基于最小一乘估计的多传感器信息融合方法

针对多个传感器对某一特性指标进行测量实验的数据融合问题,从稳健性角度,利用统计理论中的最小一乘估计,提出一种多传感器数据的融合方法。该方法基于自适应加权,以最小化传感器测量数据的绝对偏差为目标函数,通过求解条件极值问题,得到各传感器数据的权数,从而给出融合结果。仿真实例表明方法的有效性和较好的稳健性。     

基于近似最小一乘准则的多新息辨识算法

结合梯度搜索原理及多新息思想,通过建立近似最小一乘目标函数,给出了一种基于近似最小一乘准则的多新息随机梯度辨识算法。算法在每一步计算时综合考虑当前和过去时刻的数据,用一个可导确定性函数近似代替残差的绝对值,既克服了最小二乘准则在测量数据存在异常点时残差平方项过大的缺点,又满足了算法中求导的需求。仿真结果表明,相比于以最小二乘为准则函数的辨识算法,本文算法有效的提高了参数估计精度,降低了异常点对辨识结果的影响,尤其是在存在尖峰序列噪声或大幅度干扰时显示出良好的稳健性。在实际的工业应用中,应用该算法无须事先剔除异常点数据,降低了辨识算法对测量数据质量的要求。     

基于稳健算法的直线拟合

直线是图像分析中非常重要的描述符号。对工业控制中的现象进行图像处理时常常会用到直线拟合,虽然已有的拟合方法较多,但都存在一些缺陷限制着它们的使用范围。针对图象处理中利用经典最小二乘法拟合直线出现的问题,提出了有效的稳健型最小二乘法和最小一乘法的新型解法,实验证明了该方法的有效性及高精度性。     

基于多项式统计的舰船传感器偏差估计算法

现代舰艇配置多部用于探测作战任务目标的传感器,因此必须估计距离、方位和俯仰的探测参数偏差。大部分已有算法需要从传感器获取额外信息,比如滤波增益和关联协方差矩阵。本文提出7阶多项式拟合和假设检验的新算法,使用K-S检验、卡方检验和t检验方法统计分析估计传感器系统偏差。通过比较不同传感器的航迹数据,该算法可获得多种传感器的探测精度和偏差,并提供传感器间偏差异常定位。最后,通过仿真数据和无人机测量数据验证本文所提算法的有效性。     

基于近似偏最小一乘的闭环系统辨识新方法

本文基于近似最小一乘准则和主成分分析,针对反馈通道模型阶次低于前向通道模型阶次且反馈通道不存在噪声的闭环系统,进行了近似偏最小一乘递推辨识算法的推导.为解决最小一乘准则函数不可微的问题,本文算法用确定性可导函数近似代替残差绝对值.近似偏最小一乘辨识算法可以克服基于最小二乘准则的辨识算法在受到满足(SαS)分布的尖峰噪声干扰时残差平方项过大的缺点,具有目标函数可导,计算简单的优点.同时,通过主成分分析去除数据向量各元素之间的线性相关,可以得出模型参数的唯一解.仿真实验表明,本文算法可以对反馈通道模型阶次低于前向通道模型阶次的闭环系统进行直接辨识,抑制了尖峰噪声对辨识结果的影响,具有优良的稳健性,可以更好地应用于闭环系统辨识.     

传感器输出特征线性化的稳健算法

利用最小一乘估计的稳健性 ,给出了传感器输出特征线性化的特征直线的稳健估计。该方法在稳健性方面明显优于最小二乘估计 ,更有效地刻划了传感性输出特征的本质     

基于最小一乘的系统辨识方法研究

针对系统参数辨识中最小二乘估计的稳健性较差,给出稳健性较强的最小一乘的系统辨识方法。推导出了最小一乘回归系数的估计式,使用逐次逼近迭代的方法,构造迭代序列给出最小一乘回归系数的迭代算法。并把该算法应用于控制系统参数辨识中,与最小二乘辨识相比较,当模型的观测数据有测量噪声时,最小一乘回归系数的收敛性及数值稳定性较好。仿真结果验证了理论,显示了最小一乘辨识的优越性。     

多传感器目标状态与动态偏差联合估计算法

针对多传感器系统动态偏差估计问题,在不敏粒子滤波(UPF)算法的基础上,提出了一种修正的不敏粒子滤波(Modi-fied UPF,MUPF)算法.由于系统动态偏差引起的异常量测值时,MUPF算法利用滤波预测残差构建的调节因子控制新息协方差矩阵,进而调整滤波增益的大小;在不丢失有用新息的前提下,减小了异常量测对滤波估计结果的影响.利用上述算法与不敏卡尔曼滤波(UKF)算法和扩展卡尔曼粒子滤波(EPF)算法进行了仿真比较.结果表明,MUPF算法对系统动态距离和角度偏差估计的均方根误差(RMSE)明显小于UKF算法和EPF算法的估计结果,提高了估计精度和可靠性.显然,MUPF算法也适用于系统固定测量偏差估计和目标状态估计.     

