PARAMETER ESTIMATION FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SMALL STABLE NOISES FROM DISCRETE OBSERVATIONS

We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small a-stable noises, observed at n regularly spaced time points ti = i/n, i = 1,...,n on [0, 1]. Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator （LSE） when a small dispersion parameter ε→0 and n →∞ simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal.

Parameter estimation for chaotic systems with and without noise using differential evolution-based method

We present an approach in which the differential evolution （DE） algorithm is used to address identification problems in chaotic systems with or without delay terms. Unlike existing considerations, the scheme is able to simultaneously extract （i） the commonly considered parameters, （ii） the delay, and （iii） the initial state. The main goal is to present and verify the robustness against the common white Guassian noise of the DE-based method. Results of the time-delay logistic system, the Mackey Glass system and the Lorenz system are also presented.

A CROSS-REFERENCE METHOD OF PARAMETER ESTIMATION AND NOISE REDUCTION AND ITS APPLICATIONS

This paper proposes a cross-reference method of nonlinear time series analysis, combining the tasks of dynamical system parameter estimation and noise reduction which were fulfilled separately before. With the positive interaction between the two processing modules, the method is somewhat superior. Some prior works can be viewed as special cases of this general framework and effective new algorithms may be devised according to it. Two examples of chaotic time series analysis are also given to show the applicability of the proposed method.

Automatic estimation and removal of noise on digital image

An spatially adaptive noise detection and removal algorithm is proposed.Under the assumption that an observed image and its additive noise have Gaussian distribution,the noise parameters are estimated with local statistics from an observed degraded image,and the parameters are used to define the constraints on the noise detection process.In addition,an adaptive low-pass filter having a variable filter window defined by the constraints on noise detection is used to control the degree of smoothness of the reconstructed image.Experimental results demonstrate the capability of the proposed algorithm.

MODAL PARAMETERS EXTRACTION WITH CROSS CORRELATION FUNCTION AND CROSS POWER SPECTRUM UNDER UNKNOWN EXCITATION

In most of real operational conditions only response data are measurable while the actual excitations are unknown, so modal parameter must be extracted only from responses. This paper gives a theoretical formulation for the cross-correlation functions and cross-power spectra between the outputs under the assumption of white-noise excitation. It widens the field of modal analysis under ambient excitation because many classical methods by impulse response functions or frequency response functions can be used easily for modal analysis under unknown excitation. The Polyreference Complex Exponential method and Eigensystem Realization Algorithm using cross-correlation functions in time domain and Orthogonal Polynomial method using cross-power spectra in frequency domain are applied to a steel frame to extract modal parameters under operational conditions. The modal properties of the steel frame from these three methods are compared with those from frequency response functions analysis. The results show that the modal analysis method using cross-correlation functions or cross-power spectra presented in this paper can extract modal parameters efficiently under unknown excitation.

Expectation-maximization (EM) Algorithm Based on IMM Filtering with Adaptive Noise Covariance

A novel method under the interactive multiple model (IMM) filtering framework is presented in this paper, in which the expectation-maximization (EM) algorithm is used to identify the process noise covariance Q online. For the existing IMM filtering theory, the matrix Q is determined by means of design experience, but Q is actually changed with the state of the maneuvering target. Meanwhile it is severely influenced by the environment around the target, i.e., it is a variable of time. Therefore, the experiential covariance Q can not represent the influence of state noise in the maneuvering process exactly. Firstly, it is assumed that the evolved state and the initial conditions of the system can be modeled by using Gaussian distribution, although the dynamic system is of a nonlinear measurement equation, and furthermore the EM algorithm based on IMM filtering with the Q identification online is proposed. Secondly, the truncated error analysis is performed. Finally, the Monte Carlo simulation results are given to show that the proposed algorithm outperforms the existing algorithms and the tracking precision for the maneuvering targets is improved efficiently.

