Time-series interval prediction under uncertainty using modified double multiplicative neuron network

Abstract

This paper presents a hybrid intelligent approach for constructing prediction intervals (PIs) of terrain profiles over time under uncertainty. It utilizes the double multiplicative neuron (DMN) model and the modified particle swarm optimization (MPSO) algorithm to calculate the upper and lower bounds of unknown elevations ahead on terrain profiles based on the vehicles’ track. MPSO withholds particles generating the positive PIs in the training epochs, in order to prevent the occurrence of unreasonable upside-down PIs that are brought by conventional methods. MPSO adjusts the parameters of the DMN model iteratively by minimizing the value of the proposed cost function. The fitness function aims to enhance DMN’s capability of forecasting terrain trends by integrating a trend indicator with PIs coverage probability and interval widths. This study utilizes the terrain profiles of 3 arc-seconds resolution to verify the effectiveness of the proposed MPSO-DMNT approach for one-step and multi-step PIs estimation. Experimental results demonstrate that the proposed approach (1) overcomes the limitations of the conventional PIs indicators; (2) improves the prediction accuracy for terrain trends by 18.8% in the training data and 15.4% in the testing data, and reduces the computational burden by 31.6% in the training data and 8% in the testing data over the lower upper bound estimation (LUBE) method; (3) achieves comparative coverage probability and interval widths to LUBE using a low-complexity single-layered network. The proposed hybrid approach can be used as an auxiliary decision-making tool for terrain avoidance and terrain following in flight.