多无源传感器的在线配准

为估计无源传感器的角度偏差,在只有角度测量信息的前提下,提出了多无源传感器的在线配准方法.该方法运用几何知识,由传感器测量的多个角度数据得到目标的估计距离,通过估计距离进行在线滤波器的初始化,进而实时估计传感器的角度偏差;并给出了配准模型的Cramer-Rao下限(CRLB).Monte-Carlo仿真表明:该方法能有效地估计无源传感器的角度偏差,同时得到目标航迹.     

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。     

近似最小一乘意义下的鲁棒卡尔曼滤波器

当存在高污染率的野值观测时,现有的鲁棒卡尔曼滤波器的数值稳定性和抗差能力可能会严重退化.为此,基于近似最小一乘估计和修正的高斯牛顿方法提出一种新的鲁棒卡尔曼滤波器,以减小含野量测对滤波器的不利影响.通过条件数分析和影响函数分析,从理论上证明所提出方法的数值稳定性和抗差能力均好于基于Huber估计的卡尔曼滤波器.通过仿真实验对理论分析结果进行验证.仿真结果表明,在只有少量野值观测的情况下,所提出的滤波器与Huber卡尔曼滤波器的估计性能大致相当;而在含有高污染率的野值观测时,所提出的滤波器的估计性能明显好于Huber卡尔曼滤波器.在仿真实验中还对几种滤波器的计算花费进行了比较,发现所提出滤波器的计算代价小于Huber卡尔曼滤波器的计算代价.     

Identification algorithm based on the approximate least absolute deviation criteria

Considering the situation that the least-squares (LS) method for system identification has poor robustness and the least absolute deviation (LAD) algorithm is hard to construct, an approximate least absolute deviation (ALAD) algorithm is proposed in this paper. The objective function of ALAD is constructed by introducing a deterministic function to approximate the absolute value function. Based on the function, the recursive equations for parameter identification are derived using Gauss-Newton iterative algorithm without any simplification. This algorithm has advantages of simple calculation and easy implementation, and it has second order convergence speed. Compared with the LS method, the new algorithm has better robustness when disorder and peak noises exist in the measured data. Simulation results show the efficiency of the proposed method.     

New identification method for Hammerstein models based on approximate least absolute deviation

Disorder and peak noises or large disturbances can deteriorate the identification effects of Hammerstein non-linear models when using the least-square (LS) method. The least absolute deviation technique can be used to resolve this problem; however, its absolute value cannot meet the need of differentiability required by most algorithms. To improve robustness and resolve the non-differentiable problem, an approximate least absolute deviation (ALAD) objective function is established by introducing a deterministic function that exhibits the characteristics of absolute value under certain situations. A new identification method for Hammerstein models based on ALAD is thus developed in this paper. The basic idea of this method is to apply the stochastic approximation theory in the process of deriving the recursive equations. After identifying the parameter matrix of the Hammerstein model via the new algorithm, the product terms in the matrix are separated by calculating the average values. Finally, algorithm convergence is proven by applying the ordinary differential equation method. The proposed algorithm has a better robustness as compared to other LS methods, particularly when abnormal points exist in the measured data. Furthermore, the proposed algorithm is easier to apply and converges faster. The simulation results demonstrate the efficacy of the proposed algorithm.     

Estimating the fundamental matrix based on least absolute deviation

The epipolar geometry is the intrinsic projective geometry between two views, and the algebraic representation of it is the fundamental matrix. Estimating the fundamental matrix requires solving an over-determined equation. Many classical approaches assume that the error values of the over-determined equation obey a Gaussian distribution. However, the performances of these approaches may decrease significantly when the noise is large and heterogeneous. This paper proposes a novel technique for estimating the fundamental matrix based on least absolute deviation (LAD), which is also known as the L₁ method. Then a linear iterative algorithm is presented. The experimental results on some indoor and outdoor scenes show that the proposed algorithm yields the accurate and robust estimates of the fundamental matrix when the noise is non-Gaussian.     

