Time-delay estimation for filtered Poisson processes using anEM-type algorithm

We develop a modified EM algorithm to estimate a nonrandom time shift parameter of an intensity associated with an inhomogeneous Poisson process N_t, whose points are only partially observed as a noise-contaminated output X of a linear time-invariant filter excited by a train of delta functions, a filtered Poisson process. The exact EM algorithm for computing the maximum likelihood time shift estimate generates a sequence of estimates each of which attempt to maximize a measure of similarity between the assumed shifted intensity and the conditional mean estimate of the Poisson increment dN_t. We modify the EM algorithm by using a linear approximation to this conditional mean estimate. The asymptotic performance of the modified EM algorithm is investigated by an asymptotic estimator consistency analysis. We present simulation results that show that the linearized EM algorithm converges rapidly and achieves an improvement over conventional time-delay estimation methods, such as linear matched filtering and leading edge thresholding. In these simulations our algorithm gives estimates of time delay whose mean square error virtually achieves the CR lower bound for high count rates     

Maximum likelihood estimation of the parameters of discretefractionally differenced Gaussian noise process

A maximum-likelihood estimation procedure is constructed for estimating the parameters of discrete fractionally differenced Gaussian noise from an observation set of finite size N. The procedure does not involve the computation of any matrix inverse or determinant. It requires N²/2+O(N) operations. The expected value of the loglikelihood function for estimating the parameter d of fractionally differenced Gaussian noise (which corresponds to a parameter of the equivalent continuous-time fractional Brownian motion related to its fractal dimension) is shown to have a unique maximum that occurs at the true value of d. A Cramer-Rao bound on the variance of any unbiased estimate of d obtained from a finite-sized observation set is derived. It is shown experimentally that the maximum-likelihood estimate of d is unbiased and efficient when finite-size data sets are used in the estimation procedure. The proposed procedure is extended to deal with noisy observations of discrete fractionally differenced Gaussian noise     

Multi-frame super-resolution reconstruction based on mixed Poisson–Gaussian noise

In this paper, a non-blind multi-frame super-resolution (SR) model based on mixed Poisson–Gaussian noise (MPGSR) is proposed. Poisson noise arises from the stochastic nature of the photon-counting process. Readout noise and reset noise inherent to the readout circuitry can be modeled by an additive Gaussian noise. Therefore, a mixed Poisson–Gaussian noise model is more appropriate for real imaging system. Instead of deriving the data fidelity term from the perspective of error norms and the corresponding influence functions, we address the multi-frame SR problem based on a statistical noise model. The derived objective function is decomposed into sub-functions and solved by the alternating direction method of multipliers (ADMM) algorithm which allows using techniques of constrained optimization. The validation of the proposed MPGSR was performed quantitatively and qualitatively on natural and X-ray images. In comparison to the optimization-based and learning-based state-of-the-art methods, we have demonstrated the feasibility of MPGSR and the significance of applying a more appropriate noise model on the SR image reconstruction.     

Estimation of the density of the filtered Poisson impulse process:a parametric approach

The Poisson driven pth order autoregressive (PDAR(p )) process is defined as the output of a continuous-time autoregressive system, driven by a stationary Poisson impulse process. An explicit formula for estimating the density of the Poisson impulse process is derived by combining the second- and third-order cumulants of the discretized PDAR(p) process. The validity of the proposed method is assessed through Monte Carlo simulations in some specific examples     

高斯白噪声中单频复正弦信号频率估计

本文提出了一种在加性复高斯白噪声中对单频复正弦信号频率的估计方法。该方法是基于利用自相关系数对Kay的方法和扩展。它从自相关系数的相位差的最佳线性组合中提取频率值。相对于Kay的方法，自相关系数中相位差信息的信噪比提高了。新的估计方法的方差具有更低的输入信噪经阈值，而保持了Kay的方法的无偏性和频率估计范围。我们给出了新方法的均方误差分析及其数值结果。该方差分析适用于中等以上的信噪比或大样本长度的情况。给出了估计其估计方差输入信噪比阈值的近似公式，该公式得出的阈值与样本长度大于24的模拟结果相当接近。     

