General second-order covariance of Gaussian maximum likelihood estimates applied to passive source localization in fluctuating waveguides

A method is provided for determining necessary conditions on sample size or signal to noise ratio (SNR) to obtain accurate parameter estimates from remote sensing measurements in fluctuating environments. These conditions are derived by expanding the bias and covariance of maximum likelihood estimates (MLEs) in inverse orders of sample size or SNR, where the first-order covariance term is the Cramer-Rao lower bound (CRLB). Necessary sample sizes or SNRs are determined by requiring that (i) the first-order bias and the second-order covariance are much smaller than the true parameter value and the CRLB, respectively, and (ii) the CRLB falls within desired error thresholds. An analytical expression is provided for the second-order covariance of MLEs obtained from general complex Gaussian data vectors, which can be used in many practical problems since (i) data distributions can often be assumed to be Gaussian by virtue of the central limit theorem, and (ii) it allows for both the mean and variance of the measurement to be functions of the estimation parameters. Here, conditions are derived to obtain accurate source localization estimates in a fluctuating ocean waveguide containing random internal waves, and the consequences of the loss of coherence on their accuracy are quantified.     

多谐波脉冲星信号时延估计方法

针对脉冲星导航技术中延时估计这一关键问题, 提出了频域上直接使用脉冲星信号测量到达时间集合进行时延估计的方法——多谐波脉冲星信号时延估计(MHSPE)方法. 该方法建立在频域上相位时延的极大似然估计的基础上, 通过高次谐波对脉冲星观测信号提取出各谐波相位的极大似然估计, 然后取频谱上各谐波的幅值进行归一化作为各谐波相位的权值, 最后取各谐波相位的加权平均作为该时刻的相位估计. 理论上证得MHSPE算法对相位的估计是无偏、一致的, 相比于频域上一次谐波的极大似然估计, MHSPE方法的信噪比随谐波数m的增加而增加, 当各谐波幅值相同时, 信噪比可提高m_1/2倍; 与脉冲星信号时延的克拉美罗界比较, 脉冲星信号时域的导数在频域上的反映就是各谐波分量的数量, 因此随着谐波次数的增加脉冲星信号时延估计可极大趋近克拉美罗界. 采用RXTE航天器对Crab脉冲星的实测数据检验MHSPE方法的性能, 实验结果表明, 针对低信噪比的脉冲星信号, MHSPE可获得高精度的相位估计, 随观测时间增加, 估计精度快速收敛于克拉美罗界.     

Semi-coherent time of arrival estimation using regression

Time of arrival (ToA) estimation is essential for many types of remote sensing applications including radar, sonar, and underground exploration. The standard method for ToA estimation employs a matched filter for computing the maximum likelihood estimator (MLE) for ToA. The accuracy of the MLE decreases rapidly whenever the amount of noise in a received signal rises above a certain threshold. This well-known threshold effect is unavoidable in several important applications due to various limitations on the power and the spectrum of a narrowband source pulse. A measurement performed in the presence of the threshold effect employs a receiver which operates in the semi-coherent state. Therefore, the conventional methods assuming a coherent state receiver should be adapted to the semi-coherent case. In this paper, a biosonar-inspired method for the semi-coherent ToA estimation is described. The method abandons the exploration of an echo signal by a single matched filter in favor of the analysis by multiple phase-shifted unmatched filters. Each phase-shifted unmatched filter gives rise to a biased ToA estimator. The described method uses regression for combining these estimators into a single unbiased ToA estimator that outperform the MLE in the presence of the threshold effect.     

Time-domain noise reduction based on an orthogonal decomposition for desired signal extraction

This paper addresses the problem of noise reduction in the time domain where the clean speech sample at every time instant is estimated by filtering a vector of the noisy speech signal. Such a clean speech estimate consists of both the filtered speech and residual noise (filtered noise) as the noisy vector is the sum of the clean speech and noise vectors. Traditionally, the filtered speech is treated as the desired signal after noise reduction. This paper proposes to decompose the clean speech vector into two orthogonal components: one is correlated and the other is uncorrelated with the current clean speech sample. While the correlated component helps estimate the clean speech, it is shown that the uncorrelated component interferes with the estimation, just as the additive noise. Based on this orthogonal decomposition, the paper presents a way to define the error signal and cost functions and addresses the issue of how to design different optimal noise reduction filters by optimizing these cost functions. Specifically, it discusses how to design the maximum SNR filter, the Wiener filter, the minimum variance distortionless response (MVDR) filter, the tradeoff filter, and the linearly constrained minimum variance (LCMV) filter. It demonstrates that the maximum SNR, Wiener, MVDR, and tradeoff filters are identical up to a scaling factor. It also shows from the orthogonal decomposition that many performance measures can be defined, which seem to be more appropriate than the traditional ones for the evaluation of the noise reduction filters.     

