm based on adaptive polarization canceller(APC)and stochastic variance reduction gradient descent(SVRGD)is proposed.First,the polarization plane array structure and receiving signal model based on primary and auxiliary array cancellation are established,and an APC iterative algorithm model is constructed to calculate the optimal weight vector of the auxiliary channel.Second,based on the stochastic gradient descent principle,the variance reduction method is introduced to modify the gradient through internal and external iteration to reduce the variance of the stochastic gradient estimation,the airspace optimal weight vector is calculated and the equivalent weight vector is introduced to measure the beamforming effect.Third,by setting up a planar polarization array simulation scene,the performance of the algorithm against the interference of the main lobe and the side lobe is analyzed,and the effectiveness of the algorithm is verified under the condition of short snapshot number and certain signal to interference plus noise ratio.
