Research on the Threshold Determination Method of the Duffing Chaotic System Based on Improved Permutation Entropy and Poincaré Mapping.

The transition from a chaotic to a periodic state in the Duffing chaotic oscillator detection system is crucial in detecting weak signals. However, accurately determining the critical threshold for this transition remains a challenging problem. Traditional methods such as Melnikov theory, the Poincaré section quantitative discrimination method, and experimental analyses based on phase diagram segmentation have limitations in accuracy and efficiency. In addition, they require large computational data and complex algorithms while having slow convergence. Improved permutation entropy incorporates signal amplitude information on the basis of permutation entropy and has better noise resistance. According to the characteristics of improved permutation entropy, a threshold determination method for the Duffing chaotic oscillator detection system based on improved permutation entropy (IPE) and Poincaré mapping (PM) is proposed. This new metric is called Poincaré mapping improved permutation entropy (PMIPE). The simulation results and the verification results of real underwater acoustic signals indicate that our proposed method outperforms traditional methods in terms of accuracy, simplicity, and stability.

Ensemble Improved Permutation Entropy: A New Approach for Time Series Analysis.

Entropy quantification approaches have gained considerable attention in engineering applications. However, certain limitations persist, including the strong dependence on parameter selection, limited discriminating power, and low robustness to noise. To alleviate these issues, this paper introduces two novel algorithms for time series analysis: the ensemble improved permutation entropy (EIPE) and multiscale EIPE (MEIPE). Our approaches employ a new symbolization process that considers both permutation relations and amplitude information. Additionally, the ensemble technique is utilized to reduce the dependence on parameter selection. We performed a comprehensive evaluation of the proposed methods using various synthetic and experimental signals. The results illustrate that EIPE is capable of distinguishing white, pink, and brown noise with a smaller number of samples compared to traditional entropy algorithms. Furthermore, EIPE displays the potential to discriminate between regular and non-regular dynamics. Notably, when compared to permutation entropy, weighted permutation entropy, and dispersion entropy, EIPE exhibits superior robustness against noise. In practical applications, such as RR interval data classification, bearing fault diagnosis, marine vessel identification, and electroencephalographic (EEG) signal classification, the proposed methods demonstrate better discriminating power compared to conventional entropy measures. These promising findings validate the effectiveness and potential of the algorithms proposed in this paper.

Improved multivariate multiscale sample entropy and its application in multi-channel data.

Entropy, as a nonlinear feature in information science, has drawn much attention for time series analysis. Entropy features have been used to measure the complexity behavior of time series. However, traditional entropy methods mainly focus on one-dimensional time series originating from single-channel transducers and are incapable of handling the multidimensional time series from multi-channel transducers. Previously, the multivariate multiscale sample entropy (MMSE) algorithm was introduced for multi-channel data analysis. Although MMSE generalizes multiscale sample entropy and provides a new method for multidimensional data analysis, it lacks necessary theoretical support and has shortcomings, such as missing cross-channel correlation information and having biased estimation results. This paper proposes an improved multivariate multiscale sample entropy (IMMSE) algorithm to overcome these shortcomings. This paper highlights the existing shortcomings in MMSE under the generalized algorithm. The rationality of IMMSE is theoretically proven using probability theory. Simulations and real-world data analysis have shown that IMMSE is capable of effectively extracting cross-channel correlation information and demonstrating robustness in practical applications. Moreover, it provides theoretical support for generalizing single-channel entropy methods to multi-channel situations.

Sensitivity of Sniffer Dogs for a Diagnosis of Parkinson's Disease: A Diagnostic Accuracy Study.

