The structured total least squares algorithm research for passive location based on angle information

Based on the constrained total least squares (CTLS) passive location algorithm with bearing-only measurements, in this paper, the same passive location problem is transformed into the structured total least squares (STLS) problem. The solution of the STLS problem for passive location can be obtained using the inverse iteration method. It also expatiates that both the STLS algorithm and the CTLS algorithm have the same location mean squares error under certain condition. Finally, the article presents a kind of location and tracking algorithm for moving target by combining STLS location algorithm with Kalman filter (KF). The efficiency and superiority of the proposed algorithms can be confirmed by computer simulation results.     

A robust TDOA-based location method and its performance analysis

Based on time difference of arrive (TDOA), the regularized constrained total least square (RCTLS) algorithm for passive location is presented in this paper. RCLTS is used to solve the location equations by transforming the nonlinear equations about TDOA into linear equations about parameters of the position and range and expanding the true TDOA in a first-order Taylor series about measurement TDOA. A proper weight is chosen by the least mean square error (MSE) rule to obtain the location solution through analyzing the location error, whose feasibility and effectiveness are well proved by computer simulations. The CRB and GDOP for TDOA-based location are given. Supported by the Program for New Century Excellent Talents in University, Ministry of Education, China (Grant No. NCET-05-0803)     

Structural total least squares algorithm for locating multiple disjoint sources based on AOA/TOA/FOA in the presence of system error

Single-station passive localization technology avoids the complex time synchronization and information exchange between multiple observatories, and is increasingly important in electronic warfare. Based on a single moving station localization system, a new method with high localization precision and numerical stability is proposed when the measurements from multiple disjoint sources are subject to the same station position and velocity displacement. According to the available measurements including the angle-of-arrival (AOA), time-of-arrival (TOA), and frequency-of-arrival (FOA), the corresponding pseudo linear equations are deduced. Based on this, a structural total least squares (STLS) optimization model is developed and the inverse iteration algorithm is used to obtain the stationary target location. The localization performance of the STLS localization algorithm is derived, and it is strictly proved that the theoretical performance of the STLS method is consistent with that of the constrained total least squares method under first-order error analysis, both of which can achieve the Cramér-Rao lower bound accuracy. Simulation results show the validity of the theoretical derivation and superiority of the new algorithm.     

采用有限时间平均一致性协议的电力系统分布式状态估计

随着基于相量量测单元的广域量测系统在技术上的成熟与推广应用,利用WAMS量测可实现电力系统线性状态估计.本文基于广域量测系统提出一种全分布式状态估计算法.首先根据拉格朗日乘子法推导了多区域约束加权最小二乘估计模型,然后引入有限时间平均一致性协议,得到系统量测正常情况下的分布式状态估计算法.考虑了系统量测存在异常数据情况,根据最小二乘估计的几何意义扩展推导出修正算法,使其在各区域剔除异常量测后,无需改变信息矩阵,只需执行若干次有限时间平均一致性协议能收敛至信息矩阵修正后的集中式估计值.最后,理论分析和实验结果证明了算法的有效性.     

Simplified neural networks for solving linear least squares andtotal least squares problems in real time

In this paper a new class of simplified low-cost analog artificial neural networks with on chip adaptive learning algorithms are proposed for solving linear systems of algebraic equations in real time. The proposed learning algorithms for linear least squares (LS), total least squares (TLS) and data least squares (DLS) problems can be considered as modifications and extensions of well known algorithms: the row-action projection-Kaczmarz algorithm and/or the LMS (Adaline) Widrow-Hoff algorithms. The algorithms can be applied to any problem which can be formulated as a linear regression problem. The correctness and high performance of the proposed neural networks are illustrated by extensive computer simulation results.     

声呐位置误差情况下的运动目标多基地定位方法

在多基地声呐定位系统中,声呐的位置信息往往含有随机误差,这些误差会严重影响目标的定位精度。针对这一问题,提出了一种基于时间和多普勒频率的运动目标定位方法。首先,将基于时间和多普勒频率定位机制的非线性量测方程组转化为关于目标位置、速度及中间变量的伪线性方程组,利用加权最小二乘估计法对运动目标的位置、速度进行初始求解;然后,利用位置、速度及中间变量之间的相关性对位置和速度的估计偏差进行求解;最后,对位置和速度的初始解进行误差修正。分析了所提算法在量测误差较小情况下的统计有效性,并通过蒙特卡洛模拟进行了数值验证。     

加权最小二乘联合遗传算法的无源定位

针对复杂环境下运动通信辐射源的无源定位,闭式解方法对于时频差模型中的测量噪声敏感且存在定位均方根误差较大问题.为了改善大观测误差下的定位性能,本文提出一种加权最小二乘联合遗传算法的递推式混合TDOA/FDOA定位方法.该方法首先利用已知站点观测大量时频差数据并建立误差模型,基于模型对定位过程中的多组时频差序列进行数据处理;其次通过加权最小二乘求解目标位置的初始值;然后采用改进的遗传算法在初始值的基础上通过多组时频差序列不断迭代、递推求解,修正位置坐标;最后利用位置估计和频差模型完成对目标速度估计.仿真结果表明,本文定位算法相比于经典两步加权最小二乘法具有更低的均方根误差,在大观测误差下能保持较高精度.同时相比于其他混合定位算法收敛速度快,可以有效减少计算量.     

