Robust DOA Tracking of an Underwater Target in Non-Gaussian and Nonstationary Environmental Noise

This paper proposes a novel R-adaptive sigma point filter entitled variational Bayesian Gaussian sum cubature Kalman filter (VB-GSCKF) for joint estimation of harmonic amplitude, phase, and frequencies along with the noise parameters. Since Gaussian filters may not guarantee good estimates in real-time applications involving non-stationary and non-Gaussian noise, alternative techniques are required. The proposed algorithm contributes to this gap as it automatically tunes the noise covariance matrix using the variational Bayesian approach and its Gaussian sum framework effectively models the non-Gaussian noise. The proposed VB-GSCKF algorithm demonstrates its superiority over other competing adaptive Gaussian filters and new hybrid based estimation approach where the signal is first denoised using Deep Learning (DL) algorithms and then the estimation is done using GSCKF in the presence of non-Gaussian and non-stationary measurement noise. Finally, real harmonic data produced by a grid-connected inverter hardware configuration is used to demonstrate the effectiveness of the proposed VB-GSCKF.

On-line harmonic signal denoising from the measurement with non-stationary and non-Gaussian noise

The maximum correntropy Kalman filter (MCKF) is an effective algorithm that was proposed to solve the non-Gaussian filtering problem for linear systems. Compared with the original Kalman filter (KF), the MCKF is a sub-optimal filter with Gaussian correntropy objective function, which has been demonstrated to have excellent robustness to non-Gaussian noise. However, the performance of MCKF is affected by its kernel bandwidth parameter, and a constant kernel bandwidth may lead to severe accuracy degradation in non-stationary noises. In order to solve this problem, the mixture correntropy method is further explored in this work, and an improved maximum mixture correntropy KF (IMMCKF) is proposed. By derivation, the random variables that obey Beta-Bernoulli distribution are taken as intermediate parameters, and a new hierarchical Gaussian state-space model was established. Finally, the unknown mixing probability and state estimation vector at each moment are inferred via a variational Bayesian approach, which provides an effective solution to improve the applicability of MCKFs in non-stationary noises. Performance evaluations demonstrate that the proposed filter significantly improves the existing MCKFs in non-stationary noises.

Dirichlet process mixture (DPM) model, which is the state-of-the-art Bayesian nonparametric model, was introduced here to signal processing research field. In present Bayesian statistics it is used to model and inference random nongaussian distributions. We explored its ability to model and estimate nongaussian unknown stationary noise and our work will help dealing with problems in many fields of signal processing. Through some modifications, we also revealed its potential to model and estimate unknown nonstationary nongaussian noise. Sequential Monte Carlo based inference algorithm was developed to estimate time varying unknown nongaussian noise with DPM. Simulation results show the efficiency of our algorithm.

Multi-autonomous underwater vehicles (AUVs) cooperative localization has become a research hotspot in the marine navigation field. In this paper, a filtering algorithm for slave AUV with compass failure is proposed based on ‘two-master-one slave’ cooperative localization model. In this algorithm, the course angle is unknown, and non-Gaussian measurement noise caused by measurement outliers is considered. The cooperative localization model is reconstructed, and a filtering algorithm is derived whose performance will not be affected by the unknown course angle. Moreover, the maximum information potential (MIP) criterion is introduced into a recursive model to deal with the non-Gaussian measurement noise in a complicated underwater environment. Simultaneously, the kernel bandwidth is adaptively adjusted by the innovation matrix and the measurement error covariance matrix. The proposed algorithm can accurately estimate the variation of the unknown course angle without expanding the dimension of state under the condition of non-Gaussian measurement noise. Finally, the proposed algorithm is verified through field experiments. The results show that the proposed algorithm has higher accuracy and robustness than other existing algorithms.

This paper Analysis the VanDerPol-Duffing system movement perturb Ted by weak signal under Non-Gaussian noise environment. We educe out the threshold of chaotic movement of VanDerPol-Duffing non-linear system. It is found that the non-Gaussian color noise has little effect on the chaos character of this chaotic oscillator, well the values of parameters of the excitation weak sinusoidal signal appear much change of chaotic dynamic system. The tiny change to the amplitude and frequency of the excitation weak sinusoidal signal will induce the chaotic system behavior great differently, this character help us estimate parameters of weak sinusoidal signal. The simulation result shows that the Non-Gaussian noise has little effect on the non-linear system movement when it is on chaotic state, while much effect on for Non-Gaussian noise. The conclusions appear that the chaotic oscillator is immune to zero mean non-Gaussian color noise for weak sinusoidal signal frequency and amplitude parameter estimate.

