CN115632633A - Minimum error entropy self-adaptive filtering method based on robust M estimation - Google Patents

Minimum error entropy self-adaptive filtering method based on robust M estimation Download PDF

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CN115632633A
CN115632633A CN202211262408.7A CN202211262408A CN115632633A CN 115632633 A CN115632633 A CN 115632633A CN 202211262408 A CN202211262408 A CN 202211262408A CN 115632633 A CN115632633 A CN 115632633A
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estimation
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王子逸
周兴立
周玉正
钟山
张洪斌
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University of Electronic Science and Technology of China
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    • H03HIMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
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    • H03H21/0012Digital adaptive filters
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    • HELECTRICITY
    • H03ELECTRONIC CIRCUITRY
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    • H04ELECTRIC COMMUNICATION TECHNIQUE
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    • H04L25/00Baseband systems
    • H04L25/02Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006Arrangements for removing intersymbol interference
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    • H04L25/00Baseband systems
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Abstract

The invention discloses a minimum error entropy self-adaptive filtering method based on robust M estimation, which comprises the following steps: s1, constructing a self-adaptive filtering system and acquiring a prediction error; s2, according to the prediction error, constructing a target function and an optimization target based on a new steady M estimation minimum error entropy criterion, and calculating to obtain an MMEE optimization loss criterion corresponding to the prediction error sample; s3, performing partial differentiation on the error function, and updating the weight of the adaptive filtering system; and S4, iterating the steps S1 to S3 to enable the error value of the adaptive filtering system to be converged, and taking the weight of the adaptive filtering system at the moment as a final weight for filtering the input signal. The adaptive filter has extremely high convergence rate and low steady-state error, can effectively improve the robustness of the adaptive filter under various non-Gaussian noises, has good environment adaptability, and can stably process the sudden change of the noise type in the environment.

Description

一种基于稳健M估计的最小误差熵自适应滤波方法A Minimum Error Entropy Adaptive Filtering Method Based on Robust M Estimation

技术领域technical field

本发明涉及数字信号处理领域的技术研究,特别是涉及一种基于稳健M估计的最小误差熵自适应滤波方法。The invention relates to technical research in the field of digital signal processing, in particular to a minimum error entropy self-adaptive filtering method based on robust M estimation.

背景技术Background technique

近些年来,自适应滤波算法在基于维纳滤波(Wiener)、卡尔曼滤波(Kalman)算法的基础上逐渐发展了起来。自适应滤波算法被认为是一种最佳的滤波技术,它的突出优势就在于极强的适应性和改进性,并且在减少噪声对整体信号系统的影响上性能更强,从而在工程实际上,即一些实际的信号处理任务中,如回声消除、系统辨识等,得到了广泛的应用。自适应滤波的研究对象是具有不确定性的系统或信息过程。这里的“不确定性”是指所研究的处理信息过程及其环境的数学模型不是完全确定的。其中包含一些未知因素和随机因素。In recent years, adaptive filtering algorithms have been gradually developed on the basis of Wiener filtering (Wiener) and Kalman filtering (Kalman) algorithms. The adaptive filtering algorithm is considered to be the best filtering technology, its outstanding advantages lie in its strong adaptability and improvement, and its performance is stronger in reducing the impact of noise on the overall signal system, so it is practical in engineering , that is, some practical signal processing tasks, such as echo cancellation, system identification, etc., have been widely used. The research object of adaptive filtering is an uncertain system or information process. The "uncertainty" here means that the mathematical model of the studied information processing and its environment is not completely deterministic. There are some unknowns and random factors involved.

