Rafael Krummenauer

Application of natural computing algorithms to maximum likelihood estimation of direction of arrival

This work presents a study of the performance of populational meta-heuristics belonging to the field of natural computing when applied to the problem of direction of arrival (DOA) estimation, as well as an overview of the literature about the use of such techniques in this problem. These heuristics offer a promising alternative to the conventional approaches in DOA estimation, as they search for the global optima of the maximum likelihood (ML) function in a framework characterized by an elegant balance between global exploration and local improvement, which are interesting features in the context of multimodal optimization, to which the ML-DOA estimation problem belongs. Thus, we shall analyze whether these algorithms are capable of implementing the ML estimator, i.e., finding the global optima of the ML function. In this work, we selected three representative natural computing algorithms to perform DOA estimation: differential evolution, clonal selection algorithm, and the particle swarm. Simulation results involving different scenarios confirm that these methods can reach the performance of the ML estimator, regardless of the number of sources and/or their nature. Moreover, the number of points evaluated by such methods is quite inferior to that associated with a grid search, which gives support to their application.

Improving the threshold performance of maximum likelihood estimation of direction of arrival

We propose to improve the performance of some direction of arrival (DOA) estimators using array of sensors. We consider those maximum likelihood (ML) estimators that generate some DOA candidates and select one of them through an ML criterion. Our proposal modifies the candidate selection process substituting the traditional sample covariance matrix by a new one computed after filtering the received data with an optimum noise reduction filter. Simulation results indicate an improvement of the performance at low signal-to-noise ratios (SNR) and a considerable reduction of the threshold SNR. The computation of the new selection cost function implies in a small increase in the overall computational effort.

Improving the Efficiency of Natural Computing Algorithms in DOA Estimation Using a Noise Filtering Approach

We propose a novel strategy to generate initial candidate solutions for bio-inspired algorithms applied to the direction of arrival estimation problem. The idea, which aims to improve the efficiency of the estimator, consists in using the frequency response of a well-known optimum noise reduction filter as the probability density function of the set of candidate solutions. In accordance to this approach, we also employ a modified likelihood function to reduce the estimation error. Simulation results considering an immune-inspired algorithm confirm a significant improvement of its performance and efficiency, and the new estimator reaches the conditional Cramér–Rao lower bound.

Parameter estimation from non-hyperbolic reflection traveltimes for large aperture common midpoint gathers

As far as superficial seismic reflection events are concerned, the classical normal moveout (NMO) process, which leads to the construction of seismic zero-offset (or stacked) sections, encounters several difficulties due to the large data aperture. One of these difficulties is that the hyperbolic approximation of the reflection traveltime in common midpoint (CMP) gathers is no longer valid when offset largely exceeds the target depth. Recently, Fomel and Kazinnik proposed a novel, multi-parameter, non-hyperbolic formula for the traveltime of such reflection events. This formula, which will be referred to here as the FK traveltime after the authors, is exact for reflectors whose shape can be described by a hyperbola, and shows promising accuracy for long offsets and/or curved reflectors. It also depends on the same set of parameters as the common reflection surface (CRS) traveltime. In this paper, we propose strategies for estimating these CRS parameters based on the FK traveltime using large aperture data. However, in contrast to traditional CRS processing, and due to their widespread use, only common midpoint (CMP) gathers will be considered for the parameter searches. We will begin with a sensitivity analysis, showing the impact of each parameter on the traveltime. Based on this analysis, we will propose a two-step estimation strategy, that could lead to improved seismic images, especially for very shallow, high aperture events. We will then highlight, through synthetic examples and discussions, the strengths and limitations of this strategy.

Um estudo da aplicação de algoritmos bio-inspirados ao problema de estimação de direção de chegada

The classical solution to the problem of estimating the direction of arrival (DOA) of plane waves impinging on a sensor array is based on the application of the maximum likelihood method. This approach leads to the problem of optimizing a cost function which is non-linear, non-quadratic, multimodal and variant with respect to the signal-noise ratio (SNR). The methods proposed in the literature to solve this problem fail for a wide set of SNR values. This work presents the results obtained from a study on the application of natural computing algorithms to the DOA estimation problem. Computational simulations show that four of the analyzed algorithms find the global optimum for a broad range of SNR values with computational efforts lower than that associated with an exaustive search.

Pre-stack Data Recovery through Common Offset CRS Stack with Differential Evolution

The common-offset (CO) common-reflection-surface (CRS) is a generalization of the zero-offset (ZO) CRS, traditionally used to provide a simulated zero-offset (ZO) image of the subsurface in time. The 2D CO-CRS traveltime is parametrized by five attributes. This generalization can be applied in any CO section of the pre-stack data and is particularly interesting once it allows to perform the CRS method in pre-stack data, enabling the benefits of the SNR enhancement in other pre-stack processing flows. On the other hand, one of the greatest challenges for the CRS method is the trade-off between the accuracy of the estimation of the traveltime parameters and the corresponding computational complexity. In this paper, we propose the usage of the bio-inspired heuristic differential evolution (DE) to estimate all the 2D CO-CRS parameters simultaneously. This algorithm can significantly speed up the convergence velocity for the CRS parameters estimation and it has a small set of parameters to be configured. We apply the DE algorithm to estimate the 2D CO-CRS parameters in the synthetic Marmousi data set blurred by noise. The recovered prestack data presented a significant SNR enhancement.

Velocity spectrum analysis in seismic prospecting combining detection principles, beamspace techniques and coherent signal-subspace processing

We revisit the conventional velocity analysis in seismic data processing with the purpose of enhancing the temporal resolution and the sensitivity of the coherency measure in the velocity spectrum. To that end, we exploit the fact that seismic signals are coherent, wideband and tend to be sparse in the time domain. To compose an appropriate methodology, given these data features, we employ some well-established techniques of array signal processing: coherent signal-subspace approach, beamspace processing and detection theory. The proposed methodology was tested for a real 2D offshore data and has shown success for the outlined purposes.