Data-driven time series prediction based on multiplicative neuron model artificial neuron network

Abstract

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.