Variance Of White Noise Research Articles

A GLRT for multichannel radar detection in the presence of both compound Gaussian clutter and additive white Gaussian noise

Motivated by multichannel radar detection applications in the presence of both white Gaussian noise and Gaussian clutter with unknown power, we develop maximum likelihood parameter estimates for the disturbance process. Both cases with known and unknown white noise variance are treated. As the estimators do not admit closed-form solutions, numerical iterative procedures are developed that are guaranteed to at least converge to the local maximum. The developed estimates allow us to construct a generalized likelihood ratio test (GLRT) for the detection of a signal with constant but unknown amplitude. This GLRT has important applications in multichannel radar detection involving both white Gaussian noise and spherically invariant random process clutter and is shown to have better detection performance and CFAR property compared with existing statistics.

Fast and reliable structure-oriented video noise estimation

Noise can significantly impact the effectiveness of video processing algorithms. This paper proposes a fast white-noise variance estimation that is reliable even in images with large textured areas...

Fast and reliable structure-oriented video noise estimation

Noise can significantly impact the effectiveness of video processing algorithms. This paper proposes a fast white-noise variance estimation that is reliable even in images with large textured areas. This method finds intensity-homogeneous blocks first and then estimates the noise variance in these blocks, taking image structure into account. This paper proposes a new measure to determine homogeneous blocks and a new structure analyzer for rejecting blocks with structure. This analyzer is based on high-pass operators and special masks for corners to stabilize the homogeneity estimation. For typical video quality (PSNR of 20-40 dB), the proposed method outperforms other methods significantly and the worst-case estimation error is 3 dB, which is suitable for real applications such as video broadcasts. The method performs well both in highly noisy and good-quality images. It also works well in images including few uniform blocks.

New design of recursive Wiener fixed-lag smoother in linear discrete-time stochastic systems

This paper newly designs the Wiener fixed-lag smoother and filter using covariance information in linear discrete-time stochastic systems. The estimators require the information of the observation matrix, the system matrix for the state variable, related with the signal, the cross-variance function of the state variable with the observed value and the variance of the white observation noise. It is assumed that the signal is observed with additive white noise.

New design of fixed-interval smoother using covariance information in linear stochastic continuous-time systems

This paper proposes recursive least-squares fixed-interval smoothing and filtering algorithms in linear continuous-time stochastic systems. The estimators require the information of the autocovariance function of the signal, the variance of white observation noise and the observed value. The autocovariance function of the signal is expressed in the form of the semi-degenerate kernel.

New design of estimators using covariance information with uncertain observations in linear discrete-time systems

This paper proposes recursive least-squares (RLS) filtering and fixed-point smoothing algorithms with uncertain observations in linear discrete-time stochastic systems. The estimators require the information of the auto-covariance function in the semi-degenerate kernel form, the variance of white observation noise, the observed value and the probability that the signal exists in the observed value. The auto-covariance function of the signal is factorized in terms of the observation vector, the system matrix and the cross-variance function of the state variable, that generates the signal, with the signal. These quantities are obtained from the auto-covariance data of the signal. It is shown that the semi-degenerate kernel is expressed in terms of these quantities.

Regime Transitions in a Stochastically Forced Double-Gyre Model

A reduced-gravity double-gyre ocean model is used to study the influence of an additive stochastic wind stress component on the regime behavior of the wind-driven circulation. The variance of the stochastic component (spatially coherent white noise) representing the effect of atmospheric transient eddies is chosen to be spatially inhomogeneous. This is done to account for the observed concentration of eddy activity along the North Atlantic and North Pacific storm tracks. As a result the double-gyre model with a spatially inhomogeneous stochastic forcing shows a bimodal behavior. One regime shows a quasi-antisymmetric; the second regime a nonsymmetric flow pattern. It is suggested that the nonsymmetric regime corresponds to one member of a known nonsymmetric pair of stationary solutions. Actually no stationary solutions are explicitly calculated in this study. The bimodality does not appear without a spatially inhomogeneous stochastic forcing nor with spatially homogeneous stochastic forcing. Therefore, the regime transitions are induced by the inhomogeneity of the white noise variance. The study suggests that the stochastic forcing enables the system to reach the neighborhood of an unstable fixed point that is not reached without the spatially inhomogeneous stochastic wind field. The unstable fixed point then acts to steer the model in a temporarily persistent regime.