Ein Verfahren zur Behandlung von Ausgleichsaufgaben mit Intervallkoeffizienten

In this paper an algorithm for the inclusion of the solution set of a linear least squares problem with interval coefficients is given. It is based on a combination of Björck's iterative procedure for the solution of the linear least squares problem [5] and a well known algorithm for the solution of linear equations with interval coefficients.     

基于人工蜂群改进算法的无线传感器网络定位算法

针对无线传感器网络无需测距的DV-Hop定位算法中,利用最小二乘法进行节点定位时存在较大误差的问题,提出了一种改进的DV-Hop智能定位算法。首先在详细分析DV-Hop算法中最小二乘法原理的基础上,将定位问题转化成全局最优化问题;其次根据人工蜂群算法计算最优化问题的优势,结合定位具体问题,提出了一种自适应人工蜂群算法;最后将改进的人工蜂群算法运用到DV-Hop算法未知节点的坐标估计阶段实现定位。仿真实验表明,改进的定位算法与最小二乘法及基于传统人工蜂群算法的DV-Hop算法相比,在不同锚节点比例和不同节点数的情况下,定位精度和精度稳定性都有明显提高。     

无线传感器网络中的线性移动目标运动参数捕获方法

移动目标跟踪即移动目标的运动路径与参数获取在无线传感器网络应用中具有重要的研究价值.采用移动目标节点与信标节点间的TOA测量方法,提出了无线传感器网络中移动目标运动参数的捕获方法.通过建立移动目标运动参数的估计模型,本文首先推导了线性移动目标初始位置及移动速度估计的非约束线性最小二乘(ULLS)和约束线性最小二乘(CLLS)方法.将估计模型松弛为凸优化的半正定规划(SDP)问题,又设计了运动参数捕获的SDP算法.仿真分析结果表明,在3种所设计算法中ULLS算法的估计误差最大,SDP算法其次,CLLS算法的估计误差最小.随着采样周期的增加,初始位置的估计误差亦稍有增大,但速度估计误差却在减少.更多的采样点数量有利于增加测量信息量,可以有效减少位置及速度估计误差.     

On a special class of nonlinear fredholm integral equations of the first kind

In this paper a special class of nonlinear Fredholm integral equations of the first kind, the so-called Urysohn equation, is considered, where the kernel depends ont only via the unknown functionx(t). To overcome the ambiguity, a decreasing rearrangement approach is used. Moreover, a constrained least squares method helps regularizing the problem. As a specific property, the equation can be decomposed into a well-posed nonlinear part, the inversion of a function, and an ill-posed linear part, a linear Fredholm integral equation of the first kind. The linear part of this two-stage procedure was already discussed in [8]. In the present paper the two-stage procedure is compared with a one-stage nonlinear least squares approximation which is directly applied to the nonlinear original integral equation. The comparison is explained by means of a computational case study for a specific example arising in optics.     

A Framework for Moving Least Squares Method with Total Variation Minimizing Regularization

In this paper, we propose a computational framework to incorporate regularization terms used in regularity based variational methods into least squares based methods. In the regularity based variational approach, the image is a result of the competition between the fidelity term and a regularity term, while in the least squares based approach the image is computed as a minimizer to a constrained least squares problem. The total variation minimizing denoising scheme is an exemplary scheme of the former approach with the total variation term as the regularity term, while the moving least squares method is an exemplary scheme of the latter approach. Both approaches have appeared in the literature of image processing independently. By putting schemes from both approaches into a single framework, the resulting scheme benefits from the advantageous properties of both parties. As an example, in this paper, we propose a new denoising scheme, where the total variation minimizing term is adopted by the moving least squares method. The proposed scheme is based on splitting methods, since they make it possible to express the minimization problem as a linear system. In this paper, we employed the split Bregman scheme for its simplicity. The resulting denoising scheme overcomes the drawbacks of both schemes, i.e., the staircase artifact in the total variation minimizing based denoising and the noisy artifact in the moving least squares based denoising method. The proposed computational framework can be utilized to put various combinations of both approaches with different properties together.     

