Cramer-Rao bounds for source localization in shallow ocean with generalized Gaussian noise

Localization of underwater acoustic sources is a problem of great interest in the area of ocean acoustics. There exist several algorithms for source localization based on array signal processing.It is of interest to know the theoretical performance limits of these estimators. In this paper we develop expressions for the Cramer-Rao-Bound (CRB) on the variance of direction-of-arrival(DOA) and range-depth estimators of underwater acoustic sources in a shallow range-independent ocean for the case of generalized Gaussian noise. We then study the performance of some of the popular source localization techniques,through simulations, for DOA/range-depth estimation of underwater acoustic sources in shallow ocean by comparing the variance of the estimators with the corresponding CRBs.

Signal Detection in Generalized Gaussian Noise by Nonlinear Wavelet Denoising

In this paper, a nonlinear suboptimal detector whose performance in heavy-tailed noise is significantly better than that of the matched filter is proposed. The detector consists of a nonlinear wavelet denoising filter to enhance the signal-to-noise ratio, followed by a replica correlator. Performance of the detector is investigated through an asymptotic theoretical analysis as well as Monte Carlo simulations. The proposed detector offers the following advantages over the optimal (in the Neyman-Pearson sense) detector: it is easier to implement, and it is more robust with respect to error in modeling the probability distribution of noise.

Three-dimensional localization of multiple acoustic sources in shallow ocean with non-Gaussian noise

In this paper, a low-complexity algorithm SAGE-USL is presented for 3-dimensional (3-D) localization of multiple acoustic sources in a shallow ocean with non-Gaussian ambient noise, using a vertical and a horizontal linear array of sensors. In the proposed method, noise is modeled as a Gaussian mixture. Initial estimates of the unknown parameters (source coordinates, signal waveforms and noise parameters) are obtained by known/conventional methods, and a generalized expectation maximization algorithm is used to update the initial estimates iteratively. Simulation results indicate that convergence is reached in a small number of (<= 10) iterations. Initialization requires one 2-D search and one 1-D search, and the iterative updates require a sequence of 1-D searches. Therefore the computational complexity of the SAGE-USL algorithm is lower than that of conventional techniques such as 3-D MUSIC by several orders of magnitude. We also derive the Cramer-Rao Bound (CRB) for 3-D localization of multiple sources in a range-independent ocean. Simulation results are presented to show that the root-mean-square localization errors of SAGE-USL are close to the corresponding CRBs and significantly lower than those of 3-D MUSIC. (C) 2014 Elsevier Inc. All rights reserved.

Invited paper Application of the least mean fourth (LMF) adaptive algorithm to signals associated with gaussian noise

This paper considers the applicability of the least mean fourth (LM F) power gradient adaptation criteria with 'advantage' for signals associated with gaussian noise, the associated noise power estimate not being known. The proposed method, as an adaptive spectral estimator, is found to provide superior performance than the least mean square (LMS) adaptation for the same (or even lower) speed of convergence for signals having sufficiently high signal-to-gaussian noise ratio. The results include comparison of the performance of the LMS-tapped delay line, LMF-tapped delay line, LMS-lattice and LMF-lattice algorithms, with the Burg's block data method as reference. The signals, like sinusoids with noise and stochastic signals like EEG, are considered in this study.

Generalized aerodynamic noise equation

An exact aerodynamic noise equation is formulated for Newtonian fluids. The cause−effect problem is discussed. Finally, the importance of external additions of mass, momentum, and energy is examined. Physics of Fluids is copyrighted by The American Institute of Physics.

Estimation of signals in colored non gaussian noise based on Gaussian Mixture models

Non-Gaussianity of signals/noise often results in significant performance degradation for systems, which are designed using the Gaussian assumption. So non-Gaussian signals/noise require a different modelling and processing approach. In this paper, we discuss a new Bayesian estimation technique for non-Gaussian signals corrupted by colored non Gaussian noise. The method is based on using zero mean finite Gaussian Mixture Models (GMMs) for signal and noise. The estimation is done using an adaptive non-causal nonlinear filtering technique. The method involves deriving an estimator in terms of the GMM parameters, which are in turn estimated using the EM algorithm. The proposed filter is of finite length and offers computational feasibility. The simulations show that the proposed method gives a significant improvement compared to the linear filter for a wide variety of noise conditions, including impulsive noise. We also claim that the estimation of signal using the correlation with past and future samples leads to reduced mean squared error as compared to signal estimation based on past samples only.

