Ali Wasiq, Khan Wasim Ullah, Raja Muhammad Asif Zahoor, He Yigang, Li Yaan
School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China.
Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan.
Entropy (Basel). 2021 Apr 29;23(5):550. doi: 10.3390/e23050550.
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.
在本研究中,提出了一种基于具有深度学习能力的非线性自回归外生(NARX)反馈神经网络模型构建的智能计算范式,用于水下被动目标的精确状态估计。在水下场景中,被动物体的实时运动参数通常采用非线性滤波技术提取。在滤波算法中,非线性被动测量与目标的线性动力学相关联,由状态空间方法控制。为了提高跟踪精度、有效进行特征估计并最小化动态被动物体的位置误差,利用了基于NARX的监督学习的优势。包含抽头延迟线的动态人工神经网络适用于预测水下被动物体的未来状态。基于神经网络的智能计算有效地应用于估计遵循半弯曲路径的被动移动物体的实时实际状态。通过跟踪仅方位跟踪现象,针对白高斯测量噪声标准差的六种不同场景评估了基于NARX的神经网络的性能分析。计算了被动目标在直角坐标系中估计位置与实际位置之间的均方根误差,以评估所提出的NARX反馈神经网络方案的价值。进行了蒙特卡罗模拟,结果证明了在给定状态估计模型下,智能计算相对于传统非线性滤波算法(如球径向容积卡尔曼滤波器和无迹卡尔曼滤波器)的能力。