基于核函数的系统模型辨识

本文提出一种基于核函数的系统模型辨识方法。首先通过线性最小二乘确定低维空间中的非线性子空间,并经主分量分析提取与线性子空间基向量近似正交的非线性主分量,再经核密度估计进行聚类,自适应选择多个核将非线性子空间映射到高维空间,从而将任何一个线性和非线性的联合问题最终变成一个高维空间中的线性问题,最后借助线性最小二乘获得一个精确参数的系统模型。经过实验验证,该方法具有较好的效果。     

一种基于改进遗传算法的只测向无源定位技术

从单站序贯测向无源定位的误差分析出发,提出了基于遗传算法的最大似然只测向(Bearing-Only)定位方法,并以最小二乘法进行粗估计,对遗传算法采用了一维编码改进。实验表明,该方法既提高了算法的精度,又解决了二维定位中遗传算法搜索空间过大的问题,提高了算法的实用性。     

一种基于迭代滤波的Chirp信号参数估计算法

线性调频信号广泛应用于雷达、声纳、通信等领域中,其相位参数估计具有研究意义.本文研究了噪声中线性调频信号相位参数的估计问题,提出了基于最小二乘的相位展开和迭代滤波的相位参数估计方法.该算法提高了基于最小二乘相位展开算法得到的初估计的精度,并将本文算法与HAF方法得到的估计的均方误差进行比较,同时,通过仿真实验表明,本文的算法对于相位参数a2的估计在信噪比大于3dB时接近CRLB,验证了算法的有效性.     

一种基于最小二乘的K-分布参数估计方法

提出了一种基于最小二乘的K-分布参数估计方法,并利用仿真对该方法进行了验证。这种方法利用变量替换将杂波矩量和分布参数之间的关系转换为线性函数,然后通过最小二乘方法求解线性超定方程组获得K-分布参数的估计,这样能够避免常规矩量法在处理实际杂波数据时由于数据长度和噪声所导致的错误估计的发生,利用最小二乘法提高了估计精度。     

基于DOA-TDOA-FDOA的单站无源相干定位代数解

针对利用单站接收多个外辐射源信号实现目标定位的问题,该文提出一种基于两步加权最小二乘的到达角度(DOA)、时差(TDOA)和频差(FDOA)联合定位代数解算法。首先,在第1步加权最小二乘估计中,通过引入辅助参数,将非线性的角度、时差和频差方程转化为伪线性形式,并利用加权最小二乘得到目标位置和速度的粗估计;而后在第2步加权最小二乘估计中利用辅助参数和目标位置参数之间的约束关系来构造另外一组线性方程,并再次利用加权最小二乘得到目标位置和速度的精确估计。推导了联合角度、时差和频差定位的克拉美罗界。理论分析和仿真结果表明,算法在观测误差较小时的定位误差可以达到克拉美罗界。     

基于线性最小二乘方法的主动段目标初值估计

主动段目标初值估计是导弹目标战术参数估计的重要内容,是监视系统进行实时跟踪的前提条件。在天基观测背景下,该问题是非线性最小二乘求解问题。该文建立了主动段8态重力转弯模型和天基测量模型,通过用常加加速度线性模型来近似目标运动学参数,并对非线性测量进行伪线性化处理,将非线性最小二乘转化为线性最小二乘求解问题。特别地,给出了天基伪线性化测量及其统计特征的详尽推导,并进一步考察了测量伪线性化方法的适用范围。仿真实验中,通过与CRLB和传统的Gauss-Newton迭代方法比较,证明了该文方法在估计精度和运算效率上的优势。     

加权最小二乘法和MUSIC法联合测向技术研究

针对传统相位干涉仪测向法精度不高和MUSIC算法空间谱峰搜索耗时长的问题,提出了一种基于加权最小二乘法和MUSIC算法相结合的均匀圆阵测向技术。首先根据阵列短基线组求解相位模糊,并通过引入中间变量将相位差测量方程转化为线性方程组,然后运用加权最小二乘法对其进行求解,并利用信号到达角与中间变量的关系得到信号到达角初始估计,最后MUSIC算法依据信号到达角初始估计进行空间谱峰搜索,得到高精度信号到达角估计。仿真实验对比了所提方法与现有相位干涉仪及MUSIC算法的角度估计精度和耗时,证实了所提方法的正确性和有效性。     

基于进化策略的测试系统非线性校正研究

提出了将进化策略算法用于对测试系统中信号转换电路的非线性误差进行校正.该算法基于实数编码,采用(μ λ)选择策略和高斯变异算子,即父代种群参与竞争;同时建立了用进化策略校正非线性误差时目标函数的数学模型.实验结果表明,用进化策略对信号转换电路进行非线性校正不仅能够自动搜索到最优多项式,而且精度高于最小二乘法和改进遗传算法.该方法同样适用于对测试系统中传感器等其它电子测量元件中存在的非线性误差进行校正.     

