非高斯冲激干扰下基于Softplus函数的核自适应滤波算法

针对非高斯环境下一般自适应滤波算法性能严重下降问题,本文提出了一种基于Softplus函数的核分式低次幂自适应滤波算法(kernel fractional lower algorithm based on Softplus function,SP-KFLP),该算法将Softplus函数与核分式低次幂准则相结合,利用输出误差的非线性饱和特性通过随机梯度下降法更新权重.一方面利用Softplus函数的特点在保证了SP-KFLP算法具有良好的抗脉冲干扰性能的同时提高了其收敛速度;另一方面将低次幂误差的倒数作为权重向量更新公式的系数,利用误差突增使得权重向量不更新的方法来抵制冲激噪声,并对其均方收敛性进行了分析.在系统辨识环境下的仿真表明,该算法很好地兼顾了收敛速度和跟踪性能稳定误差的矛盾,在收敛速度和抗脉冲干扰鲁棒性方面优于核最小均方误差算法、核分式低次幂算法和S型核分式低次幂自适应滤波算法.     

应用于声反馈抑制的变步长归一化子带自适应滤波算法*

针对自适应滤波算法中稳态失调量和收敛速度之间的矛盾,提出了一种新的变步长归一化子带自适应滤波算法。该算法在系统噪声抵消原理的基础上,用迭代收缩的方法估计得到无噪先验子带误差的功率,对每个子带步长进行更新。对所提出的算法进行数学分析,可以得出该算法是稳定的和收敛的。在长回声路径和短回声路径两种情况下,将该算法应用于助听器声反馈抑制系统中。相对于其他归一化子带自适应滤波算法,仿真实验表明,所提算法实现了更快的收敛速度,获得了更低的失调量。     

互补型自适应滤波器在心磁信号处理中的应用

将心磁信号从干扰噪声中加以提取并有效地消除噪声干扰是心磁信号处理中尤为重要的环节 .从改进算法的角度出发，提出互补型自适应滤波器结构以实现心磁信号的消噪处理.该滤波器针对心磁这类非平稳信号进行设计，有效地解决了常规自适应滤波器应用于心磁信号处理时收敛速度和稳态误差的矛盾.通过仿真实验和心磁实验结果表明，该算法能有效地消除心磁信号的背景噪声和工频干扰噪声.同时该算法也可用于其他非平稳信号的消噪处理. 关键词： 自适应滤波 心磁图 最小均方误差     

基于自适应SRUKF的无人机位姿预测方法

针对无人机自主导航的实时性差、精度低且对时变噪声的鲁棒性弱的问题，建立了机器视觉和惯性导航相融合的组合导航系统，并提出了一种自适应平方根无迹卡尔曼滤波(adaptive square-root unscented kalman filter, ASRUKF)算法。该算法通过观测值与估计值残差的Mahalanobis距离时刻修正系统噪声协方差，再与采用最小偏度采样的SRUKF算法相融合，从而达到时变噪声自适应抑制，滤波快速且对噪声鲁棒性高的效果。仿真结果表明，相比标准SRUKF，ASRUKF计算耗时减少约38.8%，位移、速度和姿态角预测精度分别提高超过4倍和6倍，且对于时变噪声鲁棒性更强。     

基于相空间邻域的混沌时间序列自适应预测滤波器(Ⅱ)非线性自适应滤波

根据相空间重构理论、最小均方误差准则和最陡下降原理，提出了一种基于相空间邻域的非线性自适应滤波算法.实验结果表明：这种非线性自适应预测滤波器能够有效预测一些混沌序列，在某种程度上具有抗噪声的能力. 关键词： 混沌时间序列 重构矢量 最小均方误差准则 非线性自适应预测     

