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.

中文翻译：

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基于非线性自回归外生模型的智能计算水下被动目标的有效状态估计设计。

在这项研究中，提出了一种基于非线性自回归外生（NARX）反馈神经网络模型的智能计算范例，该模型具有深度学习的优势，可用于精确估计水下被动目标的状态。在水下情况下，通常使用非线性滤波技术来提取被动对象的实时运动参数。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，这取决于状态空间方法。为了提高跟踪精度，有效的特征估计以及最大程度地减少动态无源物体的位置误差，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无源物体的未来状态。基于神经网络的智能计算可有效地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。通过遵循仅轴承的跟踪现象，针对六种不同的白高斯测量噪声标准偏差场景评估了基于NARX的神经网络的性能分析。计算矩形目标中被动目标的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。进行了蒙特卡洛模拟，结果证明了针对给定状态估计模型的常规非线性滤波算法（例如球面径向容积卡尔曼滤波器和无味卡尔曼滤波器）的智能计算能力。