Time delay estimation using the cross bispectrum

The cross bispectrum phase can be effectively used to estimate the time required for a nonGaussian signal to propagate between a pair of spatially separated sensors in the presence of highly correlated Gaussian noise. The authors present a consistent estimator of the phase of the cross bispectrum, derive the exact distribution of the phase of a complex Gaussian sample bispectrum, and show that in most cases the exact distribution can be approximated by a Gaussian distribution. Using this Gaussian approximation, the authors derive the variance of the time delay estimate computed from the sample cross bispectrum of a signal in additive correlated noise. These results allow the performance of time delay estimators based on the cross bispectrum phase to be quantified as a function of the sample size, the skewness of the signal, the signal-to-noise ratio (SNR), and the noise correlation     

Estimation and detection in non-Gaussian noise using higher orderstatistics

One of the primary applications of higher order statistics has been for detection and estimation of nonGaussian signals in Gaussian noise of unknown covariance. This is motivated by the fact that higher order cumulants of Gaussian processes vanish. We study the opposite problem, namely, detection and estimation in nonGaussian noise. We estimate cumulants of nonGaussian processes in the presence of unknown deterministic and/or Gaussian signals, which allows either parametric or nonparametric estimation of the covariance of the nonGaussian noise. Our approach is to augment existing second-order detection methods using cumulants. We propose solutions for detection of deterministic signals based on matched filters and the generalized likelihood ratio test which incorporate cumulants, where the resulting solutions are valid under either detection hypotheses. This allows for single record detection and obviates the need for noise-only training records. The problem of estimating signal strength in the presence of nonGaussian noise of unknown covariance is also considered, and a cumulant-based solution is proposed which uses a single data record. Examples are used throughout to illustrate our proposed methods     

Multivariate Signal Parameter Estimation Under Dependent Noise From 1-Bit Dithered Quantized Data

Motivated by applications in sensor networks and communications, we consider multivariate signal parameter estimation when only dithered 1-bit quantized samples are available. The observation noise is taken to be a stationary, strongly mixing process, which covers a wide range of processes including autoregressive moving average (ARMA) models. The noise is allowed to be Gaussian or to have a heavy-tail (with possibly infinite variance). An estimate of the signal parameters is proposed and is shown to be weakly consistent. Joint asymptotic normality of the parameters estimate is also established and the asymptotic mean and covariance matrices are identified.     

Spectrum estimation of short-time stationary signals in additivenoise and channel distortion

In this work, spectrum estimation of a short-time stationary signal that is degraded by both channel distortion and additive noise is addressed. A maximum likelihood estimation (MLE) algorithm is developed to jointly identify the degradation system and estimate short-time signal spectra. The source signal is assumed to be generated by a hidden Markov model (HMM) with state-dependent short-time spectral distributions described by mixtures of Gaussian densities. The distortion channel is linear time-invariant, and the noise is Gaussian. The algorithm is derived by using the principle of expectation-maximization (EM), where the unknown parameters of channel and noise are estimated iteratively, and the short-time signal power spectra are obtained from the posterior sufficient statistics of the source signal. Other spectral representation parameters, such as autoregressive model parameters or cepstral parameters, are obtained by minimum mean-squared error (MMSE) estimation from the power spectral estimates. The estimation algorithm was evaluated on simulated signals at the signal-to-noise ratios (SNRs) of 20 dB down to 0 dB, where it produced convergent estimation and significantly reduced spectral distortion     

基于高阶累积量和多相滤波器联合处理的PRBC-LFM参数提取

针对传统算法在进行伪码-线性调频信号参数提取时存在的条件限制和在低信噪比下提取精度不高的问题,文章提出了一种利用多相滤波器组和高阶累积量相结合进行参数的提取方法,该方法能够完成伪码-线性调频信号（PRBC-LFM）参数在高斯噪声下的提取。首先通过多相滤波器组能快速完成信号在频域上的均匀划分,接着对子带信号进行三阶累积量的短时估计,从而达到了抑制高斯噪声和实现在低信噪比下进行信号参数的提取的目的。测试结果表明,在低信噪比下使用该方法进行参数估计时精度很高。     

On Posterior Distributions for Signals in Gaussian Noise With Unknown Covariance Matrix