Chandrasekhar-type filter using covariance information for white Gaussian plus colored observation noise

This paper proposes recursive least-squares (RLS) Chandrasekhar-type filtering equations using the covariance information in the case of white Gaussian plus colored observation noise in linear continuous-time wide-sense stationary stochastic systems. Here, it is assumed that the system matrices in the state-space models for the signal and the colored noise, the cross-variance functions of the state variables for the signal and the colored noise with the observed value, the observation vectors for the signal and the colored noise, the variance of white Gaussian noise and the observed value are known. The number of differential equations included in the current Chandrasekhar-type filter is less than the previous filter using the covariance information. The Chandrasekhar-type equations are derived based on the invariant imbedding method. The Chandrasekhar-type filter brings numerically efficient algorithm in computation time.

NONPARAMETRIC IDENTIFICATION FOR NONLINEAR AUTOREGRESSIVE TIME SERIES MODELS: CONVERGENCE RATES

In this paper, the optimal convergence rates of estimators based on kernel approach for nonlinear AR model are investigated in the sense of Stone[17,18]. By combining the α–mixing property of the stationary solution with the characteristics of the model itself, the restrictive conditions in the literature which are not easy to be satisfied by the nonlinear AR model are removed, and the mild conditions are obtained to guarantee the optimal rates of the estimator of autoregression function. In addition, the strongly consistent estimator of the variance of white noise is also constructed.

Achievable rates for Tomlinson-Harashima precoding

This article examines Tomlinson-Harashima precoding (1971, 1972) on discrete-time channels having intersymbol interference and additive white Gaussian noise. An exact expression for the maximum achievable information rate of zero-forcing (ZF) THP is derived as a function of the channel impulse response, the input power constraint, and the additive white Gaussian noise variance. Information rate bounds are provided for the minimum mean-square error (MMSE) THP. The performance of ZF-THP and MMSE-THP relative to each other and to channel capacity is explored in general and for some example channels. The importance of symbol rate to ZF-THP performance is demonstrated.

Methods for estimating the seismic reflection response

The convolutional model of the seismic trace consists of a seismic pulse convolved with a reflectivity series plus measurement noise. The seismic deconvolution problem is to estimate the reflectivity series, given the data and an estimate of the seismic pulse. The classical solution to this problem is a weighted least‐squares estimate of the reflectivity series, which is optimal when the noise covariance matrix is known and there are no errors in the pulse. The seismic convolutional model has been reformulated, taking into account errors in the pulse and measurement noise, which is taken to be white noise filtered by a finite‐impulse‐response filter. All variables are assumed to be Gaussian, with known a priori mean values and covariance matrices. The unknown parameters may be the reflectivity series, the noise‐filter coefficients, and the white noise variance or, when the noise covariance matrix is known, just the reflectivity series. This results in maximum a posteriori (MAP) and maximum likelihood (ML) estimates of the reflectivity series that take into account uncertainty in the seismic pulse and colored noise. These estimates generally can be computed by solving a nonlinear minimization problem. The constrained total least‐squares (CTLS) estimate of the reflectivity series is found by minimizing a function that contains one less term than does the function that gives the ML estimate. When there is no uncertainty in the pulse and the noise covariance matrix is known all estimates are linear functions of the data corresponding to weighted least squares. The stabilized least‐squares (SLS) estimate of the reflectivity series is a special case of the MAP estimate with a simple statistical model. The problem of estimating the seismic pulse, given seismic data and an estimate of the reflectivity series, is identical to the problem of estimating the reflectivity series, except that the initial conditions in the convolutional model are slightly different.

Estimation technique using covariance information with uncertain observations in linear discrete-time systems

This paper proposes the recursive estimation technique using the covariance information in linear stationary discrete-time systems when the uncertain observations are given. At first, recursive least-squares algorithms for the filtering, fixed-point smoothing and one-step ahead prediction estimates are designed. The estimators use the crossvariance function of the state variable, that generates the signal process, with the signal, the observation vector, the system matrix, the variance of white Gaussian observation noise, the observed value and the probability that the signal exists in the uncertain observation. Second, to obtain the necessary information related to the covariance function of the signal in the estimators, we show the factorization method for the observation vector, the crossvariance function and the system matrix from the autocovariance function of the signal. As a result, the proposed technique uses finite number of autocovariance data of the stationary stochastic signal, the variance of white Gaussian observation noise, the uncertain observations and the probability.

Estimating the autocorrelation function of the control process for the variance of nonstationary gaussian white noise

A model is described for nonstationary Gaussian white noise and estimators are proposed for its characteristics.