Patch-based and multiresolution optimum bilateral filters for denoising images corrupted by Gaussian noise

We propose optimal bilateral filtering techniques for Gaussian noise suppression in images. To achieve maximum denoising performance via optimal filter parameter selection, we adopt Stein's unbiased risk estimate (SURE)-an unbiased estimate of the mean-squared error (MSE). Unlike MSE, SURE is independent of the ground truth and can be used in practical scenarios where the ground truth is unavailable. In our recent work, we derived SURE expressions in the context of the bilateral filter and proposed SURE-optimal bilateral filter (SOBF). We selected the optimal parameters of SOBF using the SURE criterion. To further improve the denoising performance of SOBF, we propose variants of SOBF, namely, SURE-optimal multiresolution bilateral filter (SMBF), which involves optimal bilateral filtering in a wavelet framework, and SURE-optimal patch-based bilateral filter (SPBF), where the bilateral filter parameters are optimized on small image patches. Using SURE guarantees automated parameter selection. The multiresolution and localized denoising in SMBF and SPBF, respectively, yield superior denoising performance when compared with the globally optimal SOBF. Experimental validations and comparisons show that the proposed denoisers perform on par with some state-of-the-art denoising techniques. (C) 2015 SPIE and IS&T

Comparison Of If Estimation Methods For Noise Robustness

Non-stationary signal modeling is a well addressed problem in the literature. Many methods have been proposed to model non-stationary signals such as time varying linear prediction and AM-FM modeling, the later being more popular. Estimation techniques to determine the AM-FM components of narrow-band signal, such as Hilbert transform, DESA1, DESA2, auditory processing approach, ZC approach, etc., are prevalent but their robustness to noise is not clearly addressed in the literature. This is critical for most practical applications, such as in communications. We explore the robustness of different AM-FM estimators in the presence of white Gaussian noise. Also, we have proposed three new methods for IF estimation based on non-uniform samples of the signal and multi-resolution analysis. Experimental results show that ZC based methods give better results than the popular methods such as DESA in clean condition as well as noisy condition.

Polymer melt dynamics: Microscopic roots of fractional viscoelasticity

The rheological properties of polymer melts and other complex macromolecular fluids are often successfully modeled by phenomenological constitutive equations containing fractional differential operators. We suggest a molecular basis for such fractional equations in terms of the generalized Langevin equation (GLE) that underlies the renormalized Rouse model developed by Schweizer [J. Chem. Phys. 91, 5802 (1989)]. The GLE describes the dynamics of the segments of a tagged chain under the action of random forces originating in the fast fluctuations of the surrounding polymer matrix. By representing these random forces as fractional Gaussian noise, and transforming the GLE into an equivalent diffusion equation for the density of the tagged chain segments, we obtain an analytical expression for the dynamic shear relaxation modulus G(t), which we then show decays as a power law in time. This power-law relaxation is the root of fractional viscoelastic behavior.

The stretching of single poly-ubiquitin molecules: Static versus dynamic disorder in the non-exponential kinetics of chain unfolding

Static disorder has recently been implicated in the non-exponential kinetics of the unfolding of single molecules of poly-ubiquitin under a constant force Kuo, Garcia-Manyes, Li, Barel, Lu, Berne, Urbakh, Klafter, and Fernandez, Proc. Natl. Acad. Sci. U. S. A. 107, 11336 (2010)]. In the present paper, it is suggested that dynamic disorder may provide a plausible, alternative description of the experimental observations. This suggestion is made on the basis of a model in which the barrier to chain unfolding is assumed to be modulated by a control parameter r that evolves in a parabolic potential under the action of fractional Gaussian noise according to a generalized Langevin equation. The treatment of dynamic disorder within this model is pursued using Zwanzig's indirect approach to noise averaging Acc. Chem. Res. 23, 148 (1990)]. In conjunction with a self-consistent closure scheme developed by Wilemski and Fixman J. Chem. Phys. 58, 4009 (1973); ibid. 60, 866 (1974)], this approach eventually leads to an expression for the chain unfolding probability that can be made to fit the corresponding experimental data very closely. (C) 2011 American Institute of Physics.