传统的自适应滤波技术基于的是最小均方误差准则(MMSE),其是在高斯假设下线性滤波器的最佳准则,然而在各种实际应用场景中,信号可能会受到一些非高斯噪声的污染,在面对的系统或者信息过程属于非高斯情况时,最小误差准则的二阶统计量将不足以完全提取来自数据样本的有效信息,这种情况下,基于最小均方误差准则的方法的滤波性能将严重下降。在这样的背景下,基于信息理论学习(ITL)的相关算法准则就被广泛研究而来,其中,最小误差熵(MEE)算法其扩展,能够捕获到信号误差样本的高阶统计量,对比最小均方误差准则,最小误差熵准则在分析被非高斯噪声污染的信号系统时,具有更好的效果。通常情况下,最小误差熵准则采用基于Parzen窗口的非参数高斯核估计法来得到所处理数据样本的二阶瑞丽熵的估计值,以此对于非高斯的信号过程提供一个较为鲁棒的最优化准则。最小误差熵能够运用在自适应系统辨识的迭代更新过程上,并被认为是处理非高斯噪声的有效方法。Traditional adaptive filtering techniques are based on the minimum mean square error criterion (MMSE), which is the best criterion for linear filters under the Gaussian assumption. However, in various practical application scenarios, the signal may be affected by some non-Gaussian noise. pollution, when the system or information process is non-Gaussian, the second-order statistics of the minimum error criterion will not be enough to fully extract the effective information from the data sample. In this case, the method based on the minimum mean square error criterion Filtering performance will be severely degraded. In this context, related algorithm guidelines based on information theory learning (ITL) have been widely studied. Among them, the minimum error entropy (MEE) algorithm and its extension can capture the high-order statistics of signal error samples, and the minimum contrast The mean square error criterion and the minimum error entropy criterion have better effects when analyzing signal systems polluted by non-Gaussian noise. Usually, the minimum error entropy criterion uses the non-parametric Gaussian kernel estimation method based on the Parzen window to obtain the estimated value of the second-order Rayleigh entropy of the processed data samples, so as to provide a more robust optimization for the non-Gaussian signal process guidelines. The minimum error entropy can be used in the iterative update process of adaptive system identification, and is considered to be an effective method for dealing with non-Gaussian noise.

然而,上述准则仍然存在一定的限制,当所需信号受到重尾或多峰冲激噪声的干扰时(数据样本中会相应出现极大离群值),直接使用包含离群值的误差样本将难以实现对瑞丽熵的高度精确估计,这可能会限制算法在性能上的提高;此外,一旦迭代参数(如核宽和窗长)选择不当,准则所使用的高斯核概率密度估计法对参数的高敏感性也会进一步导致滤波性能的下降。However, the above criterion still has certain limitations. When the desired signal is interfered by heavy-tailed or multi-peak impulse noise (a large outlier will appear in the data sample), directly using the error sample containing the outlier will reduce the It is difficult to achieve a highly accurate estimation of the Rayleigh entropy, which may limit the performance improvement of the algorithm; in addition, once the iteration parameters (such as kernel width and window length) are not selected properly, the Gaussian kernel probability density estimation method used in the criterion will not affect the parameters. High sensitivity will further lead to the degradation of filtering performance.

瑞利(Renyi’s)熵作为一种非常重要的非线性信息量相似度量,是最小误差熵(MEE)准则的核心要素,由于传统的最小误差熵(MEE)准则无法实现对瑞利熵的准确估计,尤其是当误差样本包含大量异常值时,因此存在着算法性能提升的巨大空间。Rayleigh (Renyi's) entropy, as a very important nonlinear information similarity measure, is the core element of the minimum error entropy (MEE) criterion, because the traditional minimum error entropy (MEE) criterion cannot achieve accurate estimation of Rayleigh entropy , especially when the error samples contain a large number of outliers, so there is a huge room for algorithm performance improvement.

发明内容Contents of the invention

为了克服现有技术中存在的上述不足之处,本发明提供一种基于稳健M估计的最小误差熵自适应滤波方法,该方法将最小误差熵算法和M估计数值统计理论相结合,在保持高收敛速度的同时在非高斯环境工作下滤波性能表现更好。In order to overcome the above-mentioned deficiencies in the prior art, the present invention provides a minimum error entropy adaptive filtering method based on robust M estimation. The filtering performance is better when working in a non-Gaussian environment while converging faster.

本发明是通过以下技术方案来实现的:基于稳健M估计的最小误差熵自适应滤波方法,其特征在于:包括以下步骤:The present invention is achieved through the following technical solutions: a minimum error entropy adaptive filtering method based on robust M estimation, characterized in that: comprising the following steps:

S1.构建自适应滤波系统,在每一个时刻,输入信号经过自适应滤波系统得到输出信号作为预测值,并与期望输出信号作差,得到预测误差;S1. Build an adaptive filtering system. At each moment, the input signal passes through the adaptive filtering system to obtain the output signal as the predicted value, and make a difference with the expected output signal to obtain the prediction error;

所述步骤S1中包括:Include in the described step S1:

S101.构建自适应滤波系统:自适应滤波器系统的权重为wn;设n时刻输入信号un是均值为0,方差为1的高斯白噪声,预先设定自适应滤波系统的最佳权重为woS101. Build an adaptive filtering system: the weight of the adaptive filtering system is w n ; assuming that the input signal u n at time n is Gaussian white noise with a mean value of 0 and a variance of 1, the optimal weight of the adaptive filtering system is preset for w o ;

