基于序贯最小二乘的多传感器误差配准方法

为实时估计多传感器系统偏差,针对广义最小二乘(GLS)配准方法不能实时估计传感器偏差的问题,提出了基于序贯最小二乘的多传感器误差估计方法,该方法在GLS配准模型基础上,采用最小二乘的序贯方法来估计系统偏差,不必存储过去的测量数据,能够实时估计系统偏差。仿真结果表明了该方法的有效性。     

基于准最小二乘法的光伏阵列模型鲁棒参数估计方法

光伏阵列的模型参数估计在光伏发电系统的仿真、输出功率预测、最大功率点跟踪等方面有重要意义。当测量数据中只含随机误差时,以加权最小二乘（WLS）为优化函数的参数估计方法有较好的辩识效果。但是当测量数据中含有显著误差时,WLS参数辩识的效果较差。为解决此问题,本文提出了一种以准加权最小二乘法（QWLS）为优化函数的参数估计方法来减小显著误差的影响,采用了赤池信息量准则(AIC)设计QWLS最优参数,将该方法应用于光伏阵列中构造模型鲁棒参数估计问题。最后将WLS和QWLS分别结合序列二次规划（SQP）算法,进行光伏阵列模型的参数估计仿真与实验测试。测试结果显示QWLS参数估计结果更准确,验证了准最小二乘法的鲁棒性与有效性。     

新型联邦最小二乘滤波算法及应用

为克服多传感器信息融合时联邦Kalman滤波在系统噪声和测量噪声的统计信息不准 确时所存在的局限性,提出了一种基于最小二乘估计的新型联邦滤波算法,定义为联邦最小二乘 滤波.定性讨论了它与联邦Kalman滤波的关系,通过在INS/双星/GPS组合导航系统中的 实际应用进一步地比较两种算法.实测数据的仿真结果证明,在系统噪声和测量噪声不准确的情 况下,联邦最小二乘滤波的精度要高于联邦Kalman滤波.     

联合ADS-B的最小二乘雷达系统误差估计方法

为了解决两坐标雷达系统误差估计问题,提出一种联合ADS-B的最小二乘雷达系统误差估计方法.提出方法首先将ADS-B量测从地理坐标系转换到雷达局部直角坐标系,建立统一的配准空间;其次以雷达航迹的采样时间为基准,对ADS-B航迹进行插值,构造新的ADS-B航迹;然后采用直线拟合算法分别计算雷达航迹和ADS-B航迹的直线方程,并计算两条直线的夹角,再利用该夹角补偿雷达航迹的航向角数据;最后采用最小二乘算法估计雷达系统误差.实测数据实验结果表明,与传统直线拟合方法和最小二乘方法相比,提出方法能够更有效地估计雷达系统误差;经过提出方法配准处理后,雷达航迹数据的平均斜距离误差和方位角误差分别降低71.7%和52.7%.     

基于递推最小二乘估计的动力学模型参数识别

动力学建模过程中,模型参数的不确定性和参数的未知变化使得建模精度大为降低。通过对非线性最小二乘估计理论的研究,提出动力学模型参数的最小二乘估计,并设计出相应的估计器,基于现场数据给予模型较为准确的定论。应用于曲柄滑块机构中滑块与滑动面间的摩擦系数的估计,经过较少的迭代次数获得满意的估计效果。为动力学模型参数识别,建立更精确模型提供一个有效的途径。     

最小二乘法数据处理

本文阐述在Visual C++ 6.0中实现数据最小二乘法的处理方法,通过实例介绍了最小二乘法的算法和本系统新特点功能。     

最小二乘法数据处理

本文阐述在Visual C＋＋6.0中实现数据最小二乘法的处理方法．通过实例介绍了最小二乘法的算法和本系统新特点功能。     

工业数据挖掘中应用最小二乘法的缺陷

工业数据建模常常使用最小二乘法进行参数估计,在数据满足一定条件的前提下,可得到被估计参数的无偏估计值。但是工业数据一般含有测量误差,当基于误差数据作为自变量进行最小二乘回归时,得到的参数估计值往往是有偏的,其结果不能正确反映数据变量之间的结构关系。因此,对二元变量模型进行了深入分析,通过对测量误差进行合理假设,建立了在统计意义下被估计参数真值与测量误差和参数有偏估计值之间的解析关系式,为进一步参数校正奠定了理论基础。仿真实例表明了该方法的有效性。     