相干多普勒测风激光雷达低信噪比区域回波信号的估计方法

相干多普勒测风激光雷达通常会采用周期图最大值法（PM）提取不同距离门信号的多普勒频移（对应风速）信息。由于噪声和相干效率的影响,个别距离门信号会出现信噪比（SNR）突然降低的情况,从而导致系统的探测概率降低,影响系统整体的探测性能。为了解决个别距离门信号多普勒频移的错误估计问题,提出了一种新的非线性自适应多普勒频移估计方法。该方法利用风速的连续性,标定错误距离门,并自适应地利用强信噪比区域的多普勒频移统计数据来弥补信噪比变差而出现的估计错误。分别利用了仿真模型和一套1.54μm全光纤相干激光雷达系统获得了风场测量数据,对比了使用该技术前后反演得到的风速趋势,证明该方法能够有效地解决上述问题。     

Particle multiplicity of unbiased gluon jets from \mathrme^+\mathrme^- three-jet events

The charged particle multiplicities of two- and three-jet events from the reaction ee Z are measured for Z decays to light quark (uds) flavors. Using recent theoretical expressions to account for biases from event selection, results corresponding to unbiased gluon jets are extracted over a range of jet energies from about 11 to 30 GeV. We find consistency between these results and direct measurements of unbiased gluon jet multiplicity from and Z decays. The unbiased gluon jet data including the direct measurements are compared to corresponding results for quark jets. We perform fits based on analytic expressions for particle multiplicity in jets to determine the ratio of multiplicities between gluon and quark jets as a function of energy. We also determine the ratio of slopes, , and of curvatures, , where y specifies the energy scale. At 30 GeV, we find and , where the uncertainties are the statistical and systematic terms added in quadrature. These results are in general agreement with theoretical predictions. In addition, we use the measurements of the energy dependence of and to determine an effective value of the ratio of QCD color factors, . Our result, (total), is consistent with the QCD value of 2.25. Received: 25 October 2001 / Revised version: 20 January 2002 / Published online: 5 April 2002     

Estimating the instantaneous velocity of randomly moving target swarms in a stratified ocean waveguide by Doppler analysis

Doppler analysis has been extensively used in active radar and sonar sensing to estimate the speed and direction of a single target within an imaging system resolution cell following deterministic theory. For target swarms, such as fish and plankton in the ocean, and raindrops, birds and bats in the atmosphere, multiple randomly moving targets typically occupy a single resolution cell, making single-target theory inadequate. Here, a method is developed for simultaneously estimating the instantaneous mean velocity and position of a group of randomly moving targets within a resolution cell, as well as the respective standard deviations across the group by Doppler analysis in free-space and in a stratified ocean waveguide. While the variance of the field scattered from the swarm is shown to typically dominate over the mean in the range-velocity ambiguity function, cross-spectral coherence remains and maintains high Doppler velocity and position resolution even for coherent signal processing algorithms such as the matched filter. For pseudo-random signals, the mean and variance of the swarms' velocity and position can be expressed in terms of the first two moments of the measured range-velocity ambiguity function. This is shown analytically for free-space and with Monte-Carlo simulations for an ocean waveguide.     

A Bayesian approach to matched field processing in uncertain ocean environments

An approach of Bayesian Matched Field Processing （MFP） was discussed in the uncertain ocean environment. In this approach, uncertainty knowledge is modeled and spatial and temporal data received by the array are fully used. Therefore, a mechanism for MFP is found, which well combines model-based and data-driven methods of uncertain field processing. By theoretical derivation, simulation analysis and the validation of the experimental array data at sea, we find that （1） the basic components of Bayesian matched field processors are the cor- responding sets of Bartlett matched field processor, MVDR （minimum variance distortionless response） matched field processor, etc.; （2） Bayesian MVDR/Bartlett MFP are the weighted sum of the MVDR/Bartlett MFP, where the weighted coefficients are the values of the a posteriori probability; （3） with the uncertain ocean environment, Bayesian MFP can more correctly locate the source than MVDR MFP or Bartlett MFP; （4） Bayesian MFP can better suppress sidelobes of the ambiguity surfaces.     

Wavelet Filter and Noise Rejection for the Pulse Laser Radar

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A matched filter echo summation technique for MRI

A technique is presented to increase the signal-to-noise ratio (SNR) in two-dimensional (2D), phase-encoded imaging at low SNR. The essence of this technique is to combine multiple echoes in the time domain. As analyzed in the paper, phase discrepancies exist among different echoes and may deteriorate the combined echo. In particular, extraneous phase shifts can be created if unshielded gradient coils are used. To overcome these phase discrepancies, a matched filter was derived from the k = 0 component of image. This matched filter has the same phase discrepancies among its echoes as the imaging signal and its magnitude decays with an average T₂. In the echo summation with the matched filter, the phase of the matched filter was subtracted from the imaging signal and the magnitude of the matched filter was used as the weighting function. We have shown that this matched filter echo summation technique has better SNR than the case of 2D, phase-encoded imaging in both simulation and experiment. The SNR improvement is up to 60% in a phantom experiment. This technique is mostly useful in low SNR imaging that requires long imaging time, such as spectroscopic imaging and ¹⁹F imaging.     