S102.将输入信号un与滤波器期望的最佳权重wo相乘,再加上噪声信号v(n),得到期望输出信号d(n):S102. Multiply the input signal u n with the optimal weight w o expected by the filter, and add the noise signal v(n) to obtain the desired output signal d(n):

Figure BDA0003891683280000021
Figure BDA0003891683280000021

其中vn为混合高斯噪声,且vn~0.95N(0,0.01)+0.05N(0,10),Where v n is mixed Gaussian noise, and v n ~0.95N(0,0.01)+0.05N(0,10),

其中输入信号un与噪声信号vn不相关;where the input signal u n is uncorrelated with the noise signal v n ;

S102.将输入信号un与自适应滤波器系统的权重wn相乘,得到预测输出信号ynS102. Multiply the input signal u n with the weight w n of the adaptive filter system to obtain the predicted output signal y n :

Figure BDA0003891683280000022
Figure BDA0003891683280000022

S103.计算期望输出信号d(n)和预测输出信号yn之间的预测误差,记为:S103. Calculate the prediction error between the expected output signal d(n) and the predicted output signal yn, denoted as:

en=dn-yne n =d n -y n .

S2.根据预测误差,基于新的稳健M估计最小误差熵准则来构建目标函数和最优化目标,计算得到预测误差样本所对应的MMEE最优化损失准则;S2. According to the prediction error, construct the objective function and optimization objective based on the new robust M estimation minimum error entropy criterion, and calculate the MMEE optimization loss criterion corresponding to the prediction error sample;

所述步骤S2包括:Described step S2 comprises:

S201.每轮次迭代前,按照步骤S1计算包括时刻n在内的前L个窗长内的误差:en-L+1到en,作为Parzen窗滑动一次所需的误差样本向量,其中n为不小于L的整数;S201. Before each round of iteration, calculate the error in the first L window lengths including time n according to step S1: e n-L+1 to e n , as the error sample vector required for the Parzen window to slide once, where n is an integer not less than L;

S202.基于新的稳健M估计最小误差熵准则来构建损失函数和最优化目标:利用M估计的统计特性,在传统最小误差熵准则的基础上,设置M估计权重因子对误差进行加权或是截断,通过重新设置误差样本的分布,减小离群值对自适应系统估计的影响,进而得到一个基于稳健M估计的最小误差熵损失函数,具体为:S202. Construct the loss function and optimization objective based on the new robust M-estimation minimum error entropy criterion: use the statistical characteristics of M estimation, on the basis of the traditional minimum error entropy criterion, set the M estimation weight factor to weight or truncate the error , by resetting the distribution of error samples, reducing the impact of outliers on adaptive system estimation, and then obtaining a minimum error entropy loss function based on robust M estimation, specifically:

Figure BDA0003891683280000031
Figure BDA0003891683280000031

其中εn=[en,en-1,...,en-L+1]T表示误差样本向量;Where ε n =[e n ,e n-1 ,...,e n-L+1 ] T represents the error sample vector;

稳健M估计最小误差熵准则旨在最大化上述损失函数,进而最小化自适应滤波系统预测输出与期望输出的差距,其中

Figure BDA0003891683280000032
表示基于窗长内L个误差样本计算所得到的M估计权重因子,取值范围限制在(0,1)之间,其中Δ1、Δ2、Δ3是分界参数,均为预先设置的常数,所述M估计权函数包括Hampel权函数,记为:The minimum error entropy criterion for robust M estimation aims to maximize the above loss function, thereby minimizing the gap between the predicted output and the expected output of the adaptive filtering system, where
Figure BDA0003891683280000032
Indicates the M estimated weight factor calculated based on L error samples in the window length, and the value range is limited between (0,1), where Δ 1 , Δ 2 , and Δ 3 are boundary parameters, all of which are preset constants , the M estimated weight function includes the Hampel weight function, denoted as:

Figure BDA0003891683280000033
Figure BDA0003891683280000033

S3.采用随机梯度上升法来进行自适应滤波系统的权重进行更新:先对误差函数进行偏微分,再对自适应滤波系统的权重进行更新;S3. Use the stochastic gradient ascent method to update the weight of the adaptive filtering system: first perform partial differentiation on the error function, and then update the weight of the adaptive filtering system;

所述步骤S3中,在得到目标函数后,采用随机梯度上升法来进行自适应滤波权重参数地更新,具体包括:In the step S3, after obtaining the objective function, the stochastic gradient ascending method is used to update the weight parameters of the adaptive filtering, specifically including:

先对目标进行偏微分:Partially differentiate the objective first:

