This paper develops a hybrid approach combining the neural network and the nonlinear filtering to model and predict terrain profiles for both air and ground vehicles. To simplify the neural network structures and reduce the number of synaptic weights and biases, the multiplicative neuron model (MNM) is utilized to describe the relationship between the unknown elevation ahead and the last few height values on the terrain profile. This paper adopts the gradient descent algorithm (GDA) to train the MNM terrain model and stores the MNM parameters into a nonlinear state-space model. The state vector in the state-space model (i.e., parameters of MNM) evolve agilely once absorbing new observations and measurement of elevation values by the Bootstrap Particle Filter (BPF) algorithm. Data-driven predictions on terrain profiles can be achieved through the updated MNM model. This study utilizes two types of terrain profiles to verify the effectiveness of the proposed MNM–BPF approach. Experimental results on two public datasets indicate that the proposed approach not only overcomes the limitations of conventional terrain models that cannot dynamically tune model parameters according to the newly input information, but also provides a simple but effective single-layered network for modeling terrain profiles. The well-trained MNM–BPF model can achieve the lowest root mean square errors (RMSE) (i.e., 17.3211 on the NS profile, 19.0366 on the EW profile) and average error (AE) (i.e., 1.5852 on the NS profile, 0.14885 on the EW profile) in the low-resolution dataset. The lowest RMSE (i.e., 0.16549 on the left profile, 0.29926 on the right profile) and mean absolute error (MAE) (i.e., 0.13467 on the left profile, 0.23933 on the right profile) results are obtained in the high-resolution dataset. Overall, the developed model is superior to the state-of-the-art models in at least four of the six performance metrics and reduces RMSE by 40.8%, 17.2%, 13.1%, and 6.8% on average on the four testing terrain profiles, respectively. The developed approach can be used as a decision tool for the accurate prediction of terrain profiles with different resolutions.

本文开发了一种混合方法，将神经网络和非线性滤波相结合，以对飞机和地面车辆的地形进行建模和预测。为了简化神经网络结构并减少突触权重和偏倚的数量，可乘神经元模型（MNM）用于描述前方未知海拔与地形轮廓上最后几个高度值之间的关系。本文采用梯度下降算法（GDA）训练MNM地形模型，并将MNM参数存储到非线性状态空间模型中。一旦通过Bootstrap粒子滤波器（BPF）算法吸收了新的观测值和高程值测量值，状态空间模型中的状态向量（即MNM的参数）就会敏捷地演化。可以通过更新的MNM模型实现对地形剖面的数据驱动预测。这项研究利用两种类型的地形剖面来验证所提出的MNM–BPF方法的有效性。在两个公共数据集上的实验结果表明，该方法不仅克服了常规地形模型的局限性，即传统地形模型无法根据新输入的信息动态调整模型参数，而且为地形图建模提供了一个简单而有效的单层网络。训练有素的MNM–BPF模型可以实现最低的均方根误差（在两个公共数据集上的实验结果表明，该方法不仅克服了常规地形模型的局限性，即传统地形模型无法根据新输入的信息动态调整模型参数，而且为地形图建模提供了一个简单而有效的单层网络。训练有素的MNM–BPF模型可以实现最低的均方根误差（在两个公共数据集上的实验结果表明，该方法不仅克服了传统地形模型的局限性，即传统地形模型无法根据新输入的信息动态调整模型参数，而且为地形图建模提供了一个简单而有效的单层网络。训练有素的MNM–BPF模型可以实现最低的均方根误差（RMSE）（即NS轮廓上的17.3211，EW轮廓上的19.0366）和低分辨率数据集中的平均误差（AE）（即NS轮廓上的1.5852，EW轮廓上的0.14885）。在高分辨率数据集中获得最低的RMSE（即，左侧轮廓为0.16549，右侧轮廓为0.29926）和平均绝对误差（MAE）（即左侧轮廓为0.13467，右侧轮廓为0.23933）。总体而言，在六个性能指标中的至少四个方面，已开发的模型优于最新模型，并降低了RMSE在四个测试地形剖面上分别平均下降40.8％，17.2％，13.1％和6.8％。所开发的方法可以用作精确预测具有不同分辨率的地形剖面的决策工具。