基于递推总体最小二乘的北斗T-Rn型被动雷达定位

对北斗卫星作为机会辐射源的可行性进行分析,研究了北斗卫星信号Kasami码的模糊函数.仿真表明:信号有良好的距离与速度分辨力.提出基于到达时间差(TDOA)的T-Rn型被动雷达总体最小二乘TLS定位方法的理论推导,并针对TLS算法的缺点给出递推TLS(RTLS)算法.仿真表明:该算法逼近TLS算法,能够实时更新且节省硬件资源.     

无线传感器网络LQI测距定位算法及其误差研究

无线传感器定位算法对无线传感器的工程应用具有重要的意义.针对基于LQ I测距的无线传感器网络,研究了测距模型的建立并对比分析了最小二乘定位算法和质心定位算法,相关仿真研究结果表明:该两种定位算法的精度与测距误差的性质具有鲜明的规律性,当测距误差正向分布时,最小二乘定位比质心算法精度高;当测距误差正负双向分布时,质心算法比最小二乘定位精度高.最后,文中通过搭建的Z igBee硬件平台实验验证了仿真的结果.本文从测距误差模型入手对无线传感器定位算法进行研究,仿真结果与实验验证相一致,有利于W SN的推广应用.     

Congau — constrained minimization of least squares objective functions

A technique for constrained parameter optimization is presented and applied to some test problems. The procedure employs an exterior penalty function to transform the constrained objective function into an unconstrained index of performance which is minimized by Gauss' method. Gauss' method recasts the minimization problem to one of solving simultaneous linear equations with the variation of the parameters as the unknowns. For the special case of a quadratic objective function and linear constraints, the penalized critical value is obtained in one step. The restriction that the objective function be of least squares form results from using Gauss' method. The restriction on each constraint is that first derivatives with respect to all parameters be obtainable.     

Linear Hopfield networks and constrained optimization

It is shown that a Hopfield neural network (with linear transfer functions) augmented by an additional feedforward layer can be used to compute the Moore-Penrose generalized inverse of a matrix. The resultant augmented linear Hopfield network can be used to solve an arbitrary set of linear equations or, alternatively, to solve a constrained least squares optimization problem. Applications in signal processing and robotics are considered. In the former case the augmented linear Hopfield network is used to estimate the "structured noise" component of a signal and adjust the parameters of an appropriate filter on-line, whereas in the latter case it is used to implement an on-line solution to the inverse kinematics problem.     

Partial Linearization of One Class of the Nonlinear Total Least Squares Problem by Using the Inverse Model Function

In this paper we consider a special nonlinear total least squares problem, where the model function is of the form . Using the fact that after an appropriate substitution, the model function becomes linear in parameters, and that the symmetry preserves the distances, this nonlinear total least squares problem can be greatly simplified. In this paper we give the existence theorem, propose an efficient algorithm for searching the parameters and give some numerical examples. Received: June 30, 1997; revised October 31, 1998     

含噪声模糊逻辑系统的参数学习算法

当采用最小方差型的误差成本函数进行输入含噪系统的参数学习时，参数不能收敛至真值，利用包含噪声方差的误差成本函数可解决此问题．本文将此误差成本函数推广到多人单出系统，将之引入到模糊逻辑系统的参数学习中，并且输入输出数据中的噪声方差也通过学习而得到，不必进行多次测量．最后通过仿真对比验证表明了该方法的有效性．     

Approximation of the Stokes–Darcy System by Optimization

A solution algorithm for the linear/nonlinear Stokes–Darcy coupled problem is proposed and investigated. The coupled system is formulated as a constrained optimal control problem, where a flow balance is forced across the interface, inflow, and outflow boundaries by minimizing a suitably defined functional. Optimization is achieved by exploiting a Neumann type boundary condition imposed on each subproblem as a control. A numerical algorithm is presented for a least squares functional whose solution yields a minimizer of the constrained optimization problem. Numerical experiments are provided to validate accuracy and efficiency of the algorithm.     

递归最小二乘循环神经网络

针对循环神经网络(Recurrent neural networks, RNNs)一阶优化算法学习效率不高和二阶优化算法时空开销过大, 提出一种新的迷你批递归最小二乘优化算法. 所提算法采用非激活线性输出误差替代传统的激活输出误差反向传播, 并结合加权线性最小二乘目标函数关于隐藏层线性输出的等效梯度, 逐层导出RNNs参数的迷你批递归最小二乘解. 相较随机梯度下降算法, 所提算法只在RNNs的隐藏层和输出层分别增加了一个协方差矩阵, 其时间复杂度和空间复杂度仅为随机梯度下降算法的3倍左右. 此外, 本文还就所提算法的遗忘因子自适应问题和过拟合问题分别给出一种解决办法. 仿真结果表明, 无论是对序列数据的分类问题还是预测问题, 所提算法的收敛速度要优于现有主流一阶优化算法, 而且在超参数的设置上具有较好的鲁棒性.