BACKGROUND: The diagnostic criteria for Parkinson's disease (PD) remain complex, which is especially problematic for nonmovement disorder experts. A test is required to establish a diagnosis of PD with improved accuracy and reproducibility. OBJECTIVE: The study aimed to investigate the sensitivity and specificity of tests using sniffer dogs to diagnose PD. METHODS: A prospective, diagnostic case-control study was conducted in four tertiary medical centers in China to evaluate the accuracy of sniffer dogs to distinguish between 109 clinically established medicated patients with PD, 654 subjects without PD, 37 drug-naïve patients with PD, and 185 non-PD controls. The primary outcomes were sensitivity and specificity of sniffer dog's identification. RESULTS: In the study with patients who were medicated, when two or all three sniffer dogs yielded positive detection results in a sample tested, the index test sensitivity, specificity, and positive and negative likelihood ratios were 91% (95% CI: 84%-96%), 95% (95% CI: 93%-97%), and 19.16 (95% CI: 13.52-27.16) and 0.10 (95% CI: 0.05-0.17), respectively. The corresponding sensitivity, specificity, and positive and negative likelihood ratios in patients who were drug-naïve were 89% (95% CI: 75%-96%), 86% (95% CI: 81%-91%), and 6.6 (95% CI: 4.51-9.66) and 0.13 (95% CI: 0.05-0.32), respectively. CONCLUSIONS: Tests using sniffer dogs may be a useful, noninvasive, fast, and cost-effective method to identify patients with PD in community screening and health prevention checkups as well as in neurological practice. © 2022 International Parkinson and Movement Disorder Society.

State Estimation of an Underwater Markov Chain Maneuvering Target Using Intelligent Computing.

In this study, an application of deep learning-based neural computing is proposed for efficient real-time state estimation of the Markov chain underwater maneuvering object. The designed intelligent strategy is exploiting the strength of nonlinear autoregressive with an exogenous input (NARX) network model, which has the capability for estimating the dynamics of the systems that follow the discrete-time Markov chain. Nonlinear Bayesian filtering techniques are often applied for underwater maneuvering state estimation applications by following state-space methodology. The robustness and precision of NARX neural network are efficiently investigated for accurate state prediction of the passive Markov chain highly maneuvering underwater target. A continuous coordinated turning trajectory of an underwater maneuvering object is modeled for analyzing the performance of the neural computing paradigm. State estimation modeling is developed in the context of bearings only tracking technology in which the efficiency of the NARX neural network is investigated for ideal and complex ocean environments. Real-time position and velocity of maneuvering object are computed for five different cases by varying standard deviations of white Gaussian measured noise. Sufficient Monte Carlo simulation results validate the competence of NARX neural computing over conventional generalized pseudo-Bayesian filtering algorithms like an interacting multiple model extended Kalman filter and an interacting multiple model unscented Kalman filter.

Design of Nonlinear Autoregressive Exogenous Model Based Intelligence Computing for Efficient State Estimation of Underwater Passive Target.

In this study, an intelligent computing paradigm built on a nonlinear autoregressive exogenous (NARX) feedback neural network model with the strength of deep learning is presented for accurate state estimation of an underwater passive target. In underwater scenarios, real-time motion parameters of passive objects are usually extracted with nonlinear filtering techniques. In filtering algorithms, nonlinear passive measurements are associated with linear kinetics of the target, governing by state space methodology. To improve tracking accuracy, effective feature estimation and minimizing position error of dynamic passive objects, the strength of NARX based supervised learning is exploited. Dynamic artificial neural networks, which contain tapped delay lines, are suitable for predicting the future state of the underwater passive object. Neural networks-based intelligence computing is effectively applied for estimating the real-time actual state of a passive moving object, which follows a semi-curved path. Performance analysis of NARX based neural networks is evaluated for six different scenarios of standard deviation of white Gaussian measurement noise by following bearings only tracking phenomena. Root mean square error between estimated and real position of the passive target in rectangular coordinates is computed for evaluating the worth of the proposed NARX feedback neural network scheme. The Monte Carlo simulations are conducted and the results certify the capability of the intelligence computing over conventional nonlinear filtering algorithms such as spherical radial cubature Kalman filter and unscented Kalman filter for given state estimation model.

Underwater 3D Doppler-Angle Target Tracking with Signal Time Delay.