This paper Analysis the VanDerPol-Duffing system movement perturb Ted by weak signal under Non-Gaussian noise environment. we educe out the threshold of chaotic movement of VanDerPol-Duffing non-linear system. It is found that the nonGaussian color noise has little effect on the chaos character of this chaotic oscillator, well the values of parameters of the excitation weak sinusoidal signal appear much change of chaotic dynamic system. The tiny change to the amplitude and frequency of the excitation weak sinusoidal signal will induce the chaotic system behavior great differently, this character help us estimate parameters of weak sinusoidal signal. The simulation result shows that the Non-Gaussian noise has little effect on the nonlinear system movement when it is on chaotic state; while much effect on for Non-Gaussian noise. The conclusions appear that the chaotic oscillator is immune to zero mean non-Gaussian color noise for weak sinusoidal signal frequency and amplitude parameter estimate.

Modulation classification (MC) is an important field in cognitive radios. Most MCs based on the cyclic spectral density (CSD) can only apply to the stationary noise environment, but fail to inhibit non-stationary noise which is common in practical use. In this paper, we propose a MC method for cognitive radios with robustness against non-stationary additive noise, which is based on the fourth-order cyclic polyspectrum (FOCP). The proposed method is robust to non-stationary noise and can identify the modulation scheme of primary user's signal in cognitive radios. Monte Carlo simulation results demonstrate that our method can achieve better classification accuracy than the existing CSD-based MC method in non-stationary additive noise case.

The most challenging in speech enhancement technique is tracking non-stationary noises for long speech segments and low Signal-to-Noise Ratio (SNR). Different speech enhancement techniques have been proposed but, those techniques were inaccurate in tracking highly non-stationary noises. As a result, Empirical Mode Decomposition and Hurst-based (EMDH) approach is proposed to enhance the signals corrupted by non-stationary acoustic noises. Hurst exponent statistics was adopted for identifying and selecting the set of Intrinsic Mode Functions (IMF) that are most affected by the noise components. Moreover, the speech signal was reconstructed by considering the least corrupted IMF. Though it increases SNR, the time and resource consumption were high. Also, it requires a significant improvement under nonstationary noise scenario. Hence, in this article, EMDH approach is enhanced by using Sliding Window (SW) technique. In this SWEMDH approach, the computation of EMD is performed based on the small and sliding window along with the time axis. The sliding window depends on the signal frequency band. The possible discontinuities in IMF between windows are prevented by the total number of modes and the number of sifting iterations that should be set a priori. For each module, the number of sifting iterations is determined by decomposition of many signal windows by standard algorithm and calculating the average number of sifting steps for each module. Based on this approach, the time complexity is reduced significantly with suitable quality of decomposition. Finally, the experimental results show the considerable improvements in speech enhancement under non-stationary noise environments.

Spectrum sensing is important for a cognitive radio (CR) system to protect primary users (PUs) from harmful interference. At present, most of the existing sensing schemes are proposed in Gaussian noise environments. Nevertheless, a CR system actually also suffers from non-Gaussian noise, such as man-made impulsive noise, ultrawideband interference and co-channel interference. In this article, to handle the degradation of detection performance in non-Gaussian impulsive noise environments, a robust spectrum sensing scheme named hyperbolic tangent-based energy detector (HT-ED) is proposed. The hyperbolic tangent function is applied to suppress the impulsive noise by the nonlinear behavior, but without restraining the normal noise by the linear behavior. This property enables the new method to achieve the good detection performance in both Gaussian and non-Gaussian noise environments. In addition, it is similar to an energy detector, the new detector does not need to know the characteristics of the PU's signal. The performance analysis of the proposed HT-ED scheme is also presented. The simulation results show the HT-ED is robust against impulsive noise, which is modeled as Laplace or α-stable noise. Moreover, the HT-ED provides a superior detection performance compared with the other existing relative methods in a wide range of non-Gaussian noise.

The problem of the non-Gaussian and non-stationary noise in the data of the International Gravitational Wave Event Collaboration (IGEC) is investigated for the two detectors Explorer and Nautilus. We report simple tests that show how part of the IGEC events belong to non-Gaussian and non-stationary noise.