Figure BDA0003891683280000034
Figure BDA0003891683280000034

其中

Figure BDA0003891683280000035
in
Figure BDA0003891683280000035

再对滤波器区权重参数wn进行梯度上升更新算法,wn表示第n时刻权重参数,下标n+1代表自适应滤波器第n+1时刻权重参数,更新公式如下:Then perform a gradient ascent update algorithm on the weight parameter w n of the filter area, w n represents the weight parameter at the nth moment, and the subscript n+1 represents the weight parameter at the n+1th moment of the adaptive filter. The update formula is as follows:

Figure BDA0003891683280000036
Figure BDA0003891683280000036

S4.迭代步骤S1至S3使得自适应滤波系统的误差值收敛,即自适应滤波系统的预测输出与期望输出之间的差距小于设定阈值,将此时自适应滤波系统的权重作为最终权重,用于输入信号的滤波处理。S4. Iterative steps S1 to S3 make the error value of the adaptive filtering system converge, that is, the gap between the predicted output of the adaptive filtering system and the expected output is smaller than the set threshold, and the weight of the adaptive filtering system at this time is used as the final weight. It is used for filtering processing of input signal.

本发明的有益效果如下:本发明利用M-估计的稳健统计特性,将最小误差熵算法和M估计数值统计理论相结合,引入了若干M-估计权重因子来重新计算误差样本的统计分布,旨在最大限度地减少大离群值的影响,在保持高收敛速度的同时在非高斯环境工作下滤波性能表现更好,并且对参数变化高度不敏感,算法灵活易调整,适应多种非高斯环境。The beneficial effects of the present invention are as follows: the present invention utilizes the robust statistical characteristics of M-estimation, combines the minimum error entropy algorithm and M-estimation numerical statistics theory, introduces some M-estimation weight factors to recalculate the statistical distribution of error samples, aiming at Minimize the influence of large outliers, while maintaining a high convergence speed, the filtering performance is better in non-Gaussian environments, and it is highly insensitive to parameter changes. The algorithm is flexible and easy to adjust, and adapts to a variety of non-Gaussian environments. .

附图说明Description of drawings

图1为一般的自适应滤波算法的基本原理框图;Fig. 1 is the basic principle block diagram of general adaptive filtering algorithm;

图2为本发明所述的基于稳健M估计的最小误差熵自适应滤波算法的原理框图;Fig. 2 is the functional block diagram of the minimum error entropy adaptive filtering algorithm based on robust M estimation of the present invention;

图3为本发明的流程示意图;Fig. 3 is a schematic flow sheet of the present invention;

图4为本发明的基于稳健M估计的最小误差熵自适应滤波方法的稳态性能随步长变化的理论分析与实验结果对比示意图;Fig. 4 is the theoretical analysis and experimental result comparison schematic diagram of the steady-state performance of the minimum error entropy adaptive filtering method based on the robust M estimation of the present invention as the step size changes;

图5为本方法与其它相关的鲁棒自适应滤波方法的稳态均方误差效果对比图;Fig. 5 is the steady-state mean square error effect comparison figure of this method and other relevant robust adaptive filtering methods;

图6为在环境噪声突变情况下:自适应系统在分别1000点和2000点发生噪声类型突变的系统收敛曲线对比示意图。Fig. 6 is a schematic diagram of the comparison of the system convergence curves of the sudden change of the noise type in the adaptive system at 1000 points and 2000 points respectively in the case of a sudden change in the environmental noise.

具体实施方式Detailed ways

下面结合附图和实例对本发明的技术方案进行进一步地详细描述,但本发明的保护范围不局限于以下所述。The technical solution of the present invention will be further described in detail below in conjunction with the accompanying drawings and examples, but the protection scope of the present invention is not limited to the following description.

基础的自适应滤波器的基本原理框图如图1所示,输入信号un通过参数可调自适应数字滤波器后产生输出信号yn,将其与期望信号dn进行比较,形成误差信号en,通过自适应算法对滤波器参数进行调整,最终使损失函数最小。自适应滤波可以利用前一时刻已得的滤波器参数的结果,自动调节当前时刻的滤波器参数,以适应信号和噪声未知的或随时间变化的统计特性,从而实现最优滤波。由于目标函数的不同,不同准则下的自适应滤波算法也具有不同的效果。The basic block diagram of the basic adaptive filter is shown in Figure 1. The input signal u n passes through the parameter-adjustable adaptive digital filter to generate an output signal y n , which is compared with the expected signal d n to form an error signal e n , adjust the filter parameters through an adaptive algorithm, and finally minimize the loss function. Adaptive filtering can use the results of the filter parameters obtained at the previous moment to automatically adjust the filter parameters at the current moment to adapt to the unknown or time-varying statistical characteristics of the signal and noise, thereby achieving optimal filtering. Due to the different objective functions, the adaptive filtering algorithms under different criteria also have different effects.