The traditional target tracking is a process of estimating the state of a moving target using measurement information obtained by sensors. However, underwater passive acoustic target tracking will confront further challenges, among which the system incomplete observability and time delay caused by the signal propagation create a great impact on tracking performance. Passive acoustic sensors cannot accurately obtain the target range information. The introduction of Doppler frequency measurement can improve the system observability performance; signal time delay cannot be ignored in underwater environments. It varies with time, which has a continuous negative impact on the tracking accuracy. In this paper, the Gauss-Helmert model is introduced to solve this problem by expanding the unknown signal emission time as an unknown variable to the state. This model allows the existence of the previous state and current state at the same time, while handling the implicit equations. To improve the algorithm accuracy, this paper further takes advantage of the estimated state and covariance for the second stage iteration and propose the Gauss-Helmert iterated Unscented Kalman filter under a three-dimensional environment. The simulation shows that the proposed method in this paper shows superior estimation accuracy and more stable performance compared with other filtering algorithms in underwater environments.

A New Feature Extraction Method for Ship-Radiated Noise Based on Improved CEEMDAN, Normalized Mutual Information and Multiscale Improved Permutation Entropy.

Extracting useful features from ship-radiated noise can improve the performance of passive sonar. The entropy feature is an important supplement to existing technologies for ship classification. However, the existing entropy feature extraction methods for ship-radiated noise are less reliable under noisy conditions because they lack noise reduction procedures or are single-scale based. In order to simultaneously solve these problems, a new feature extraction method is proposed based on improved complementary ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), normalized mutual information (norMI), and multiscale improved permutation entropy (MIPE). Firstly, the ICEEMDAN is utilized to obtain a group of intrinsic mode functions (IMFs) from ship-radiated noise. The noise reduction process is then conducted by identifying and eliminating the noise IMFs. Next, the norMI and MIPE of the signal-dominant IMFs are calculated, respectively; and the norMI is used to weigh the corresponding MIPE result. The multi-scale entropy feature is finally defined as the sum of the weighted MIPE results. Experimental results show that the recognition rate of the proposed method achieves 90.67% and 83%, respectively, under noise free and 5 dB conditions, which is much higher than existing entropy feature extraction algorithms. Hence, the proposed method is more reliable and suitable for feature extraction of ship-radiated noise in practice.

A Feature Extraction Method of Ship-Radiated Noise Based on Fluctuation-Based Dispersion Entropy and Intrinsic Time-Scale Decomposition.

To improve the feature extraction of ship-radiated noise in a complex ocean environment, fluctuation-based dispersion entropy is used to extract the features of ten types of ship-radiated noise. Since fluctuation-based dispersion entropy only analyzes the ship-radiated noise signal in single scale and it cannot distinguish different types of ship-radiated noise effectively, a new method of ship-radiated noise feature extraction is proposed based on fluctuation-based dispersion entropy (FDispEn) and intrinsic time-scale decomposition (ITD). Firstly, ten types of ship-radiated noise signals are decomposed into a series of proper rotation components (PRCs) by ITD, and the FDispEn of each PRC is calculated. Then, the correlation between each PRC and the original signal are calculated, and the FDispEn of each PRC is analyzed to select the Max-relative PRC fluctuation-based dispersion entropy as the feature parameter. Finally, by comparing the Max-relative PRC fluctuation-based dispersion entropy of a certain number of the above ten types of ship-radiated noise signals with FDispEn, it is discovered that the Max-relative PRC fluctuation-based dispersion entropy is at the same level for similar ship-radiated noise, but is distinct for different types of ship-radiated noise. The Max-relative PRC fluctuation-based dispersion entropy as the feature vector is sent into the support vector machine (SVM) classifier to classify and recognize ten types of ship-radiated noise. The experimental results demonstrate that the recognition rate of the proposed method reaches 95.8763%. Consequently, the proposed method can effectively achieve the classification of ship-radiated noise.

A Comparative Study of Multiscale Sample Entropy and Hierarchical Entropy and Its Application in Feature Extraction for Ship-Radiated Noise.