前后向子分段相位差频率估计法

为提高直接频率估计法的精度并推导出估计误差方差的闭合表达式,本文提出基于前后向子分段相位差的直接频率估计法. 该方法对样本的前向和后向两个子段做快速傅里叶变换,再提取这两个子段变换后的峰值谱相位差而获得频率估计. 本文证明了该估计器具有无偏性,并推导出其频率估计方差的闭合理论表达式. 仿真实验验证了该闭合表达式的正确性,故本文方法具有更高的测频精度和广泛的应用前景. 关键词： 频率估计 前后向子段 相位差 克拉美罗限     

Optimization of the algorithms for estimating the ultrasonic attenuation along the propagation path

In this study, we perform statistical analysis on two methods used to estimate the total ultrasound attenuation along the propagation path from the surface of the transducer to a region of interest at a particular depth; namely, the spectral-fit method and the multiple-filter method. We derive mathematical equations for the bias and variance in the attenuation estimates as a function of region of interest (ROI) size, imaging system bandwidth, and number of independent Gaussian filters (for the multiple filter method). We use numerical simulations to validate the mathematical equations and compare the two algorithms. The results show that the variance in the total attenuation coefficient estimates obtained with the two methods are comparable, and that the estimates are unbiased. For the multiple filter method, the optimal number of Gaussian filters is two.     

Performance analysis of direct-sequence spread-spectrum underwater acoustic communications with low signal-to-noise-ratio input signals

Direct-sequence spread-spectrum signals collected from the TREX04 experiment are analyzed to determine the bit-error-rate (BER) as a function of the input signal-to-noise ratio (SNR) for a single receiver. A total of 1160 packets of data are generated by adding ambient noise data collected at sea to the signal data (in postprocessing) to create signals with different input-SNR, some as low as -15 dB. Two methods are analyzed in detail, both using a time-updated channel impulse-response estimate as a (matched) filter to mitigate the multipath-induced interferences. The first method requires an independent estimate of the time-varying channel impulse-response function; the second method uses the channel impulse-response estimated from the previous symbol as the matched filter. The first method yields an average BER <10(-2) for input-SNR as low as -12 dB and the second method yields a similar performance for input-SNR as low as -8 dB. The measured BERs are modeled using the measured signal amplitude fluctuation statistics and processing gain obtained by de-spreading the received signal with the transmitted code sequence. Performance losses caused by imprecise symbol synchronization at low input-SNR, uncertainty in channel estimation, and signal fading are quantitatively modeled and compared with data.     

Optimal Filtering Applied to the Inversion of the Laplace Transform

Inversion of the Laplace transform, used in the laser scattering measurement of colloidal particle size distributions, presents severe numerical difficulties. In the presence of noise the variance of the inversion integral is infinite, indicating maximum uncertainty in the inversion. This paper applies the method of minimum variance, or “optimal”, filtering to the eigenfunction spectrum of the Laplace transform, giving an inversion which has finite variance. Spectral decomposition using the eigenfunctions of the Laplace transform gives a representation of the noise and desired signals analogous to the Fourier spectrum used in linear system theory. It is possible to obtain a filtered estimate of the unknown linewidth distribution. The requirement that the variance of this filtered estimate is minimum leads to a Wiener-Hopf integral equation defining the optimal filter. The results of this paper provide a basis of comparison of all methods of inversion of the Laplace transform, including the extensive literature of colloidal particle sizing by laser scattering or photon correlation.     

Determining tomographic arrival times based on matched filter processing: considering the impact of ocean waves

Reflection of high-frequency acoustic signals from an air-sea interface with waves is considered in terms of determining travel times for acoustic tomography. Wave-induced, multi-path rays are investigated to determine how they influence the assumption that the time of the largest matched filter magnitude between the source and receiver signals is the best estimate of the arrival time of the flat-surface specular ray path. A simple reflection model is developed to consider the impact of in-plane, multi-path arrivals on the signal detected by a receiver. It is found that the number of multi-path rays between a source and receiver increases significantly with the number of times the ray paths strike the ocean surface. In test cases, there was always one of the multi-path rays that closely followed the flat-surface specular ray path. But all the multi-path rays arrive at the receiver almost simultaneously, resulting in interference with the signal from the flat-surface specular ray path. As a result, multi-path arrivals due to open ocean surface waves often distort the received signal such that maxima of matched filtering magnitudes will not always be a reliable indicator of the arrival time of flat-surface specular ray paths.     