Estimation of multivariate signal by output autocovariance data in linear discrete-time systems

The recursive least-squares filter and fixed-point smoother for the multivariate signal are designed in linear discrete-time systems. The estimators require the information of the system matrix, the observation matrix, and the variances of the state and white Gaussian observation noise in the signal generating model besides the updated observed value. By appropriate choices of the observation matrix and the state variables, the state-space model corresponding to the AR (autoregressive) model of order n is introduced. Here, some elements of the system matrix consist of the AR parameters. This paper proposes an iterative technique regarding the estimation of the variance of white Gaussian observation noise by use of the autocovariance data of the observed value. It is shown that the system matrix, the multivariate AR parameters, the variances of the state and observation noise, and the crossvariance of the input noise with the observation noise are estimated from the sampled autocovariance data of finite number. As a consequence, the multivariate signal is estimated in terms of the observed value and its autocovariance data.

Modulated Weiner process

We define and develop a novel process, related to stochastic resonance, in which a particle experiences three forces: a constant drift, a zero-mean white noise, and a time-periodic modulation. Upon reaching a threshold, the particle immediately returns to the starting point. The resulting process exhibits multiple maxima in the output power at the modulation frequency as a function of the white-noise variance, multimodal first-passage-time densities, and evidence of phase locking. Our model is an extension of the Gerstein-Mandelbrot model of neuron firing to the case of periodic stimuli, and therefore has applications in neural modeling.

Testing for a Change in the Parameter Values and Order of an Autoregressive Model

The problem of testing whether or not a change has occurred in the parameter values and order of an autoregressive model is considered. It is shown that if the white noise in the AR model is weakly stationary with finite fourth moments, then under the null hypothesis of no changepoint, the normalized Gaussian likelihood ratio test statistic converges in distribution to the Gumbel extreme value distribution. An asymptotically distribution-free procedure for testing a change of either the coefficients in the AR model, the white noise variance or the order is also proposed. The asymptotic null distribution of this test is obtained under the assumption that the third moment of the noise is zero. The proofs of these results rely on Horvath's extension of Darling-Erdos' result for the maximum of the norm of a $k$-dimensional Ornstein-Uhlenbeck process and an almost sure approximation to partial sums of dependent random variables.

Optimal filtering algorithm using covariance information in linear discrete-time distributed parameter systems

This paper presents an optimal discrete-time filtering algorithm using covariance information in linear distributed parameter systems. It is assumed that observation noise is a white Gaussian process. The autocovariance function of the signal, the variance of white Gaussian noise and the observed value are used in the filtering algorithm. It is an advantage that the current filtering algorithm is applied to the case where a difference equation, which generates a signal process, is unknown in linear stochastic distributed parameter systems.

Noise-filtering properties of numerical methods for the inverse Abel transform

The noise-filtering properties of polynomial interpolation-based numerical methods for computing inverse Abel transforms are studied. It is shown that, when sample spacing allows the use of the modified Abel transform, the methods are all in the form of serial products (discrete convolutions). Impulse responses and power spectra are used to show that the amplification of a single perturbation is proportional to the square root of the sampling rate and that the amplification of the variance of normal zero-mean white noise is proportional to the sampling rate. It is also shown that increasing the degree of the interpolating polynomial leads to more smoothing in methods based on the inverse transform, but to less smoothing in methods based on an inversion of the forward transform. These results are supported by a numerical example. >

On estimation of noise variance in two-dimensional signal processing

Estimation of noise variance is an important component of digital signal processing, in particular of image processing. In this paper we develop methods for estimating the variance of white noise in a two-dimensional degraded signal. We discuss optimal configurations of pixels for difference-based estimation, and describe asymptotically optimal selection of weights for the component pixels. After extensive analysis of possible configurations we recommend averaging linear configurations over a variety of different orientations (usually two or four). This approach produces estimators with properties of both statistical and numerical efficiency.

On estimation of noise variance in two-dimensional signal processing

Estimation of noise variance is an important component of digital signal processing, in particular of image processing. In this paper we develop methods for estimating the variance of white noise in a two-dimensional degraded signal. We discuss optimal configurations of pixels for difference-based estimation, and describe asymptotically optimal selection of weights for the component pixels. After extensive analysis of possible configurations we recommend averaging linear configurations over a variety of different orientations (usually two or four). This approach produces estimators with properties of both statistical and numerical efficiency.