The presence of marine ambient noise makes it difficult to extract effective features from ship-radiated noise. Traditional feature extraction methods based on the Fourier transform or wavelets are limited in such a complex ocean environment. Recently, entropy-based methods have been proven to have many advantages compared with traditional methods. In this paper, we propose a novel feature extraction method for ship-radiated noise based on hierarchical entropy (HE). Compared with the traditional entropy, namely multiscale sample entropy (MSE), which only considers information carried in the lower frequency components, HE takes into account both lower and higher frequency components of signals. We illustrate the different properties of HE and MSE by testing them on simulation signals. The results show that HE has better performance than MSE, especially when the difference in signals is mainly focused on higher frequency components. Furthermore, experiments on real-world data of five types of ship-radiated noise are conducted. A probabilistic neural network is employed to evaluate the performance of the obtained features. Results show that HE has a higher classification accuracy for the five types of ship-radiated noise compared with MSE. This indicates that the HE-based feature extraction method could be used to identify ships in the field of underwater acoustic signal processing.

Hierarchical Cosine Similarity Entropy for Feature Extraction of Ship-Radiated Noise.

The classification performance of passive sonar can be improved by extracting the features of ship-radiated noise. Traditional feature extraction methods neglect the nonlinear features in ship-radiated noise, such as entropy. The multiscale sample entropy (MSE) algorithm has been widely used for quantifying the entropy of a signal, but there are still some limitations. To remedy this, the hierarchical cosine similarity entropy (HCSE) is proposed in this paper. Firstly, the hierarchical decomposition is utilized to decompose a time series into some subsequences. Then, the sample entropy (SE) is modified by utilizing Shannon entropy rather than conditional entropy and employing angular distance instead of Chebyshev distance. Finally, the complexity of each subsequence is quantified by the modified SE. Simulation results show that the HCSE method overcomes some limitations in MSE. For example, undefined entropy is not likely to occur in HCSE, and it is more suitable for short time series. Compared with MSE, the experimental results illustrate that the classification accuracy of real ship-radiated noise is significantly improved from 75% to 95.63% by using HCSE. Consequently, the proposed HCSE can be applied in practical applications.

A New Underwater Acoustic Signal Denoising Technique Based on CEEMDAN, Mutual Information, Permutation Entropy, and Wavelet Threshold Denoising.

Owing to the complexity of the ocean background noise, underwater acoustic signal denoising is one of the hotspot problems in the field of underwater acoustic signal processing. In this paper, we propose a new technique for underwater acoustic signal denoising based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), mutual information (MI), permutation entropy (PE), and wavelet threshold denoising. CEEMDAN is an improved algorithm of empirical mode decomposition (EMD) and ensemble EMD (EEMD). First, CEEMDAN is employed to decompose noisy signals into many intrinsic mode functions (IMFs). IMFs can be divided into three parts: noise IMFs, noise-dominant IMFs, and real IMFs. Then, the noise IMFs can be identified on the basis of MIs of adjacent IMFs; the other two parts of IMFs can be distinguished based on the values of PE. Finally, noise IMFs were removed, and wavelet threshold denoising is applied to noise-dominant IMFs; we can obtain the final denoised signal by combining real IMFs and denoised noise-dominant IMFs. Simulation experiments were conducted by using simulated data, chaotic signals, and real underwater acoustic signals; the proposed denoising technique performs better than other existing denoising techniques, which is beneficial to the feature extraction of underwater acoustic signal.

Research on Ship-Radiated Noise Denoising Using Secondary Variational Mode Decomposition and Correlation Coefficient.

As the sound signal of ships obtained by sensors contains other many significant characteristics of ships and called ship-radiated noise (SN), research into a denoising algorithm and its application has obtained great significance. Using the advantage of variational mode decomposition (VMD) combined with the correlation coefficient for denoising, a hybrid secondary denoising algorithm is proposed using secondary VMD combined with a correlation coefficient (CC). First, different kinds of simulation signals are decomposed into several bandwidth-limited intrinsic mode functions (IMFs) using VMD, where the decomposition number by VMD is equal to the number by empirical mode decomposition (EMD); then, the CCs between the IMFs and the simulation signal are calculated respectively. The noise IMFs are identified by the CC threshold and the rest of the IMFs are reconstructed in order to realize the first denoising process. Finally, secondary denoising of the simulation signal can be accomplished by repeating the above steps of decomposition, screening and reconstruction. The final denoising result is determined according to the CC threshold. The denoising effect is compared under the different signal-to-noise ratio and the time of decomposition by VMD. Experimental results show the validity of the proposed denoising algorithm using secondary VMD (2VMD) combined with CC compared to EMD denoising, ensemble EMD (EEMD) denoising, VMD denoising and cubic VMD (3VMD) denoising, as well as two denoising algorithms presented recently. The proposed denoising algorithm is applied to feature extraction and classification for SN signals, which can effectively improve the recognition rate of different kinds of ships.