Simple and reliable spectrum sensing schemes are important for cognitive radio (CR) to avoid interference to the primary users (PUs). At present, most of the existing sensing schemes are proposed in Gaussian noise. Nevertheless, in practice, CR suffers from non-Gaussian noise such as man-made impulsive noise, ultra-wideband interference and co-channel interference. In this article, to handle the detection performance degradation in non-Gaussian impulsive noise environments, a robust spectrum sensing scheme namely hyperbolic tangent based energy detector (HT-ED) is proposed. The proposed HT-ED is a semi-blind method which does not require any a priori knowledge about the primary user's signals. Furthermore, the HT-ED can provide a superior detection performance compared with the conventional energy detector (ED) in a wide range of non-Gaussian noises. The simulation results show that the proposed HT-ED is very robust against impulsive noises which are modeled as the Laplace or a-stable noises. Moreover the detection performance of HT-ED is much better than those of the traditional ED and FLOM-based methods.

A pre and post processing technique is proposed to enhance the speech signal of highly non-stationary noisy speech. The purpose of this research has been to build on current speech enhancement algorithms to produce an improved algorithm for enhancement of speech contaminated with non-stationary babble type noise. The pre processing involves two stages. In stage one, the variance of the noisy speech spectrum is reduced by utilizing the Discrete or Prolate Spheroidal Sequence (DPSS) multi-taper algorithm plus a Controlled Forward Moving Average (CFMA) technique. We introduced the CFMA algorithm to smooth and reduce variance of the estimated non-stationary noise spectrum. In the second stage the noisy speech power spectrum is de-noised by applying Stein's Unbiased Risk Estimator (SURE) wavelet thresholding technique. In the third layer, use is made of a noise estimation algorithm with rapid adaptation for a highly non-stationary noise environment. The noise estimate is updated in three frequency sub-bands, by averaging the noisy speech power spectrum using a frequency dependent smoothing factor, which is adjusted, based on a signal presence probability factor. In the fourth layer a spectral subtraction algorithm is used to enhance the speech signal, by subtracting each estimated noise from the original noisy speech. The new proposed post processing is then applied to the complete signal when the speech enhancement is processed using segmental speech enhancement. The enhanced signal is further improved by applying a soft wavelet thresholding technique to the un-segmented enhanced speech at the final processing stage. The results show improvements both quantitatively and qualitatively compared to the speech enhancement that does not apply the CFMA algorithm.

The squelch problem of ultra-short wave communication under non-stationary noise and low Signal-to-Noise Ratio (SNR) in a complex electromagnetic environment is still challenging. To alleviate the problem, we proposed a squelch algorithm for ultra-short wave communication based on a deep neural network and the traditional energy decision method. The proposed algorithm first predicts the speech existence probability using a three-layer Gated Recurrent Unit (GRU) with the speech banding spectrum as the feature. Then it gets the final squelch result by combining the strength of the signal energy and the speech existence probability. Multiple simulations and experiments are done to verify the robustness and effectiveness of the proposed algorithm. We simulate the algorithm in three situations: the typical Amplitude Modulation (AM) and Frequency Modulation (FM) in the ultra-short wave communication under different SNR environments, the non-stationary burst-like noise environments, and the real received signal of the ultra-short wave radio. The experimental results show that the proposed algorithm performs better than the traditional squelch methods in all the simulations and experiments. In particular, the false alarm rate of the proposed squelch algorithm for non-stationary burst-like noise is significantly lower than that of traditional squelch methods.

Optimum threshold detection of underwater acoustic signals in nongaussian noise fields is very concisely described, in terms of canonical detection algorithms and performance measures. These systems are parametric-adaptive, with adaptive beam-forming features which allow arbitrary location of the sensor elements in the general receiving array. Basically, detection requires first a nonlinear “matching” of the receiver to the (nongaussian) noise field, followed in the usual way by a space-time matched filter for the desired signal. The former is implemented in terms of the (first-order) pdf of the nongaussian noise samples, while the latter employs a beam-formed waveform or second-moment statistic of the desired signal. Several other statistics of the interference field are described, and the critical role of independent space-time sampling is briefly discussed. References to recent work providing analytical details, numerical results, and specific physical examples are provided.