Gaussian Cramer-Rao bound for direction estimation of noncircular signals in unknown noise fields

This paper focuses on the stochastic Cramer-Rao bound (CRB) on direction of arrival (DOA) estimation accuracy for noncircular Gaussian sources in the general case of an arbitrary unknown Gaussian noise field parameterized by a vector of unknowns. Explicit closed-form expressions of the stochastic CRB for DOA parameters alone are obtained directly from the Slepian-Bangs formula for general noncircular complex Gaussian distributions. As a special case, the CRB under the nonuniform white noise assumption is derived. Our expressions can be viewed as extensions of the well-known results by Stoica and Nehorai, Ottersten et al., Weiss and Friedlander, Pesavento and Gershman, and Gershman et al. Some properties of these CRBs are proved and finally, these bounds are numerically compared with the conventional CRBs under the circular complex Gaussian distribution for different unknown noise field models.     

On probability distributions for filtered white noise

When white noise generated by an underlying Poisson process is filtered by any member of a large class of stable (not necessarily linear nor stationary) filters, the first-order probability distributions of the filter output is infinitely divisible. The Kolmogorov canonical form for the characteristic function is displayed and related to the parameters of the white noise and of the filter. In certain linear stationary cases, cubclasses of the infinitely divisible distributions are identified. An invariance property of the bilateral exponential distribution is demonstrated.     

A new algorithm for the estimation of the frequency of a complex exponential in additive Gaussian noise

The letter presents a new algorithm for the precise estimation of the frequency of a complex exponential signal in additive, complex, white Gaussian noise. The discrete Fourier transform (DFT)-based algorithm performs a frequency interpolation on the results of an N point complex fast Fourier transform. For large N and large signal to noise ratio, the frequency estimation error variance obtained is 0.063 dB above the Cramer-Rao bound. The algorithm has low computational complexity and is well suited for real time digital signal processing applications, including communications, radar and sonar.     

Respiratory parameter estimation in non-invasive ventilation based on generalized Gaussian noise models

Modeling of respiratory system under non-invasive ventilation by using measured respiratory signals is of great interest in respiratory mechanics research area. Statistical processing techniques in the time-domain may be utilized as an alternative to the commonly used frequency-domain analysis to estimate model parameters. In this work, we propose using a generalized Gaussian distribution (GGD) to model the measurement noise in the respiratory system identification problem. The parameters of the GGD (i.e. the mean, the variance and the shape) are estimated by maximum likelihood (ML) and moment based estimators. However, the estimation error should also be taken into account which is in fact investigated as measurement innovations together with the measurement noise. Thus the Kalman iterations are applied with the help of the score function to compute the measurement innovations. Finally, the complete picture of the measurement noise and innovation analysis of the respiratory models is obtained which helped us to evaluate the non-Gaussian noise extension in the respiratory system analysis.     

Bayesian density functions for Gaussian pulse shapes in Gaussian noise

The probability density function for the amplitude of a Gaussian-shaped pulse of unknown arrival time is derived together with its mean and variance, when the time argument of the pulse is randomly distributed according to a Gaussian probability distribution or a uniform distribution. Then using the amplitude density as a prior distribution, the marginal density function for the pulse plus stationary Gaussian noise and its attendant expression for the probability of detection are derived. Applications to the calculation of detection probabilities in the presence of pulse peak location errors are cited.     

The estimation of a probability density function from measurements corrupted by Poisson noise (Corresp.)

The estimation of a probability density function from measurements corrupted by independent additive Poisson noise is considered. An estimate is derived that is asymptotically unbiased and consistent in the quadratic mean. Also, a practical realization of the estimator is given.     