应用于助听器反馈抑制的信噪比自适应滤波算法*

针对基于自适应滤波器的助听器反馈抑制系统,本文提出了一种基于信噪比的归一化最小均方误差算法,采用最小值统计法估计误差信号的噪声分量,从而计算出误差信号的信噪比来计算自适应滤波系数的更新步长。当误差信号信噪比越高,语音占主要成分,信号的相关性越强,此时将滤波器的更新步长控制在较小值,减小滤波器的失调量。当信噪比越低时,噪声占主要成分,信号的相关性相对较弱,更新步长取较大值,加快滤波器的收敛速度。在仿真实验中,本文提出的基于信噪比的归一化最小均方误差算法相较于传统算法在平均稳态失调量和稳态失调范围上分别低1dB和2dB,其最大稳态增益提高了4dB,同时具有更快的稳态收敛速度,验证了本文提出算法的有效性。     

鲁棒惯性地形辅助导航算法研究

传统的地形轮廓匹配(terrain contour matching, TERCOM)算法在速度误差和航向误差较大时可靠性下降,基于扩展Kalman滤波的北航惯性地形辅助惯性导航(BUAA inertial terrain aided navigation, BITAN) 算法在初始位置误差或高度表测量噪声较大时,系统无法准确定位,导致系统的鲁棒性降低. 为解决上述问题,对BITAN算法进行改进,发展了鲁棒北航惯性地形辅助导航(robust BUAA inertial terrain aided navigation, RBITAN)算法. RBITAN算法根据平均绝对差、均方差和交叉相关算法的统计决策信息设计了搜索模式算法,以基于扩展Kalman滤波原理的BITAN算法作为跟踪算法, 综合了TERCOM算法和BITAN算法的优点,提高了算法的鲁棒性.利用真实的数字高程模型和试飞数据进行仿真验证, 并和BITAN算法进行比较.仿真结果验证了RBITAN算法可以在较大初始位置误差和较大高度表测量噪声时准确定位, 提高了算法的鲁棒性.     

基于干扰对消的红外焦平面非均匀性校正算法

红外焦平面器件的非均匀性产生机理复杂,难以准确拟合探测元响应曲线。提出了一种基于相关干扰抵消的非均匀性校正算法,以预先采集到的一帧黑体面源图像做为自适应干扰对消器的参考输入图像,自适应滤波器由参考输入图像迭代计算出待校正红外图像的空间噪声的最佳估计,实现从空间噪声中提取真实图像信号。自适应滤波算法采用变步长最小均方误差算法,减少了算法的运算量,提高了算法的收敛速度。理论分析以及针对实际红外图像的仿真结果表明,提出的算法校正效果好,收敛速度快,更易于工程实现。     

一种维纳加权频域自适应时延估计算法

提出了一种基于频域自适应滤波的维纳加权时延估计算法。该算法首先实现了对输入信号的维纳自适应滤波预处理,然后在频域实现了自适应时延估计。该算法在将相位数据拟合时,做了一次加权处理,有效地改善了时延估计的精度和自适应收敛速度。最后用实测的直升机噪声数据进行了仿真,验证了新算法的有效性。     

基于颜色和空间信息的多特征融合目标跟踪算法

为解决单一特征目标跟踪鲁棒性较差的问题,提出一种基于颜色和空间信息的多特征融合目标跟踪算法。采用一种自适应划分颜色区间的方法提取目标颜色特征,利用空间直方图提取目标颜色的空间分布信息。在粒子滤波框架下将自适应颜色直方图和空间直方图相结合,在特征融合中引入特征不确定性度量方法,自适应调整不同特征对跟踪结果的贡献,提高算法的鲁棒性。仿真实验结果表明,该跟踪算法平均位置最小误差值仅6.967 像素,而单一特征跟踪算法以及传统融合算法的跟踪误差达192.576 像素和199.464像素。说明本文算法在跟踪准确性上优于单一特征跟踪算法及传统融合算法,具有更好的跟踪精度和更高的鲁棒性。     