基于稳健M估计的最小误差熵自适应滤波器的原理框图如图2所示,输入信号un经过所求的未知系统(该未知系统具有最佳权重),采用混合高斯噪声vn~0.95N(0,0.01)+0.05N(0,10)作为噪声信号,产生实际期望输出信号

Figure BDA0003891683280000041
通过自适应数字滤波器系统后卷积运算产生输出信号
Figure BDA0003891683280000042
两者相减形成误差信号en=dn-yn,迭代运算得到数个误差样本,通过M估计方法,重新计算误差样本分布,对大型误差进行归0,对中型误差进行截短,对小型误差离群值不进行操作,最终得到MMEE误差熵损失函数。The principle block diagram of the minimum error entropy adaptive filter based on robust M estimation is shown in Figure 2. The input signal u n passes through the unknown system (the unknown system has the best weight), and the mixed Gaussian noise v n ~0.95N is used (0,0.01)+0.05N(0,10) as the noise signal to generate the actual desired output signal
Figure BDA0003891683280000041
The output signal is generated by the post-convolution operation of the adaptive digital filter system
Figure BDA0003891683280000042
The two are subtracted to form an error signal e n =d n -y n , and several error samples are obtained through iterative operation, and the error sample distribution is recalculated through the M estimation method, and the large error is returned to 0, and the medium error is truncated. Small error outliers are not manipulated, and the MMEE error entropy loss function is finally obtained.

本发明是基于M估计和最小误差熵的自适应滤波方法,是在最小误差熵准则下的自适应滤波算法上的改进,图3(a)的本方法的整体流程图,图3(b)则对本方法的前步骤一、二、三进行具体的介绍:The present invention is based on the adaptive filtering method of M estimation and minimum error entropy, is the improvement on the adaptive filtering algorithm under the minimum error entropy criterion, the overall flowchart of this method of Fig. 3 (a), Fig. 3 (b) Then, the first, second and third steps of this method are introduced in detail:

1.输入信号un向量服从均值为0,方差为1的高斯分布,瞬时测量噪声信号服从混合高斯分布:vn~0.95N(0,0.01)+0.05N(0,10);1. The input signal u n vector obeys a Gaussian distribution with a mean value of 0 and a variance of 1, and the instantaneous measurement noise signal obeys a mixed Gaussian distribution: v n ~0.95N(0,0.01)+0.05N(0,10);

2.理想回归输出信号

Figure BDA0003891683280000051
其中T为转置算子,同时可得到滤波器实际输出
Figure BDA0003891683280000052
其中w0为被估计的系统权重向量,它是一个未知但实际存在的值,可以给其赋予任何初值,但这个初值却是我们假设未知的,自适应滤波的任务便是通过wn的迭代更新去逼近真实值wo。2. Ideal regression output signal
Figure BDA0003891683280000051
Where T is the transpose operator, and the actual output of the filter can be obtained at the same time
Figure BDA0003891683280000052
Among them, w 0 is the estimated system weight vector, which is an unknown but actually existing value, and any initial value can be assigned to it, but this initial value is assumed to be unknown. The task of adaptive filtering is to pass w n Iterative update to approximate the true value w o .

3.计算估计输出值与实际值之差,也即预测误差en=dn-yn3. Calculate the difference between the estimated output value and the actual value, that is, the prediction error e n =d n −y n .

4.建立基于稳健M估计的最小误差熵准则(MMEE),确定优化对象,考虑误差en为一个随机变量,其概率密度函数(PDF)为pe,通过信息理论学习知识我们可以得知二次瑞丽熵可以写成:4. Establish the minimum error entropy criterion (MMEE) based on robust M estimation, determine the optimization object, consider the error e n as a random variable, and its probability density function (PDF) is p e , we can know the two The sub-Rayli entropy can be written as:

Figure BDA0003891683280000053
Figure BDA0003891683280000053

其中V2(e)为二次信息潜力,很显然,最小化二次瑞丽熵等价于最大化二次信息潜力。通过M估计方法重新计算误差分布,同时构建目标函数,以求通过实际可行的非参估计计算式,并在最大程度上逼近理论上的二次信息潜力及二次瑞丽熵值。Among them, V 2 (e) is the secondary information potential. Obviously, minimizing the secondary Rayleigh entropy is equivalent to maximizing the secondary information potential. The error distribution is recalculated by the M estimation method, and the objective function is constructed at the same time, in order to approach the theoretical quadratic information potential and quadratic Rayleigh entropy to the greatest extent through the practical and feasible non-parametric estimation formula.