Direction of arrival estimation in the presence of distributed noise sources: Cumulant based approach

In the past few years there have been attempts to develop subspace methods for DoA (direction of arrival) estimation using a fourth?order cumulant which is known to de?emphasize Gaussian background noise. To gauge the relative performance of the cumulant MUSIC (MUltiple SIgnal Classification) (c?MUSIC) and the standard MUSIC, based on the covariance function, an extensive numerical study has been carried out, where a narrow?band signal source has been considered and Gaussian noise sources, which produce a spatially correlated background noise, have been distributed. These simulations indicate that, even though the cumulant approach is capable of de?emphasizing the Gaussian noise, both bias and variance of the DoA estimates are higher than those for MUSIC. To achieve comparable results the cumulant approach requires much larger data, three to ten times that for MUSIC, depending upon the number of sources and how close they are. This is attributed to the fact that in the estimation of the cumulant, an average of a product of four random variables is needed to make an evaluation. Therefore, compared to those in the evaluation of the covariance function, there are more cross terms which do not go to zero unless the data length is very large. It is felt that these cross terms contribute to the large bias and variance observed in c?MUSIC. However, the ability to de?emphasize Gaussian noise, white or colored, is of great significance since the standard MUSIC fails when there is colored background noise. Through simulation it is shown that c?MUSIC does yield good results, but only at the cost of more data.

Capacity of Gaussian Channels With Energy Harvesting and Processing Cost

Energy harvesting sensor nodes are gaining popularity due to their ability to improve the network life time and are becoming a preferred choice supporting green communication. In this paper, we focus on communicating reliably over an additive white Gaussian noise channel using such an energy harvesting sensor node. An important part of this paper involves appropriate modeling of energy harvesting, as done via various practical architectures. Our main result is the characterization of the Shannon capacity of the communication system. The key technical challenge involves dealing with the dynamic (and stochastic) nature of the (quadratic) cost of the input to the channel. As a corollary, we find close connections between the capacity achieving energy management policies and the queueing theoretic throughput optimal policies.

l(1)-K-SVD: A robust dictionary learning algorithm with simultaneous update

We develop a new dictionary learning algorithm called the l(1)-K-svp, by minimizing the l(1) distortion on the data term. The proposed formulation corresponds to maximum a posteriori estimation assuming a Laplacian prior on the coefficient matrix and additive noise, and is, in general, robust to non-Gaussian noise. The l(1) distortion is minimized by employing the iteratively reweighted least-squares algorithm. The dictionary atoms and the corresponding sparse coefficients are simultaneously estimated in the dictionary update step. Experimental results show that l(1)-K-SVD results in noise-robustness, faster convergence, and higher atom recovery rate than the method of optimal directions, K-SVD, and the robust dictionary learning algorithm (RDL), in Gaussian as well as non-Gaussian noise. For a fixed value of sparsity, number of dictionary atoms, and data dimension, l(1)-K-SVD outperforms K-SVD and RDL on small training sets. We also consider the generalized l(p), 0 < p < 1, data metric to tackle heavy-tailed/impulsive noise. In an image denoising application, l(1)-K-SVD was found to result in higher peak signal-to-noise ratio (PSNR) over K-SVD for Laplacian noise. The structural similarity index increases by 0.1 for low input PSNR, which is significant and demonstrates the efficacy of the proposed method. (C) 2015 Elsevier B.V. All rights reserved.

A robust initialization scheme for faster convergence of the dichotomous search algorithm for single frequency estimation

The estimation of the frequency of a sinusoidal signal is a well researched problem. In this work we propose an initialization scheme to the popular dichotomous search of the periodogram peak algorithm(DSPA) that is used to estimate the frequency of a sinusoid in white gaussian noise. Our initialization is computationally low cost and gives the same performance as the DSPA, while reducing the number of iterations needed for the fine search stage. We show that our algorithm remains stable as we reduce the number of iterations in the fine search stage. We also compare the performance of our modification to a previous modification of the DSPA and show that we enhance the performance of the algorithm with our initialization technique.

Comparison of the Radar and Seeker Modes of Pursuer Guidance

This paper compares closed-loop performance of seeker-based and radar-based estimators for surface-to-air interception through 6-degree-of-freedom simulation using proportional navigation guidance.Ground radar measurements are evader range, azimuth and elevation angles contaminated by Gaussian noise. Onboard seeker measurements are pursuer-evader relative range, range rate also contaminated by Gaussian noise. The gimbal angles and line-of-sight rates in the gimbal frame,contaminated by time-correlated non-Gaussian noise with realistic numerical values are also available as measurements. In both the applications, extended Kalman filter with Gaussian noise assumption are used for state estimation. For a typical engagement, it is found that,based on Monte Carlo studies, seeker estimator outperforms radar estimator in terms of autopilot demand and reduces the miss distance.Thus, a seeker estimator with white Gaussian assumption is found to be adequate to handle the measurements even in the presence of non-Gaussian correlated noise. This paper uses realistic numerical values of all noise parameters.