Improving robustness of filtered-x least mean p-power algorithm for active attenuation of standard symmetric-α-stable impulsive noise

The paper concerns active control of impulsive noise having peaky distribution with heavy tail. Such impulsive noise can be modeled using non-Gaussian stable process for which second order moments do not exist. The most famous filtered-x least mean square (FxLMS) algorithm for active noise control (ANC) systems is based on the minimization of variance (second order moment) of error signal, and hence, becomes unstable for the impulsive noise. In order to improve the robustness of adaptive algorithms for processes having distributions with heavy tails (i.e. signals with outliers), either (1) a robust optimization criterion may be used to derive the adaptive algorithm or (2) the large amplitude samples may be ignored or replaced by an appropriate threshold value. Among the existing algorithms for ANC of impulsive noise, one is based on the minimizing least mean p-power (LMP) of the error signal, resulting in FxLMP algorithm (approach 1). The other is based on modifying; on the basis of statistical properties; the reference signal in the update equation of the FxLMS algorithm (approach 2). In this paper we propose two solutions to improve the robustness of the FxLMP algorithm. In first proposed algorithm, the reference and the error signals are thresholded before being used in the update equation of FxLMP algorithm. As another solution to improve the performance of FxLMP algorithm, a modified normalized step size is proposed. The computer simulations are carried out, which demonstrate the effectiveness of the proposed algorithms.     

Improving performance of FxRLS algorithm for active noise control of impulsive noise

Active noise control (ANC) systems employing adaptive filters suffer from stability issues in the presence of impulsive noise. New impulsive noise control algorithms based on filtered-x recursive least square (FxRLS) algorithm are presented. The FxRLS algorithm gives better convergence than the filtered-x least mean square (FxLMS) algorithm and its variants but lacks robustness in the presence of high impulsive noise. In order to improve the robustness of FxRLS algorithm for ANC of impulsive noise, two modifications are suggested. First proposed modification clips the reference and error signals while, the second modification incorporates energy of the error signal in the gain of FxRLS (MGFxRLS) algorithm. The results demonstrate improved stability and robustness of proposed modifications in the FxRLS algorithm. However, another limitation associated with the FxRLS algorithm is its computationally complex nature. In order to reduce the computational load, a hybrid algorithm based on proposed MGFxRLS and normalized step size FxLMS (NSS-FXLMS) is also developed in this paper. The proposed hybrid algorithm combines the stability of NSS-FxLMS algorithm with the fast convergence speed of the proposed MGFxRLS algorithm. The results of the proposed hybrid algorithm prove that its convergence speed is faster than that of NSS-FxLMS algorithm with computational complexity lesser than that of FxRLS algorithm.     

基于分数阶最大相关熵算法的混沌时间序列预测

为提高最大相关熵算法对混沌时间序列的预测速度和精度,提出了一种新的分数阶最大相关熵算法.在采用最大相关熵准则的基础上,利用分数阶微分设计了一种新的权重更新方法.在alpha噪声环境下,采用新的分数阶最大相关熵算法对Mackey-Glass和Lorenz两类具有代表性的混沌时间序列进行预测,并分析了分数阶的阶数对混沌时间序列预测性能的影响.仿真结果表明:与最小均方算法、最大相关熵算法以及分数阶最小均方算法三类自适应滤波算法相比,所提分数阶最大相关熵算法在混沌时间序列预测中能够有效地抑制非高斯脉冲噪声干扰的影响,具有较快收的敛速度和较低的稳态误差.     