Figure BDA0003891683280000054
Figure BDA0003891683280000054

其中L为窗长样本个数,κσ()为高斯核函数,

Figure BDA0003891683280000055
为M估计权函数Among them, L is the number of samples of the window length, κ σ () is the Gaussian kernel function,
Figure BDA0003891683280000055
Estimate the weight function for M

Figure BDA0003891683280000056
Figure BDA0003891683280000056

估计权函数以上述的Hampel函数最为合适,但也可以根据所处理的情况选择其他M估计权函数:The above-mentioned Hampel function is the most suitable estimation weight function, but other M estimation weight functions can also be selected according to the situation being dealt with:

Figure BDA0003891683280000057
Figure BDA0003891683280000057

Figure BDA0003891683280000058
Figure BDA0003891683280000058

5.对目标函数关于wn求偏导

Figure BDA0003891683280000059
由于需要最大化目标函数,在基于稳健M估计的最小误差熵的准则下理想的权重向量可以由此获得
Figure BDA00038916832800000510
根据梯度上升法得到滤波器权重向量的迭代更新公式:5. Find the partial derivative of the objective function with respect to w n
Figure BDA0003891683280000059
Since the objective function needs to be maximized, the ideal weight vector can be obtained under the criterion of minimum error entropy based on robust M estimation
Figure BDA00038916832800000510
According to the gradient ascent method, the iterative update formula of the filter weight vector is obtained:

Figure BDA0003891683280000061
Figure BDA0003891683280000061

其中η为步长参数,

Figure BDA0003891683280000062
n表示第n步迭代。where η is the step size parameter,
Figure BDA0003891683280000062
n represents the nth iteration.

综上所述,本发明提供的方法和改进创新,对现有的最小误差熵自适应滤波进行了扩展和改进,通过重新计算误差样本统计分布,减小离群值对瑞丽熵估计的影响,提高了误差准则对概率信息的利用,通过采用稳健M估计,提高了算法在处理多种非高斯噪声下的鲁棒性和针对实际情况的灵活性。In summary, the method and innovation provided by the present invention extend and improve the existing minimum error entropy adaptive filtering, and reduce the influence of outliers on Rayleigh entropy estimation by recalculating the statistical distribution of error samples. The utilization of probability information by the error criterion is improved, and the robustness of the algorithm in dealing with various non-Gaussian noises and the flexibility for practical situations are improved by using the robust M estimation.

此外本申请还进行了所发明方法的所对应的理论分析与验证,包括均值稳定性和均方稳态性能,极大地确保了发明的理论立足。该滤波器与一些现有的针对非高斯噪声的鲁棒滤波器相比,具有极强的优越性和有效性,可以适用于各种类型的非高斯系统或信号过程,同时满足快速收敛和低稳态误差的性能指标;该方法具有良好的普适性和灵活的调整空间,通过对参数的灵活调整可以适用于不同的实际应用场景,具有较为重要的研究意义和广泛的工程应用价值通过数据验证仿真和对比实验对本方法进一步说明:In addition, the present application has also carried out corresponding theoretical analysis and verification of the invented method, including mean value stability and mean square steady-state performance, which greatly ensured the theoretical basis of the invention. Compared with some existing robust filters for non-Gaussian noise, this filter is extremely superior and effective, and can be applied to various types of non-Gaussian systems or signal processes, while satisfying fast convergence and low The performance index of steady-state error; this method has good universality and flexible adjustment space, and can be applied to different practical application scenarios through flexible adjustment of parameters, which has relatively important research significance and extensive engineering application value. Verification simulation and comparative experiments further illustrate this method:

如图4所示,对本发明的极限稳态性能理论立足分析进行实验验证,证明仿真实验结果与理论分析结果有很好的一致性。其中,MSD意思是稳态均方误差,η代表步长,theory代表理论值,simulation代表实验值。As shown in FIG. 4 , the theoretical analysis of the ultimate steady-state performance of the present invention is based on experimental verification, which proves that the simulation experimental results are in good agreement with the theoretical analysis results. Among them, MSD means the steady-state mean square error, η represents the step size, theory represents the theoretical value, and simulation represents the experimental value.