基于DOA-TDOA-FDOA的单站无源相干定位代数解

针对利用单站接收多个外辐射源信号实现目标定位的问题,该文提出一种基于两步加权最小二乘的到达角度(DOA)、时差(TDOA)和频差(FDOA)联合定位代数解算法.首先,在第1步加权最小二乘估计中,通过引入辅助参数,将非线性的角度、时差和频差方程转化为伪线性形式,并利用加权最小二乘得到目标位置和速度的粗估计;而后在第2步加权最小二乘估计中利用辅助参数和目标位置参数之间的约束关系来构造另外一组线性方程,并再次利用加权最小二乘得到目标位置和速度的精确估计.推导了联合角度、时差和频差定位的克拉美罗界.理论分析和仿真结果表明,算法在观测误差较小时的定位误差可以达到克拉美罗界.     

直流伺服系统静态摩擦的最小二乘辨识

文章研究了含有静态摩擦的伺服系统的摩擦参数辨识问题.首先,将系统摩擦分为线性摩擦部分和非线性摩擦部分,使用最小二乘法得到摩擦参数的估计值;然后,为了算法在实际DSP芯片中的实用性,使用Pade逼近来表示非线性摩擦部分;最后,设计了使用前馈补偿的PD控制器.仿真实验结果表明:文章使用的简捷的方法,既能很好地对摩擦参数进行...     

一种基于互相关处理的极点提取新算法

针对传统极点提取算法在低信噪比时估计性能严重退化的缺点,该文从理论上推导了指数衰减正弦和信号在互相关处理后仍可表示为指数衰减正弦和信号的条件,定义了一种新的信号互相关函数估计方法,在此基础上提出了使用互相关消噪作为预处理的信号极点提取新方法.仿真实验表明,在相同精度的条件下文中提出的新方法较之改进KT法和基于四阶累量方法需要的信噪比降低了5dB.     

指数阻尼正弦模型阶选择算法

 本文针对指数阻尼正弦信号模型提出了一种新的基于子空间和结构总体最小范数的阶选择算法.该方法利用信号子空间移不变性以及阶与信号分量数匹配时总体误差最小原理建立模型阶估计准则.实验表明该方法获得了更高的阶估计精度.算法无需设置阈值和惩罚项,自动完成阶估计过程.它可以应用到高分辨率的谐波恢复算法中.     

Parameter estimation of exponentially damped sinusoids using ahigher order correlation-based approach

A very common problem in signal processing is parameter estimation of exponentially damped sinusoids from a finite subset of noisy observations. When the signal is contaminated with colored noise of unknown power spectral density, a cumulant-based approach provides an appropriate solution to this problem. We propose a new class of estimator, namely, a covariance-type estimator, which reduces the deterministic errors associated with imperfect estimation of higher order correlations from finite-data length. This estimator allows a higher order correlation sequence to be modeled as a damped exponential model in certain slices of the moments plane. This result shows a useful link with well-known linear-prediction-based methods, such as the minimum-norm principal-eigenvector method of Kumaresan and Tufts (1982), which can be subsequently applied to extracting frequencies and damping coefficients from the 1-D correlation sequence. This paper discusses the slices allowed in the moments plane, the uses and limitations of this estimator using multiple realizations, and a single record in a noisy environment. Monte Carlo simulations applied to standard examples are also performed, and the results are compared with the KT method and the standard biased-estimator-based approach. The comparison shows the effectiveness of the proposed estimator in terms of bias and mean-square error when the signals are contaminated with additive Gaussian noise and a single data record with short data length is available     

A two-dimensional Prony's method for spectral estimation

The problem of estimating the parameters of a model for bidimensional data made up by a linear combination of damped two-dimensional sinusoids is considered. Frequencies, amplitudes, phases, and damping factors are estimated by applying a generalization of the monodimensional Prony's method to spatial data. This procedure finds the desired quantities after an autoregressive model fitting to the data, a polynomial rooting, and a least-squares problem solution. The autoregressive models involved have a particular nature that simplifies the analysis. In fact, their characteristic polynomial factors into two parts so that many of their properties can be easily determined. Quick estimates of the parameters computed are found by using standard one-dimensional autoregressive estimation methods. An iterative procedure for refining the autoregressive parameters estimates which gives rise to better frequency estimates is also discussed. Some simulation results are reported     