A constant modulus algorithm for blind equalization in α-stable noise

Channel noise is often assumed to be Gaussian in most of the existing channel equalization algorithms. The performance of these algorithms will degrade seriously when the noise is non-Gaussian. This paper deals with the problem of blind channel equalization in impulsive noise environment that is modeled as α-stable process. A modified adaptive error-constrained constant modulus algorithm (MAECCMA) is proposed by soft-limiting the amplitude of the equalizer input and transforming the error signal of the original adaptive error-constrained constant modulus algorithm (AECCMA) nonlinearly to suppress the influence of α-stable noise. Computer simulation results of two underwater acoustic channels show that, MAECCMA has almost the same performance as AECCMA and they both have faster convergence rate than constant modulus algorithm (CMA) and normalized least mean absolute deviation (NLMAD) algorithm in Gaussian noise, while MAECCMA provides the best performance of those four algorithms in α-stable noise.     

A variational Bayesian method to inverse problems with impulsive noise

We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness with respect to outliers. A hierarchical model with all hyper-parameters automatically determined from the given data is described. An algorithm of variational type by minimizing the Kullback–Leibler divergence between the true posteriori distribution and a separable approximation is developed. The numerical method is illustrated on several one- and two-dimensional linear and nonlinear inverse problems arising from heat conduction, including estimating boundary temperature, heat flux and heat transfer coefficient. The results show its robustness to outliers and the fast and steady convergence of the algorithm.     

Adaptive nonlinear neuro-controller with an integrated evaluation algorithm for nonlinear active noise systems

An adaptive nonlinear neuro-controller with an integrated evaluation algorithm for nonlinear active noise control systems is proposed to attenuate the nonlinear and non-Gaussian noises. Inspired by the structure of the Hammerstein or Wiener model, the proposed controller is realized by the static nonlinear memory function mapping on the basis of a single neuron. A generalized filtered-X gradient descent algorithm based on an integrated evaluation criterion is developed to adaptively adjust the weights of the controller, where the weighted sum of Renyi's quadratic error entropy and the mean square error is applied as the integrated performance index, which improves the performance of the adaptive algorithm by introducing the information entropy. In addition, the convergence of the proposed approach is analyzed, and the computational complexity among different methods is investigated. The proposed scheme can effectively attenuate the nonlinear and non-Gaussian noises and has a relative simple structure and less learning parameters. The simulation results demonstrate the validity of the proposed method for attenuating the nonlinear and non-Gaussian noises.     

基于广义M估计的鲁棒容积卡尔曼滤波目标跟踪算法

为减小测量异常误差对非线性目标跟踪系统的影响, 提出了一种基于广义M估计的鲁棒容积卡尔曼滤波算法. 首先将非线性测量方程等价变换, 利用约束总体最小二乘准则构建广义M估计极值函数, 在不进行线性化近似的前提下将其引入到容积卡尔曼滤波求解框架中. 然后根据Mahalanobis距离构建异常误差判别量, 利用卡方分布的置信水平确定判决门限, 并建立改进的三段Huber权函数, 使其能够降低小异常误差权值, 剔除大异常误差. 理论分析表明, 该方法具有无需求导、跟踪精度高、实时性好等优点, 且无需已知异常误差的统计特性; 实验结果表明, 所提算法能够有效减小异常误差的影响, 在实际非线性物理系统中具有广阔的应用空间.     

A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction

A method of modifying the architecture of fractional least mean square （FLMS） algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square （MFLMS） algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts.     

Verhulst model with Lévy white noise excitation

The transient dynamics of the Verhulst model perturbed by arbitrary non-Gaussian white noise is investigated. Based on the infinitely divisible distribution of the Lévy process we study the nonlinear relaxation of the population density for three cases of white non-Gaussian noise: (i) shot noise; (ii) noise with a probability density of increments expressed in terms of Gamma function; and (iii) Cauchy stable noise. We obtain exact results for the probability distribution of the population density in all cases, and for Cauchy stable noise the exact expression of the nonlinear relaxation time is derived. Moreover starting from an initial delta function distribution, we find a transition induced by the multiplicative Lévy noise, from a trimodal probability distribution to a bimodal probability distribution in asymptotics. Finally we find a nonmonotonic behavior of the nonlinear relaxation time as a function of the Cauchy stable noise intensity.