图5是采用本方法和文献中的其它相关的鲁棒自适应滤波方法的效果对比图,纵坐标表示100次实验平均得到的稳态误差

Figure BDA0003891683280000063
横坐标代表迭代次数:每次实验迭代运行了1500次,噪声采用的混合高斯噪声。我们为每个算法选择了不同的参数,以确保具有相同初始收敛速度以及理想的性能。从仿真结果中可以看出,与其他算法相比,本发明提出的方法综合性能最佳,收敛速度快,稳态误差低,其中采用Hampel估计权函数的MMEE方法表现最为突出。Figure 5 is a comparison chart of the effect of this method and other related robust adaptive filtering methods in the literature, and the ordinate represents the steady-state error obtained by averaging 100 experiments
Figure BDA0003891683280000063
The abscissa represents the number of iterations: each experimental iteration runs 1500 times, and the noise uses a mixed Gaussian noise. We chose different parameters for each algorithm to ensure the same initial convergence rate and ideal performance. It can be seen from the simulation results that compared with other algorithms, the method proposed by the present invention has the best comprehensive performance, fast convergence speed and low steady-state error, among which the MMEE method using Hampel estimation weight function is the most outstanding.

本方法提出的MMEE算法在非高斯噪声下表现良好,而且,总体上对核宽的变化不敏感。因此,我们可以利用MMEE算法的这一特点,进一步探索其在非稳态条件下的性能。图6是自适应系统在第1000个点和2000个点发生时变,即未知系统的噪声类型突然从高斯噪声转变为非高斯噪声,采用本方法中的稳健M估计方法和其他传统的最小均方误差和最小误差熵方法,运行3000次获得的均方误差平均值对比图。从图6中可以看出,在1000个和2000点时发生时变之后:受到重尾脉冲噪声的干扰,这在现实中其实是很常见的,传统固定步长LMS方法以及MEE方法在第1000-2000个采样点过程中仍抑制噪声的性能严重下降,而MMEE-Hampel方法仍能操持一致的滤波能力,不受环境中噪声类型变化的影响,本发明提出的方法在系统环境发生噪声跳变时,回到稳态的速度更快,跟踪性能更强,滤波性能更好。这进一步证明了本方法提出的MMEE算法在系统环境突变情况下的极佳鲁棒性。The MMEE algorithm proposed in this method performs well in non-Gaussian noise, and, in general, is insensitive to changes in kernel width. Therefore, we can take advantage of this feature of the MMEE algorithm to further explore its performance under unsteady conditions. Figure 6 shows that the adaptive system changes time at the 1000th point and the 2000th point, that is, the noise type of the unknown system suddenly changes from Gaussian noise to non-Gaussian noise, using the robust M estimation method in this method and other traditional least mean Square error and minimum error entropy methods, running 3000 times to obtain the comparison chart of the average value of the mean square error. It can be seen from Figure 6 that after time-varying at 1000 and 2000 points: interference by heavy-tail impulse noise, which is actually very common in reality, the traditional fixed-step LMS method and the MEE method at the 1000th point -2000 sampling points, the performance of suppressing noise is still severely degraded, while the MMEE-Hampel method can still maintain consistent filtering capabilities, and is not affected by changes in noise types in the environment. The method proposed by the present invention has noise jumps in the system environment When , the speed of returning to the steady state is faster, the tracking performance is stronger, and the filtering performance is better. This further proves the excellent robustness of the MMEE algorithm proposed by this method in the case of sudden changes in the system environment.

上述说明示出并描述了本发明的一个优选实施例,但如前所述,应当理解本发明并非局限于本文所披露的形式,不应看作是对其他实施例的排除,而可用于各种其他组合、修改和环境,并能够在本文所述发明构想范围内,通过上述教导或相关领域的技术或知识进行改动。而本领域人员所进行的改动和变化不脱离本发明的精神和范围,则都应在本发明所附权利要求的保护范围内。The above description shows and describes a preferred embodiment of the present invention, but as mentioned above, it should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments, but can be used in various Various other combinations, modifications, and environments can be made within the scope of the inventive concept described herein, by the above teachings or by skill or knowledge in the relevant field. However, changes and changes made by those skilled in the art do not depart from the spirit and scope of the present invention, and should all be within the protection scope of the appended claims of the present invention.