RKHS approach to detection and estimation problems--I: Deterministic signals in Gaussian noise

First it is shown how the Karhunen-Loève approach to the detection of a deterministic signal can be given a coordinate-free and geometric interpretation in a particular Hilbert space of functions that is uniquely determined by the covariance function of the additive Gaussian noise. This Hilbert space, which is called a reproducing-kernel Hilbert space (RKHS), has many special properties that appear to make it a natural space of functions to associate with a second-order random process. A mapping between the RKHS and the linear Hilbert space of random variables generated by the random process is studied in some detail. This mapping enables one to give a geometric treatment of the detection problem. The relations to the usual integral-equation approach to this problem are also discussed. Some of the special properties of the RKHS are developed and then used to study the singularity and stability of the detection problem and also to suggest simple means of approximating the detectability of the signal. The RKHS for several multidimensional and multivariable processes is presented; by going to the RKHS of functionals rather than functions it is also shown how generalized random processes, including white noise and stationary processes whose spectra grow at infinity, are treated.     

Performance of a d.p.s.k. detector when presented with a distorted signal plus filtered Gaussian noise

A new approach to the problem of analysing differential phase-shift-keyed (d.p.s.k.) systems, in the presence of distortion and filtered noise is described. The result is presented in a form suitable for fast computation, and is shown to agree with previous workers' results for more idealised systems.     

The approximation of a Poisson distribution by a Gaussian distribution

This letter describes a modified Gaussian approximation to a Poisson distribution which, unlike the usual Gaussian approximation, gives good agreement on the tails of the distribution. It is therefore useful in error-rate calculations where the usual Gaussian approximation often is not.     

Continuous-time AR process parameter estimation in presence ofadditive white noise

Must existing work so far on continuous-time AR (CAR) parameter estimation concentrates on the noiseless measurement case. When measurement noise is present, our previous results on CAR parameter estimation need to be revised accordingly. Here we model the additive measurement noise as continuous-time white noise, and consider some approaches including average sampling and the direct LS method which we developed previously. Their advantages and disadvantages in this application are discussed     

Optimal, causal, simultaneous detection and estimation of random signal fields in a Gaussian noise field

Two methods are presented for simultaneously detecting a random signal field and estimating its Markovian parameters in the qq prurience of a white Gaussian noise field. The first method provides the Neyman-Pearson decision rule for determining the absence-or-presence of the signal and the maximum {em a posteriori} likelihood estimators of the parameters. The second provides the Bayes decision rule for the absence-or-presence of the signal and the minimum mean-square error estimators of the parameters. Both methods allow continual causal detection and estimation based on the continuous space-time data, and their detection and estimation statistics are given in terms of a single statistic, which is the solution of a certain stochastic integral equation. Furthermore, an approximate scheme is developed for recursively generating this statistic by using spatially and temporally sampled data.     

Recursive nonlinear estimation of a diffusion acting as the rate of an observed Poisson process

A conditional Poisson process is observed, whose rate is a diffusion process of known structure. The problem is to estimate the rate from the observed point process. Recursive equations are given for the conditional moment generating function and for an unnormalized conditional probability density of the rate. By studying these equations separately in between jumps and at the jumps, series expansions are obtained for these generating functions and densities in a number of examples that arise in applications to optical modulation and communications networks.     

高斯白噪声下L阵二维波达方向快速估计

针对L型阵列,提出一种在高斯白噪声环境下的二维波达方向( DOA)快速估计方法。首先利用阵列结构特点构建两个互协方差矩阵,同时实现了噪声分量的有效抑制,再依据协方差矩阵的性质构造了波达方向矩阵。对该矩阵进行一次特征分解即可分别得到包含方位角和俯仰角信息的方向矢量和方向元素,实现二维DOA估计。该算法避免了传统算法的谱峰搜索或大矩阵构造及其特征分解过程,计算量小,且参数自动配对。仿真结果表明,该算法在低性噪比和少快拍下的估计精度与2 D ESPRIT算法近似,但计算复杂度大幅降低,适用于实时性高的工程应用背景。