A Novel Probabilistic Data Association for Target Tracking in a Cluttered Environment.

The problem of data association for target tracking in a cluttered environment is discussed. In order to improve the real-time processing and accuracy of target tracking, based on a probabilistic data association algorithm, a novel data association algorithm using distance weighting was proposed, which can enhance the association probability of measurement originated from target, and then using a Kalman filter to estimate the target state more accurately. Thus, the tracking performance of the proposed algorithm when tracking non-maneuvering targets in a densely cluttered environment has improved, and also does better when two targets are parallel to each other, or at a small-angle crossing in a densely cluttered environment. As for maneuvering target issues, usually with an interactive multi-model framework, combined with the improved probabilistic data association method, we propose an improved algorithm using a combined interactive multiple model probabilistic data association algorithm to track a maneuvering target in a densely cluttered environment. Through Monte Carlo simulation, the results show that the proposed algorithm can be more effective and reliable for different scenarios of target tracking in a densely cluttered environment.

Parameter Estimation of a Ground Moving Target Using Image Sharpness Optimization.

Motion parameter estimation of a ground moving target is an important issue in synthetic aperture radar ground moving target indication (SAR-GMTI) which has significant applications for civilian and military. The SAR image of a moving target may be displaced and defocused due to the radial and along-track velocity components, respectively. The sharpness cost function presents a measure of the degree of focus of the image. In this work, a new ground moving target parameter estimation algorithm based on the sharpness optimization criterion is proposed. The relationships between the quadratic phase errors and the target's velocity components are derived. Using two-dimensional searching of the sharpness cost function, we can obtain the velocity components of the target and the focused target image simultaneously. The proposed moving target parameter estimation method and image sharpness metrics are analyzed in detail. Finally, numerical results illustrate the effective and superior velocity estimation performance of the proposed method when compared to existing algorithms.

PMHT Approach for Multi-Target Multi-Sensor Sonar Tracking in Clutter.

Multi-sensor sonar tracking has many advantages, such as the potential to reduce the overall measurement uncertainty and the possibility to hide the receiver. However, the use of multi-target multi-sensor sonar tracking is challenging because of the complexity of the underwater environment, especially the low target detection probability and extremely large number of false alarms caused by reverberation. In this work, to solve the problem of multi-target multi-sensor sonar tracking in the presence of clutter, a novel probabilistic multi-hypothesis tracker (PMHT) approach based on the extended Kalman filter (EKF) and unscented Kalman filter (UKF) is proposed. The PMHT can efficiently handle the unknown measurements-to-targets and measurements-to-transmitters data association ambiguity. The EKF and UKF are used to deal with the high degree of nonlinearity in the measurement model. The simulation results show that the proposed algorithm can improve the target tracking performance in a cluttered environment greatly, and its computational load is low.

On the dynamics of ocean ambient noise: Two decades later.

Two decades ago, it was shown that ambient noise exhibits low dimensional chaotic behavior. Recent new techniques in nonlinear science can effectively detect the underlying dynamics in noisy time series. In this paper, the presence of low dimensional deterministic dynamics in ambient noise is investigated using diverse nonlinear techniques, including correlation dimension, Lyapunov exponent, nonlinear prediction, and entropy based methods. The consistent interpretation of different methods demonstrates that ambient noise can be best modeled as nonlinear stochastic dynamics, thus rejecting the hypothesis of low dimensional chaotic behavior. The ambient noise data utilized in this study are of duration 60 s measured at South China Sea.