A practical filter error method for aerodynamic parameter estimation of aircraft in turbulence

It is common for aircraft to encounter atmospheric turbulence in flight tests.Turbulence is usually modeled as stochastic process noise in the flight dynamics equations.In this paper,parameter estimation of nonlinear dynamic system with both process and measurement noise was studied,and a practical filter error method was proposed.The linearized Kalman filter of first-order approximation was used for state estimation,in which the filter gain,along with the system parameters and the initial states,constituted the parameter vector to be estimated.The unknown parameters and measurement noise covariance were estimated alternately by a relaxation iteration method,and the sensitivities of observations to unknown parameters were calculated by finite difference approximation.Some practical aspects of the method application were discussed.The proposed filter error method was validated by the flight simulation data of a research aircraft.Then,the method was applied to the flight tests of a subscale aircraft,and the aerodynamic stability and control derivatives were estimated.All the estimation results were compared with the results of the output error method to demonstrate the effectiveness of the approach.It is shown that the filter error method is superior to the output error method for flight tests in atmospheric turbulence.

AN ADAPTIVE OPTIMAL KALMAN FILTER FOR STOCHASTIC VIBRATION CONTROL SYSTEM WITH UNKNOWN NOISE VARIANCES

In this paper, an optimal criterion is presented for adaptive Kalman filter in a control system with unknown variances of stochastic vibration by constructing a function of noise variances and minimizing the function. We solve the model and measure variances by using DFP optimal method to guarantee the results of Kalman filter to be optimized. Finally, the control of vibration can be implemented by LQG method.

Estimation of a Type of Form-Invariant Combined Signals under Autoregressive Operators

We focus on a type of combined signals whose forms remain invariant under the autoregressive operators. To extract the true signal from the autoregressive noise, we develop a strategy to separate parameters and use a two-step least squares approach to estimate the autoregressive parameters directly and then further give the estimate of the signal parameters. This method overcomes the difficulty that the autoregressive noise remains unknown in other methods. It can effectively separate the noise and extract the true signal. The algorithm is linear. The solution of the problem is computationally cheap and practical with high accuracy.

基于总体最小二乘-旋转不变算法的地表核磁共振信号参数估计

在地表核磁共振(SNMR)找水系统中,根据SNMR信号的参数能够预估地下含水层的储水量、导电性以及孔隙结构等信息。然而在实际应用中探测现场采集的SNMR信号十分微弱,易受到环境噪声干扰,导致无法直接获取SNMR信号的参数。针对这一问题,该文提出基于总体最小二乘-旋转不变法(TLS-ESPRIT)的地表核磁共振信号参数估计方法。基于谐波噪声与SNMR信号的相似信号特征构成一个由多个正弦衰减信号叠加的混合信号模型,使用TLS-ESPRIT将混合信号参数提取问题转换为旋转不变矩阵的广义特征值求解,从而获得SNMR信号的拉莫尔频率和弛豫时间,并结合最小二乘法求得其初始振幅和相位。仿真信号和实测信号实验结果表明此方法能够估计出混有随机噪声和工频谐波噪声的SNMR信号的参数,相比传统的谐波建模方法,在参数提取精度上效果更好。

基于线性调频连续波的合作式通信辐射源测距

针对加速运动目标参数估计中,离散多项式变换方法无法进行非整数估计的问题,本文提出基于瑞夫算法的离散多项式变换法和基于Chirp-Z变换的离散多项式变换法2种新型离散多项式变换算法,对加速运动目标速度和加速度进行估计,并对2种算法的估计误差和计算量进行了分析比较。结果表明:2种算法在信噪比-20 dB时均方误差开始接近克拉美罗界。基于瑞夫算法的离散多项式变换法与3次迭代基于Chirp-Z变换的离散多项式变换法均可在较低信噪比下可实现任意频率的有效估计且性能接近,二者均可实现低信噪比下速度、加速度的有效估计,但基于瑞夫算法的离散多项式变换法计算量远小于3次迭代基于Chirp-Z变换的离散多项式变换法。

A parameter estimator based on adaptive noise canceller

The application of an adaptive noise canceller to parameter estimation is restricted for its unsatisfactory performance in the condition of high SNR input. In this paper based on an adaptive noise canceller, is presented a parameter estAnating method, which shows ulce filtering function and good tracking ability with ullknown prior information of interference and motion model of the object. The presented estimator only needs that the interference lloise varies faster than the parameter to be estimated. The presented method as a beedng esthaator was used to process the data collected in a sea experiment and the results show exciting property.

