Automatic Detection of the Number of Raypaths in a Shallow-Water Waveguide

International audienceCorrect identification and tracking of stable raypaths are critical for shallow-water acoustic tomography. Separating raypaths using high-resolution methods has been presented to improve resolution ability based on the prior knowledge of the number of raypaths. It is clear that the precise knowledge of the number of raypaths largely determines the separation performance. Therefore, a noise-whitening exponential fitting test (NWEFT) using short-length samples is proposed in this paper to automatically detect the number of raypaths in a shallow-water waveguide. Two information-theoretic criteria are considered as comparative methods in terms of the capability of correct detection. Their performances are tested with simulation data and real data obtained from a small-scale experiment. The experimental results show that the NWEFT can provide satisfactory detection compared to the two classic information-theoretic criteria--the Akaike information criterion (AIC) and the minimum description length (MDL). MDL is asymptotically consistent while AIC overestimates even if analyzed asymptotically. Compared to these criteria, the proposed method is more suitable for short-length data

Determining the Number of Coherent/Correlated Sources Using FBSS-based Methods

Abstract Determining the number of sources from observed data, is a fundamental problem in array signal processing. In this paper, first we focus on two popular estimators based on information theoretic criteria, AIC and MDL. Then another algorith m based on eigenvalue grads, namely EGM is presented. The co mputer simu lation results prove the effective performance of the EGM for non-coherent signals but in the small differences between the incident angles of non-coherent sources, MDL and AIC have a much better detection performance than EGM . These methods can detect only non-coherent signals, and the performance of them will be sharply declined even signals are coherent and/or correlated. So, first forward/backward spatial s moothing (FBSS) method is used as a pre-processing step to solve the coherency/correlation, and then MDL, AIC and EGM algorithms are run to estimate the number of signals. Nu merical results show that FBSS-based EGM offers higher detection probability rather than FBSS-based MDL and AIC in the case of coherent sources as well as correlated ones. Also, the higher detection probability can be achieved for correlated case compared to coherent one

Gridless Evolutionary Approach for Line Spectral Estimation with Unknown Model Order

Gridless methods show great superiority in line spectral estimation. These methods need to solve an atomic $l_0$ norm (i.e., the continuous analog of $l_0$ norm) minimization problem to estimate frequencies and model order. Since this problem is NP-hard to compute, relaxations of atomic $l_0$ norm, such as nuclear norm and reweighted atomic norm, have been employed for promoting sparsity. However, the relaxations give rise to a resolution limit, subsequently leading to biased model order and convergence error. To overcome the above shortcomings of relaxation, we propose a novel idea of simultaneously estimating the frequencies and model order by means of the atomic $l_0$ norm. To accomplish this idea, we build a multiobjective optimization model. The measurment error and the atomic $l_0$ norm are taken as the two optimization objectives. The proposed model directly exploits the model order via the atomic $l_0$ norm, thus breaking the resolution limit. We further design a variable-length evolutionary algorithm to solve the proposed model, which includes two innovations. One is a variable-length coding and search strategy. It flexibly codes and interactively searches diverse solutions with different model orders. These solutions act as steppingstones that help fully exploring the variable and open-ended frequency search space and provide extensive potentials towards the optima. Another innovation is a model order pruning mechanism, which heuristically prunes less contributive frequencies within the solutions, thus significantly enhancing convergence and diversity. Simulation results confirm the superiority of our approach in both frequency estimation and model order selection.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl