Clarifying clairvoyance: Analysis of forecasting models for near-sinusoidal periodic motion as applied to AUVs in shallow bathymetry

Abstract This paper shows that Gaussian Process Regression (GPR) with a periodic kernel has better mean prediction accuracy and uncertainty bounds than time series or Fourier series when forecasting motion data of underwater vehicles subject to wave excitation. Many robotic systems, such as autonomous underwater vehicles (AUVs), are required to operate in environments with disturbances and relative motion that make task performance difficult. This motion often exhibits periodic, near-sinusoidal behaviour. By predicting this motion, control strategies can be developed to improve accuracy. Moreover, factoring in uncertainty can aid the robustness of these predictive control methods. Time series and Fourier series have been applied to several predictive control problems in a variety of fields. However, there are contradictory results in performance based on parameters, assessment criteria, and application. This paper seeks to clarify these discrepancies using AUV motion as a case study. GPR is also introduced as a third candidate for prediction based on previous applications to time series forecasting in other fields of science. In addition to assessing mean prediction accuracy, the ability of each model to adequately bound prediction error is also considered as a key performance indicator.