基于FRFT的低信噪比LFM信号参数快速估计算法

基于分数阶傅里叶变换(Fractional Fourier Transform,FRFT)对线性调频(Linear Frequency Modulated,LFM)信号参数进行估计,问题关键是确定FRFT最佳阶数,根据误差迭代思想提出新的参数估计算法,该算法利用归一化带宽和旋转角的转化关系,由估计误差推算角度差值,有效降低了运算量,不需要调频斜率正负的先验信息,改进的对数搜索算法可以进一步提高参数估计结果的稳定性和可靠性。仿真结果表明,信噪比在-8 dB以上时该方法在高效率的前提下仍具有良好的参数估计性能,平均估计误差在1%以内,估计结果接近Cramer-Rao下限,满足工程实时处理需求。

基于自适应动态滑动窗口的锂电池参数辨识与SOC协同估计

锂电池的安全高效运行依赖于准确的荷电状态(SOC)估计,但是传统的电池模型和SOC协同估计在噪声干扰下的鲁棒性和可靠性较差。针对噪声干扰下SOC协同估计问题,首先对电池的最大可用容量和电池开路电压(OCV)特性进行分析,研究了锂电池SOC—OCV的曲线特性。然后研究了噪声干扰下的在线模型参数辨识和SOC估计问题,提出了基于自适应动态滑动窗口的双粒子群协同优化参数辨识(TCPSO)方法,通过实验验证了所提方法的SOC估计最大误差小于1%,表明所提方法可实现在线参数辨识,并且在抗噪性能和SOC估计精度等方面均优于现有协同估计方法。

基于L1-TV模型参数自适应的脉冲噪声去除

在医学影像、军事目标识别、网络安全、图像处理等多个领域,由于其严重的噪声干扰和大幅度信号突变,脉冲噪声问题广泛存在。针对受脉冲噪声影响的图像去噪问题,研究基于L1-TV模型去除脉冲噪声方法中的自动选取正则化参数问题。对于约束模型的求解问题,采用原对偶方法进行求解。鉴于模型中正则化参数难确定的问题,提出了一种自动求解正则化参数项的方法,减少了反复实验的次数。实验结果表明,提出的自适应选取模型中正则化参数方法具有鲁棒性,不仅能够去除图像中的脉冲噪声,而且较好地保留图像的边缘及细节信息。

脉冲噪声下基于CNN-FRFT的线性调频信号参数估计方法

由于脉冲噪声破坏了线性调频(LFM)信号的分数谱特征,使得基于分数谱特征的参数估计方法无法有效估计参数。针对这个问题,提出一种脉冲噪声环境下基于CNN-FRFT的LFM信号参数估计方法。首先,利用α稳定分布拟合随机脉冲噪声,构建加性含噪信号,输入卷积神经网络(CNN)进行训练和测试;其次,利用训练好的CNN模型对信号进行去噪,并验证模型的去噪能力和泛化能力;最后,利用分数阶傅里叶变换(FRFT)建立去噪信号的分数谱,通过峰值点位置来估计LFM信号的参数。实验结果表明,相比于传统的基于非线性函数的方法,该方法在强脉冲噪声环境下具有更好的精度和噪声鲁棒性,CNN的应用使其具有更强的泛化能力,在实测脉冲噪声下仍可以准确估计参数。