A Bayesian approach to estimate parameters of signals embedded in complex Gaussian noise with unknown color is presented. The study specifically focuses on a Bayesian treatment of the unknown noise covariance matrix making up a nuisance parameter in such problems. By integrating out uncertainties regarding the noise color, an enhanced ability to estimate both the signal parameters as well as properties of the error is exploited. Several noninformative priors for the covariance matrix, such as the reference prior, the Jeffreys prior, and modifications to this, are considered. Some of the priors result in analytical solutions, whereas others demand numerical approximations. In the linear signal model, connections are made between the standard Adaptive Maximum Likelihood (AML) estimate and a Bayesian solution using the Jeffreys prior. With adjustments to the Jeffreys prior, correspondence to the regularized solution is also established. This in turn enables a formal treatment of the regularization parameter. Simulations indicate that significant improvements, compared to the AML estimator, can be obtained by considering both the derived regularized solutions as well as the one obtained using the reference prior. The simulations also indicate the possibility of enhancing the predictions of properties of the error as uncertainties in the noise color are acknowledged.     

Multiple frequencies and AR parameters estimation from one bitquantized signal via the EM algorithm

The authors present a novel algorithm which is used to estimate the coefficients of q AR processes from a coarsely quantized signal. The input signal to the quantizer is the superposition of q AR processes and noise. In a related problem a modified version of the above algorithm is used to estimate the frequencies of coarsely quantized data obtained from q sinusoids embedded in noise. The proposed algorithm can accommodate a nonuniform m-level quantizer, as well as the special case of a one bit quantizer. The proposed estimator is based on the maximum likelihood (ML) criterion, and is realized by judiciously combining the expectation-maximization (EM) algorithm of Dempster, Laird and Rubin (1977), and the “Gaussian fit” scheme of Curry (1970). Simulations reveal that they can accurately estimate the coefficients of several AR processes, or the frequencies of several sinusoids, from one bit quantized data at low signal to noise ratios and moderate number of observations     

A blind detector for Rayleigh flat-fading channels with non-Gaussian interference via the particle learning algorithm

A blind particle learning detector (BPLD) is developed for signal detection in Rayleigh flat-fading channels with non-Gaussian interference. The parameters of the fading channel model and the noise model are all unknown. The impulsive noise is modeled as a mixture of Gaussian distributions, which is capable of representing a broad class of non-Gaussian noise. The particle learning algorithm is employed to simultaneously estimate signal and parameters of the fading channel model and the noise model. The delay weight method is used to improve the performance. Simulation results show that the performance of the BPLD proposed can follow closely the performance of the detector with known parameters of the fading channel model and the noise model.     

Doppler-channel blind identification for noncircular transmissions in multiple-access systems

The problem of blindly estimating the parameters of a Doppler channel for noncircular transmissions in multiple-access communication systems is addressed. A nondata-aided algorithm based on the cyclostationarity features of the received signal is proposed to estimate amplitude, phase, time delay, and frequency shift of each user. Under mild assumptions on the disturbance and user signals, the proposed method provides estimates of the unknown parameters that are mean-square consistent. Moreover, the proposed algorithm is asymptotically near-far resistant, and is not based on the usual assumption of white and/or Gaussian noise.     

Nonparametric cyclic-polyspectral analysis of AM signals andprocesses with missing observations

By viewing discrete-time amplitude-modulated signals and processes with missing observations as cyclostationary signals, nonparametric, mean-square-sense consistent, and asymptotically normal single record estimators are developed for their kth-order cumulants and polyspectra, along with the asymptotic covariances. The proposed estimation schemes use cyclic cumulants and polyspectra, and are theoretically insensitive to any additive stationary noise. In addition, schemes of order k⩾3 convey complete phase information and are insensitive to additive cyclostationary Gaussian noise of unknown covariance. The conventional approaches cannot recover mixed-phase linear processes, are susceptible to additive noise, and are a special case of the proposed schemes. Simulations demonstrate superior performance of the proposed algorithms     