全最小一乘准则下的LGA新算法

为克服传统提取数据集中线性结构的LGA对噪声数据比较敏感的缺陷,提出了两种基于稳健的全最小一乘准则下的LGA新算法。首先证明了全最小一乘准则下数据集最优划分的存在性,并据此给出一种有限步终止算法。其次为提高计算速度,根据k-means算法、全最小一乘准则和重抽样方法给出另一种快速收敛算法。通过与传统的LGA和基于Trimmed k-means思想的稳健LGA的比较,仿真结果表明提出的算法具有较好的稳健性,可以在离群数据较多的情形下,同时找出数据集合中的所有强线性结构。     

A generalized least absolute deviation method for parameter estimation of autoregressive signals

This paper proposes a generalized least absolute deviation (GLAD) method for parameter estimation of autoregressive (AR) signals under non-Gaussian noise environments. The proposed GLAD method can improve the accuracy of the estimation of the conventional least absolute deviation (LAD) method by minimizing a new cost function with parameter variables and noise error variables. Compared with second- and high-order statistical methods, the proposed GLAD method can obtain robustly an optimal AR parameter estimation without requiring the measurement noise to be Gaussian. Moreover, the proposed GLAD method can be implemented by a cooperative neural network (NN) which is shown to converge globally to the optimal AR parameter estimation within a finite time. Simulation results show that the proposed GLAD method can obtain more accurate estimates than several well-known estimation methods in the presence of different noise distributions.     

基于递推最小二乘与互补滤波的姿态估计

针对基于微机电系统(MEMS)的惯性导航系统中陀螺噪声较大导致姿态漂移的问题,本文基于递推最小二乘(RLS)与互补滤波器提出一种提高姿态估计精度的方法.该方法从陀螺去噪算法和姿态解算原理两个方面提高姿态估计精度:在陀螺去噪方面,为克服传统递推最小二乘的不足,提出一种随机加权的递推最小二乘法,利用随机加权实现对偏差的估计;在姿态解算方面,在传统互补滤波器的基础上通过自适应调整比例-积分(PI)参数来调整滤波器的交接频率,最终得到陀螺积分值的高通滤波和加速度计的低通滤波的叠加.转台静态和动态实验结果表明,使用本文所提方法后,有效降低了陀螺噪声,姿态估计精度明显提升.     

Robust object tracking using least absolute deviation

Recently, sparse representation has been applied to object tracking, where each candidate target is approximately represented as a sparse linear combination of target templates. In this paper, we present a new tracking algorithm, which is faster and more robust than other tracking algorithms, based on sparse representation. First, with an analysis of many typical tracking examples with various degrees of corruption, we model the corruption as a Laplacian distribution. Then, a LAD–Lasso optimisation model is proposed based on Bayesian Maximum A Posteriori (MAP) estimation theory. Compared with L1 Tracker and APG-L1 Tracker, the number of optimisation variables is reduced greatly; it is equal to the number of target templates, regardless of the dimensions of the feature. Finally, we use the Alternating Direction Method of Multipliers (ADMM) to solve the proposed optimisation problem. Experiments on some challenging sequences demonstrate that our proposed method performs better than the state-of-the-art methods in terms of accuracy and robustness.     

Constrained least absolute deviation neural networks.

It is well known that least absolute deviation (LAD) criterion or L(1)-norm used for estimation of parameters is characterized by robustness, i.e., the estimated parameters are totally resistant (insensitive) to large changes in the sampled data. This is an extremely useful feature, especially, when the sampled data are known to be contaminated by occasionally occurring outliers or by spiky noise. In our previous works, we have proposed the least absolute deviation neural network (LADNN) to solve unconstrained LAD problems. The theoretical proofs and numerical simulations have shown that the LADNN is Lyapunov-stable and it can globally converge to the exact solution to a given unconstrained LAD problem. We have also demonstrated its excellent application value in time-delay estimation. More generally, a practical LAD application problem may contain some linear constraints, such as a set of equalities and/or inequalities, which is called constrained LAD problem, whereas the unconstrained LAD can be considered as a special form of the constrained LAD. In this paper, we present a new neural network called constrained least absolute deviation neural network (CLADNN) to solve general constrained LAD problems. Theoretical proofs and numerical simulations demonstrate that the proposed CLADNN is Lyapunov stable and globally converges to the exact solution to a given constrained LAD problem, independent of initial values. The numerical simulations have also illustrated that the proposed CLADNN can be used to robustly estimate parameters for nonlinear curve fitting, which is extensively used in signal and image processing.     

Fuzzy regression using least absolute deviation estimators

In fuzzy regression, that was first proposed by Tanaka et al. (Eur J Oper Res 40:389–396, 1989; Int Cong Appl Syst Cybern 4:2933–2938, 1980; IEEE Trans SystMan Cybern 12:903–907, 1982), there is a tendency that the greater the values of independent variables, the wider the width of the estimated dependent variables. This causes a decrease in the accuracy of the fuzzy regression model constructed by the least squares method. This paper suggests the least absolute deviation estimators to construct the fuzzy regression model, and investigates the performance of the fuzzy regression models with respect to a certain errormeasure. Simulation studies and examples show that the proposed model produces less error than the fuzzy regression model studied by many authors that use the least squares method when the data contains fuzzy outliers.