Parallel algorithms for maximum a posteriori estimation of spin density and spin-spin decay in magnetic resonance imaging

A maximum a posteriori (MAP) algorithm is presented for the estimation of spin-density and spin-spin decay distributions from frequency and phase-encoded magnetic resonance imaging data. Linear spatial localization gradients are assumed: the y-encode gradient applied during the phase preparation time of duration tau before measurement collection, and the x-encode gradient applied during the full data collection time t>/=0. The MRI signal model developed in M.I. Miller et al., J. Magn. Reson., ser. B (Apr. 1995) is used in which a signal resulting from M phase encodes (rows) and N frequency encode dimensions (columns) is modeled as a superposition of MN sinc-modulated exponentially decaying sinusoids with unknown spin-density and spin-spin decay parameters. The nonlinear least-squares MAP estimate of the spin density and spin-spin decay distributions solves for the 2MN spin-density and decay parameters minimizing the squared-error between the measured data and the sine-modulated exponentially decay signal model using an iterative expectation-maximization algorithm. A covariance diagonalizing transformation is derived which decouples the joint estimation of MN sinusoids into M separate N sinusoid optimizations, yielding an order of magnitude speed up in convergence. The MAP solutions are demonstrated to deliver a decrease in standard deviation of image parameter estimates on brain phantom data of greater than a factor of two over Fourier-based estimators of the spin density and spin-spin decay distributions. A parallel processor implementation is demonstrated which maps the N sinusoid coupled minimization to separate individual simple minimizations, one for each processor.     

Matching pursuit and atomic signal models based on recursive filterbanks

The matching pursuit algorithm can be used to derive signal decompositions in terms of the elements of a dictionary of time-frequency atoms. Using a structured overcomplete dictionary yields a signal model that is both parametric and signal adaptive. In this paper, we apply matching pursuit to the derivation of signal expansions based on damped sinusoids. It is shown that expansions in terms of complex damped sinusoids can be efficiently derived using simple recursive filter banks. We discuss a subspace extension of the pursuit algorithm that provides a framework for deriving real-valued expansions of real signals based on such complex atoms. Furthermore, we consider symmetric and asymmetric two-sided atoms constructed from underlying one-sided damped sinusoids. The primary concern is the application of this approach to the modeling of signals with transient behavior such as music; it is shown that time-frequency atoms based on damped sinusoids are more suitable for representing transients than symmetric Gabor atoms. The resulting atomic models are useful for signal coding and analysis modification synthesis     

Mean likelihood frequency estimation

Estimation of signals with nonlinear as well as linear parameters in noise is studied. Maximum likelihood estimation has been shown to perform the best among all the methods. In such problems, joint maximum likelihood estimation of the unknown parameters reduces to a separable optimization problem, where first, the nonlinear parameters are estimated via a grid search, and then, the nonlinear parameter estimates are used to estimate the linear parameters. We show that a grid search can be avoided by using the mean likelihood estimator for estimating the unknown nonlinear parameters and how its performance can be made equivalent to that of the maximum likelihood estimator (MLE). The mean likelihood estimator requires computation of a multidimensional integral. However, using the concepts of importance sampling, we obtain the mean likelihood estimate without using integration. The technique is computationally far less burdensome than the direct maximum likelihood method but performs just as well. Simulation examples for estimating frequencies of multiple sinusoids in noise are given. The general technique can be applied to a large class of nonlinear regression problems     

Mode coupling between dielectric and semiconductor planar waveguides

Computer modeling studies on four-layer silicon-clad planar dielectric waveguides indicate that the attenuation and mode index behave as exponentially damped sinusoids when the silicon thickness is increased. This effect can be explained as a periodic coupling between the guided modes of the lossless structure and the lossy modes supported by the high refractive index silicon. Furthermore, the attenuation and mode index are significantly altered by conductivity changes in the silicon. An amplitude modulator and phase modulator have been proposed using these results. Predicted high attenuations in the device may be reduced significantly with a silicon dioxide buffer layer.     

Maximum-likelihood estimation of parameters of exponentially damped sinusoids

Maximum-likelihood estimates of the parameters of exponentially damped sinusoidal signals in noise can be found by using an iterative procedure based on Newton's method. The initial estimate is obtained by an improved linear-prediction method. The properties of the Newton estimates obtained from short data records is experimentally studied.