A method of estimating initial conditions of coupled maplattices based on time-varying symbolic dynamics

A novel computationally efficient algorithm in terms of the time-varying symbolic dynamic method is proposed to estimate the unknown initial conditions of coupled map lattices (CMLs). The presented method combines symbolic dynamics with time-varying control parameters to develop a time-varying scheme for estimating the initial condition of multi-dimensional spatiotemporal chaotic signals. The performances of the presented time-varying estimator in both noiseless and noisy environments are analysed and compared with the common time-invariant estimator. Simulations are carried out and the obtained results show that the proposed method provides an efficient estimation of the initial condition of each lattice in the coupled system. The algorithm cannot yield an asymptotically unbiased estimation due to the effect of the coupling term, but the estimation with the time-varying algorithm is closer to the Cramer--Rao lower bound (CRLB) than that with the time-invariant estimation method, especially at high signal-to-noise ratios (SNRs).     

基于最大似然的单通道交叠激光微多普勒信号参数分离估计

利用激光对目标微弱振动进行探测有利于获得明显的微多普勒效应,这为精确估计目标微动特征参数,实现对目标的分类和精细识别提供了可能.但对于多散射点或多目标激光探测,信号为单通道多分量微动混合的形式,而且补偿目标主体运动后,数值上相近的微动参数还会导致信号在时频域存在严重的交叠.为从这类混合信号中精确估计各分量的微动参数,本文提出了基于最大似然框架的参数分离估计方法.利用精细化扫描的奇异值比谱法从混合信号中获得目标微动频率,并得到各分量的幅值比信息.推导了微动参数最大似然估计的解析表达形式,根据激光微多普勒信号的特点从频谱能量分布的角度重新设计了似然函数,解决了传统似然函数在激光微动信号中出现的高度非线性问题,降低了初始化的要求,提高了抗噪性能,并采用马尔可夫-蒙特卡罗方法具体实现了参数的估计.在微动参数得到估计的基础上给出了信号的幅值和初相的估计方法.用本文方法对仿真和实验数据进行处理,得到了接近克拉美罗下界的估计结果,验证了方法的有效性.与传统非参数化估计方法的对比结果体现了所提方法对混合微动参数精确估计上的优势.     

基于矩孔光学傅里叶变换的匹配滤波器缩放比例标定方法研究

为了使待识别目标的傅里叶变换频谱与匹配滤波器频谱分布严格重合,提出了一种基于矩孔图像光学傅里叶变换的匹配滤波器缩放比例标定方法。针对范德卢格特型光学相关器,在分析场景空间光调制器傅里叶变换频谱分布的基础上,以矩孔图像的频谱间距作为基准标定匹配滤波器的缩放比例;并利用焦距为400mm的傅里叶透镜作为一个实例,计算出其匹配滤波器缩放比例为1.068,对标定结果进行了实验验证。结果表明,此方法适用于范德卢格特型光学相关器中匹配滤波器的缩放比例标定,能够有效提高相关峰的能量和信噪比。     

Stochastic resonance in a bias monostable system with frequency mixing force and multiplicative and additive noise

The stochastic resonance in a bias monostable system subject to frequency mixing force and multiplicative and additive noise is investigated. Based on the adiabatic elimination theory, the analytic expressions of the signal-to-noise ratio (SNR) for the fundamental and higher harmonics are obtained. It is shown that the SNR is a non-monotonic function of the intensities of the multiplicative and additive noise, as well as the system parameter. Moreover, the SNR for the fundamental harmonic decreases with the increase of the system bias, while the SNR for the higher harmonics behaves non-monotonically as the system bias varies.     

基于抛物方程的海陆环境信号时延与到达角估计

针对复杂海陆环境中的无线信号传播预测问题,研究了适用于抛物方程的信号时延与到达角估计方法。将自由空间中抛物方程轴向波前信号视为本地副本信号,然后利用信号的自相关特性,将接收信号与副本信号进行互相关运算,最后通过相关函数的峰值检索,得到脉冲信号在复杂环境中传播的附加时延。采用数值算例,验证了该方法的正确性和有效性。此外,采用多重信号分类算法,由抛物方程构建接收阵列的协方差矩阵,并对其进行特征值分解,然后利用信号子空间和噪声子空间的正交性,实现复杂环境中的信号到达角估计。仿真结果表明,相比于传统的平面波谱方法,该方法具有更高的多径分辨率。基于上述方法,并结合数字地图,在典型的海陆环境中进行了仿真实验,分析了蒸发波导对脉冲信号传播时延和到达角的影响。