Noise-limited reading of bar codes

The ubiquitous supermarket checkout scanner is a well-engineered and effective device. Existing scanners rely on simple and low-cost signal processing to interpret bar-code signals, which imposes restrictions on the system noise power that they can tolerate. In this paper, the authors describe the relationships between engineering parameters of the system that limit reader performance. If the combined noise is Gaussian, they show that the reader error probability depends on a single parameter, which they call a timing signal-to-noise ratio     

基于HFM和感知后滤波器的语音增强

研究了只能获得带噪信号的情况下的语音增强问题。将语音信号看作由高斯噪声激励的自回归(AR)过程,观测噪声为加性高斯白噪声,把信号转化为状态空间模型。首先用隐马尔可夫模型(HMM)估计AR参数和噪声的方差作为卡尔曼滤波器初值,估计信号作为参数估计的中间值给出,然后将估计信号通过一个感知滤波器平滑以消除残余噪声。仿真结果表明该算法有良好的性能。     

A general likelihood-ratio formula for random signals in Gaussian noise

It is shown that the likelihood ratio for the detection of a random, not necessarily Gaussian, signal in additive white Gaussian noise has the same form as that for a known signal in white Gaussian noise. The role of the known signal is played by the casual least-squares estimate of the signal from the observations. However, the "correlation" integral has to be interpreted in a special sense as an Itô stochastic integral. It will be shown that the formula includes all known explicit formulas for signals in white Gaussian noise. However, and more important, the formula suggests an "estimator-correlator" philosophy for engineering approximation of the optimum receiver. Some extensions of the above result are also discussed, e.g., additive finite-variance, not necessarily Gaussian, noise plus a white Gaussian noise component. Purely colored Gaussian noise can be treated if whitening filters can be specified. The analog implementation of Itô integrals is briefly discussed. The proofs of the formulas are based on the concept of an innovation process, which has been useful in certain related problems of linear and nonlinear least-squares estimation, and on the concept of covariance factorization.     

On the application of the jackknife to the estimation of theparameters of short multisinusoidal signals using the data-matrixformulation

It is demonstrated that the jackknife can be applied to the estimation of the parameters of a single short segment of a noisy, complex multisinusoid signal where the estimation process itself is based on the data-matrix formulation. The parameters of interest are the frequency, amplitude, and initial phase of each sinusoid, and the key role of the jackknife is to provide an estimate of the standard deviation of the estimates of these parameters from the single record available. The jackknife is shown to be especially appropriate where the primary estimator is well-behaved and its performance is broadly optimum where the sub-segment length used in creating the data matrix is about one-half of the record length and improves somewhat as the data length itself increases. This is inferred from a series of simulations involving three different algorithms with one, two, and three complex sinusoids in complex white noise. The application of the jackknife in the presence of phase noise and additive colored noise is also briefly examined. Due to the correlation between the columns of the data matrix, the successful application of the jackknife to this problem cannot be assumed a priori     

A Spatiotemporal Framework for Estimating Trial-to-Trial Amplitude Variation in Event-Related MEG/EEG

A spatiotemporal framework for estimating trial-to-trial variability in evoked response (ER) data is presented. Spatial and temporal bases capture the aspects of the response that are consistent across trials, while the basis expansion coefficients represent the variable components of the response. We focus on the simplest case of constant spatiotemporal response shape and varying amplitude across trials. Two different constraints on the amplitude evolution are employed to effectively integrate the individual responses and improve robustness at low SNR. The linear dynamical system response constraint estimates the current trial amplitude as an unknown constant scaling of the estimate in the previous trial plus zero-mean Gaussian noise with unknown variance. The independent response constraint estimates response amplitudes across trials as independent Gaussian random variables having unknown mean and variance. We develop a generalized expectation-maximization algorithm to obtain the maximum-likelihood (ML) estimates of the signal waveform, noise covariance matrix, and unknown constraint parameters. ML source localization is achieved by scanning the likelihood over different sets of spatial bases. We demonstrate the variability estimation and source localization effectiveness of the proposed algorithms using both real and simulated ER data.     

Realization of the Gauss-in-Gauss detector using minimum-mean-squared-error filters (Corresp.)