脉冲噪声下基于Sigmoid的LFM信号参数估计

由于脉冲噪声具有的短时大幅值特性,使得基于高斯假设的信号参数估计方法无法在脉冲噪声环境下有效估计参数。针对此问题,利用α稳定分布模拟随机脉冲噪声,提出了一种基于Sigmoid-CFRFT的LFM信号参数估计方法。首先,建立了一种自适应Sigmoid函数,证明了信号经过此非线性变换后,信号的2阶矩由无界变为有界,且信号的相位信息保持不变。其次,将变换后的信号进行离散时间CFRFT,建立了数学优化模型,并使用水循环算法搜索最优值点。最后,利用了非标准SαS分布噪声的修正方法,分析了标准和非标准分布下参数估计的性能。仿真结果说明,所提方法不仅可以有效抑制脉冲噪声对LFM信号分数谱特征的影响,而且能够实现低信噪比信号参数的高精度估计。相比于现有的基于非线性变换的参数估计方法,本文方法具有更好的精度,稳定性和噪声鲁棒性。

基于参数解耦的变分贝叶斯自适应卡尔曼滤波

针对噪声协方差矩阵失配情况下的状态估计问题,本文基于变分贝叶斯框架,提出了一种适用于过程噪声协方差矩阵和测量噪声协方差矩阵均未知条件下的参数解耦的变分贝叶斯自适应卡尔曼滤波算法。所提算法选取预测误差协方差矩阵作为变分优化变量,并引入了其马尔可夫演化模型,构造了参数解耦的变分推断模型。同时,采用固定点迭代优化实现状态、预测误差协方差矩阵和测量噪声协方差矩阵的联合后验概率分布求解,并设计了算法的收敛性判断准则。仿真结果验证了算法的有效性。

基于多站数据融合的参数精估计方法

针对侦察设备处于星载SAR副瓣照射范围,从而导致截获信号湮没于强噪声背景这个问题,本文提出一种基于多站接收机之间的数据融合方法。在信号形式未知的情况下,通过此方法可以检测出淹没在噪声中的微弱信号,进行信号的分类和时频域参数的精估计。首先,将参考接收机与其他接收机之间进行互相关处理,得到峰值信息,根据峰值信息的位置得到信号与参考信号之间的延迟位置,进行延迟校准;其次,各个接收机分别进行粗步长的分数阶傅里叶变换(Fractional Fourier Transform,FrFT),记录峰值信息为精估计做准备,根据峰值角度和分数阶傅里叶反变换恢复出原始信号;最后,判定是否存在信号,若信号存在实现多站原始信号功率比的加性融合,根据多站峰值信息限定旋转角度范围,采用精步长的分数阶傅里叶变换估计出调频率和中心频率;利用联合互相关谱实现信号能量的累积,采用自适应门线和边界波谷连续取小方法,找到信号存续状态中的左右边界,估计出带宽和中心频率,计算脉宽,实现时频域信号的精估计。仿真实验表明:该方法可以在低信噪比的高斯白噪声和有色噪声背景下,对线性调频信号(Chirp)的时频参数进行有效的精估计。

Detection, parameter estimation and imaging of maneuvering target in wide-band signal

The signal-to-noise ratio may be increased by the cross-range coherence integration so as to detect the moving target in low signal-to-noise ratio （SNR） condition.But, the radial velocity, acceleration and the change of acceleration due to the maneuvering motion of target may induce serious range migration and cross-range high-order phase terms leading to the unfocused cross-range image, the reduction of signal-noise ratio and the invalidation of target detection.Therefore, in order to solve these problems, this paper proposes a new method based on the adjacent correlation and scale transform methods for detection, parameters estimation and imaging of maneuvering targets in wide-band signal.This method can align the range and remove the cross-range high-order phase terms induced by the radial motion of target, enabling us to detect the target and estimate its moving parameters better.Finally, the simulated target is used to confirm that the method proposed by this paper can perfectly detect the maneuvering target in low signal-to-noise ratio condition, estimate its motion parameters and obtain an ISAR image of target.