基于递推最小二乘的三轴磁强计在线自校正方法

针对现有三轴磁强计误差校正方法存在计算量大、依赖外界参考信息、不能在线校正等问题,提出一种基于递推最小二乘的误差在线自校正方法。根据Poisson方程对磁场测量模型的描述,导出磁场矢量误差校正模型;基于椭球假设理论,建立校正模型与椭球曲面方程系数之间的关系;推导了基于递推最小二乘的椭球方程系数在线辨识的实现过程,进而求得误差校正参数。实验结果表明:提出的方法能有效校正软磁和硬磁效应引起的数据畸变;采样点磁场强度最大波动幅度由67. 112 8μT降低至14. 064 8μT,误差标准差由15. 828 7μT降低至6. 345 1μT,适用于无外部参考基准下三轴磁强计的误差自动校正。     

加权最小二乘估计在无线传感器网络定位中的应用*

节点自身定位是目前无线传感器网络领域研究的重点之一,定位误差累积问题是节点定位中必须解决的一个关键问题,利用加权最小二乘估计的方法可以有效抑制累积误差的影响。介绍了如何将加权最小二乘估计应用于节点定位以及如何合理地选择加权系数以降低定位误差。仿真实验表明,运用加权最小二乘估计可以有效地抑制误差累积的影响,提高定位精度。     

Asymptotic properties of least squares estimation with fuzzy observations

This paper deals with the asymptotic properties of the least squares estimators for fuzzy linear regression models with fuzzy triangular input-output and random error terms. The asymptotic normality and strong consistency of the fuzzy least squares estimator (FLSE) are investigated; a confidence region based on a class of FLSEs is proposed; the asymptotic relative efficiency of FLSEs with respect to the crisp least squares estimators is also provided and a numerical example is given. Some simulation results are also presented to illustrate the behavior of FLSEs.     

基于整体最小二乘法的高分辨率图像重建算法

提出一种用于高分辨率图像重建的整体最小二乘算法。在现有多数重建算法中,假设系统矩阵是精确的而误差主要源于采样图像,但实际上抖动误差也出现在系统矩阵中。该方法能同时最小化这两种误差,采用基于正则化的Rayleigh商来光滑解,用共轭梯度算法来迭代求解该正则化Rayleigh商的最小化函数。实验证明该方法对于抖动系统矩阵是稳定和精确的。     

基于加权最小二乘的社交网络用户定位方法

社交网络在提供位置交友等服务时,会对展示的用户距离文本进行混淆处理,以保护用户位置隐私。为了验证当前社交网络采用的位置混淆机制能否有效保护用户的精确位置不被泄露,提出了一种基于加权最小二乘的社交网络用户定位方法。该方法构造测试环境,对位置交友服务中混淆后的距离文本进行大量搜集和统计,结合真实距离数据识别报告距离对应的真实距离边界;基于对目标用户所处坐标系象限的判别,优化探针位置部署,并利用三边测量定位模型得到目标用户的多个初步位置估计;基于估计位置与探针的距离关系,分别确定目标用户相较各探针的最远距离和最近距离的权重,从而构造目标函数并基于加权最小二乘求目标函数的最优解,该最优解即目标用户的最终定位结果。该方法基于距离边界约束推断社交用户位置,避免了对位置服务的频繁查询,保证了对社交用户的定位效率。基于微信平台开展了社交用户定位实验,对500个微信用户的实际定位结果表明,该方法能够实现对微信“附近的人”用户的准确定位,与现有基于空间划分、基于启发式数论等典型定位方法相比,定位精度和效率均有更好的性能表现,平均定位误差降低了10%以上,定位过程中的位置服务访问次数减少了50%以上。     

Direct and indirect least squares methods in continuous-time parameter estimation

The discrete-time least squares approach is extended to the estimation of parameters in continuous nonlinear models. The resulting direct integral least squares (DILS) method is both simple and numerically efficient and it usually improves the mean-squared error of the estimates compared with the conventional indirect least squares (ILS) method. The biasedness of the DILS estimates may become serious if the sample points are widely spaced in time and/or the signal-to-noise ratio is low and so a continuous-time symmetric bootstrap (SB) estimator which removes this problem is described. The DILS, SB and ILS methods form a three-stage procedure combining the robustness and numerical efficiency of direct methods with the asymptotic unbiasedness of ILS procedures.     