Alternative structures for the optimum detection of Gaussian signals in Gaussian noise are derived that can be interpreted in terms of minimum-mean-squared-error (MMSE) estimators of signal and noise. The realization is useful when the statistics of the signal or noise or both are unknown since the detector can be implemented in an adaptive mode by using tapped delay lines whose weights are adjusted recursively to yield the minimum-mean-squared-error estimate of certain components of the incoming waveforms.     

A geometric approach to multiple-channel signal detection

The paper introduces the generalized coherence (GC) estimate and examines its application as a statistic for detecting the presence of a common but unknown signal on several noisy channels. The GC estimate is developed as a natural generalization of the magnitude-squared coherence (MSC) estimate-a widely used statistic for nonparametric detection of a common signal on two noisy channels. The geometrical nature of the GC estimate is exploited to derive its distribution under the H₀ hypothesis that the data channels contain independent white Gaussian noise sequences. Detection thresholds corresponding to a range of false alarm probabilities are calculated from this distribution. The relationship of the H₀ distribution of the GC estimate to that of the determinant of a complex Wishart-distributed matrix is noted. The detection performance of the three-channel GC estimate is evaluated by simulation using a white Gaussian signal sequence in white Gaussian noise. Its performance is compared with that of the multiple coherence (MC) estimate, another nonparametric multiple-channel detection statistic. The GC approach is found to provide better detection performance than the MC approach in terms of the minimum signal-to-noise ratio on all data channels necessary to achieve desired combinations of detection and false alarm probabilities     

Cumulant-based method for bearing estimation in the presence ofnonGaussian noise

Bearing estimation algorithms based on the cumulants of array data have been developed to suppress additive spatially correlated Gaussian noises. In practice, however, the noises encountered in signal processing environments are often non-Gaussian, and the applications of those cumulant-based algorithms designed for Gaussian noise to non-Gaussian environments may severely degrade the estimation performance. The authors propose a new cumulant-based method to solve this problem. This approach is based on the fourth-order cumulants of the array data transformed by DFT, and relies on the statistical central limit theorem to show that the fourth-order cumulants of the additive non-Gaussian noises approach zero in each DFT cell. Simulation results are presented to demonstrate that the proposed method can effectively estimate the bearings in both Gaussian and non-Gaussian noise environments     

Iterative and sequential algorithms for multisensor signalenhancement

In problems of enhancing a desired signal in the presence of noise, multiple sensor measurements will typically have components from both the signal and the noise sources. When the systems that couple the signal and the noise to the sensors are unknown, the problem becomes one of joint signal estimation and system identification. The authors specifically consider the two-sensor signal enhancement problem in which the desired signal is modeled as a Gaussian autoregressive (AR) process, the noise is modeled as a white Gaussian process, and the coupling systems are modeled as linear time-invariant finite impulse response (FIR) filters. The main approach consists of modeling the observed signals as outputs of a stochastic dynamic linear system, and the authors apply the estimate-maximize (EM) algorithm for jointly estimating the desired signal, the coupling systems, and the unknown signal and noise spectral parameters. The resulting algorithm can be viewed as the time-domain version of the frequency-domain approach of Feder et al. (1989), where instead of the noncausal frequency-domain Wiener filter, the Kalman smoother is used. This approach leads naturally to a sequential/adaptive algorithm by replacing the Kalman smoother with the Kalman filter, and in place of successive iterations on each data block, the algorithm proceeds sequentially through the data with exponential weighting applied to allow adaption to nonstationary changes in the structure of the data. A computationally efficient implementation of the algorithm is developed. An expression for the log-likelihood gradient based on the Kalman smoother/filter output is also developed and used to incorporate efficient gradient-based algorithms in the estimation process     

高分辨距离像的运动参数估计

本文研究了加性高斯色噪声背景中一维高分辨距离成像中的运动估计.导弹和目标的相对运动对一维高分辨距离成像有较大影响,阶跃变频体制回波信号可以表示为多项式相位的形式,速度和加速度的影响分别体现在二次和三次多项式相位上.循环平稳处理方法对高斯色噪声不敏感,对非高斯色噪声也有较强的抑制作用,而且在低信噪比情况下工作良好.应用于低信噪比环境中.为了在复杂的地面环境中得到较好的距离像,本文采用循环平稳处理方法在较强的噪声背景下对速度进行估计,经过处理后得到较理想的距离像.