Claims (4)

1. A minimum error entropy self-adaptive filtering method based on robust M estimation is characterized in that: the method comprises the following steps:
s1, constructing a self-adaptive filtering system, and obtaining an output signal as a predicted value by an input signal through the self-adaptive filtering system at each moment, and subtracting an expected output signal to obtain a prediction error;
s2, according to the prediction error, constructing a target function and an optimization target based on a new steady M estimation minimum error entropy criterion, and calculating to obtain an MMEE optimization loss criterion corresponding to the prediction error sample;
s3, updating the weight of the self-adaptive filtering system by adopting a random gradient ascending method: firstly, partial differentiation is carried out on an error function, and then the weight of the self-adaptive filtering system is updated;
and S4, iterating the steps S1 to S3 to enable the error value of the adaptive filtering system to be converged, namely the difference between the predicted output and the expected output of the adaptive filtering system is smaller than a set threshold value, and taking the weight of the adaptive filtering system at the moment as a final weight for filtering the input signal.
2. The robust M-estimation based minimum error entropy adaptive filtering method of claim 1, wherein: the step S1 comprises the following steps:
s101, constructing a self-adaptive filtering system: the weight of the adaptive filter system is w n (ii) a Let n time input signal u n Is white Gaussian noise with mean value of 0 and variance of 1, and the optimal weight of the self-adaptive filtering system is preset to be w o
S102, inputting a signal u n And the optimal weight w expected by the filter o Multiplying, and adding the noise signal v (n) to obtain the desired output signal d (n):
Figure FDA0003891683270000011
wherein v is n Is a mixture of Gaussian noise, and v n ~0.95N(0,0.01)+0.05N(0,10),
Wherein the input signal u n And a noise signal v n Not related;
s102, inputting a signal u n And adaptive filter systemWeight w of n Multiplying to obtain a predicted output signal y n
Figure FDA0003891683270000012
S103, calculating an expected output signal d (n) and a prediction output signal y n The prediction error between, noted as:
e n =d n -y n
3. the robust M-estimation based minimum error entropy adaptive filtering method of claim 2, wherein: the step S2 includes:
s201, before each iteration, calculating errors in the first L window lengths including the time n according to the step S1: e.g. of the type n-L+1 To e n As an error sample vector required for sliding a Parzen window once, where n is an integer not less than L;
s202, constructing a loss function and an optimization target based on the new robust M estimation minimum error entropy criterion: by utilizing the statistical characteristic of M estimation, on the basis of the traditional minimum error entropy criterion, M estimation weight factors are set to weight or truncate errors, and the influence of outliers on the estimation of the self-adaptive system is reduced by resetting the distribution of error samples, so that a minimum error entropy loss function based on the steady M estimation is obtained, specifically:
Figure FDA0003891683270000021
wherein epsilon n =[e n ,e n-1 ,...,e n-L+1 ] T Representing an error sample vector;
the criterion of the minimum error entropy of the robust M estimation aims to maximize the loss function and further minimize the difference between the prediction output and the expected output of the adaptive filtering system, wherein
Figure FDA0003891683270000022
Represents M estimated weight factors obtained by calculation based on L error samples in the window length, and the value range is limited between (0, 1), wherein, delta 1 、Δ 2 、Δ 3 Is a boundary parameter which is a preset constant, the weight factor is calculated, and a Hampel weight function in an M estimation theory is generally adopted, namely, the order is given
Figure FDA0003891683270000023
The expression is noted as:
Figure FDA0003891683270000024
wherein r is i Is a "normalized" residual indicator,
Figure FDA0003891683270000025
med () is the median, s is e i The corresponding residual measure.
4. A method for minimum error entropy adaptive filtering based on robust M estimation according to claim 3, characterized by: in step S3, after obtaining the objective function, the adaptive filtering weight parameter is updated by using a random gradient ascent method, which specifically includes:
firstly, partial differentiation is carried out on a target:
Figure FDA0003891683270000026
wherein
Figure FDA0003891683270000027
Re-pair the filter region weight parameter w n Performing a gradient ascent update algorithm, w n Represents the weighting parameter at the nth time, the subscript n +1 represents the weighting parameter at the nth +1 th time of the adaptive filter, and the updating formula is as follows:
Figure FDA0003891683270000028
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CN116473526A (en) * 2023-06-25 2023-07-25 湖南尚医康医疗科技有限公司 Medical information acquisition method and system based on artificial intelligence and Internet of things
CN119375231A (en) * 2024-10-22 2025-01-28 赣州富尔特电子股份有限公司 Visual inspection system for rare earth permanent magnet products based on 5G network cloud computing

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116473526A (en) * 2023-06-25 2023-07-25 湖南尚医康医疗科技有限公司 Medical information acquisition method and system based on artificial intelligence and Internet of things
CN116473526B (en) * 2023-06-25 2023-09-29 湖南尚医康医疗科技有限公司 Medical information acquisition method and system based on artificial intelligence and Internet of things
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