局部近邻标准化偏最小二乘的多模态间歇过程故障检测

本文针对多模态间歇过程数据多中心和模态方差差异明显的问题,提出了一种基于局部近邻标准化偏最小二乘方法.首先,采用统计模量方法处理间歇过程数据,再利用局部近邻标准化方法将统计模量后的训练数据进行高斯化处理,建立偏最小二乘监控模型,确定控制限;然后,同样对统计模量后的测试数据进行局部近邻标准化处理,再计算测试数据的高斯偏最小二乘监控指标,进行过程监视及故障检测.最后,通过数值实例和青霉素发酵过程验证方法有效性.实验结果表明所提方法解决了故障样本近邻集跨模态问题,对多模态数据具有更好的故障检测能力.     

A revisit to block and recursive least squares for parameter estimation

In this paper, the classical least squares (LS) and recursive least squares (RLS) for parameter estimation have been re-examined in the light of the present day computing capabilities. It has been demonstrated that for linear time-invariant systems, the performance of blockwise least squares (BLS) is always superior to that of RLS. In the context of parameter estimation for dynamic systems, the current computational capability of personal computers are more than adequate for BLS. However, for time-varying systems with abrupt parameter changes, standard blockwise LS may no longer be suitable due to its inefficiency in discarding “old” data. To deal with this limitation, a novel sliding window blockwise least squares approach with automatically adjustable window length triggered by a change detection scheme is proposed. Two types of sliding windows, rectangular and exponential, have been investigated. The performance of the proposed algorithm has been illustrated by comparing with the standard RLS and an exponentially weighted RLS (EWRLS) using two examples. The simulation results have conclusively shown that: (1) BLS has better performance than RLS; (2) the proposed variable-length sliding window blockwise least squares (VLSWBLS) algorithm can outperform RLS with forgetting factors; (3) the scheme has both good tracking ability for abrupt parameter changes and can ensure the high accuracy of parameter estimate at the steady-state; and (4) the computational burden of VLSWBLS is completely manageable with the current computer technology. Even though the idea presented here is straightforward, it has significant implications to virtually all areas of application where RLS schemes are used.     

Robust least squares methods under bounded data uncertainties

We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems, where the estimator has imperfect data matrix and output vector information. We define the performance of an estimator relative to the performance of the optimal least squares (LS) estimator tuned to the underlying unknown data matrix and output vector, which is defined as the regret of the estimator. We then introduce an efficient robust LS estimation approach that minimizes this regret for the worst possible data matrix and output vector, where we refrain from any structural assumptions on the data. We demonstrate that minimizing this worst-case regret can be cast as a semi-definite programming (SDP) problem. We then consider the regularized and structured LS problems and present novel robust estimation methods by demonstrating that these problems can also be cast as SDP problems. We illustrate the merits of the proposed algorithms with respect to the well-known alternatives in the literature through our simulations.     

A novel robust data reconciliation method for industrial processes

Data reconciliation has played a significant role in rectifying process data which can meet the conservation laws in industrial processes. Generally, the actual measurements are often easily contaminated by different gross errors. Thus, it is essential to build robust data reconciliation methods to alleviate the impact of gross errors and provide accurate data. In this paper, a novel robust estimator is proposed to improve the robustness of data reconciliation method, which is based on a new robust estimation function. First, the main robust properties are analyzed with its objective and influence functions for the proposed robust estimator. Then, the effectiveness of the new robust data reconciliation method is demonstrated on a linear numerical case and a nonlinear example. Moreover, it is further used to a practical industrial evaporation production process, which also demonstrates that the process data can be better reconciled with the proposed robust estimator.     

Parameter identification of PWARX models using fuzzy distance weighted least squares method

PieceWise AutoRegressive eXogenous (PWARX) models represent one of the broad classes of the hybrid dynamical systems (HDS). Among many classes of HDS, PWARX model used as an attractive modeling structure due to its equivalence to other classes. This paper presents a novel fuzzy distance weight matrix based parameter identification method for PWARX model. In the first phase of the proposed method estimation for the number of affine submodels present in the HDS is proposed using fuzzy clustering validation based algorithm. For the given set of input–output data points generated by predefined PWARX model fuzzy c-means (FCM) clustering procedure is used to classify the data set according to its affine submodels. The fuzzy distance weight matrix based weighted least squares (WLS) algorithm is proposed to identify the parameters for each PWARX submodel, which minimizes the effect of noise and classification error. In the final phase, fuzzy validity function based model selection method is applied to validate the identified PWARX model. The effectiveness of the proposed method is demonstrated using three benchmark examples. Simulation experiments show validation of the proposed method.