Kinetic Energy Estimation of IMU-Equipped Sediment Particles with Gaussian Process Regression and Conformal Prediction

Abstract

Direct particle-scale sediment measurements remain difficult in turbid, high-energy rivers where optical methods fail. We present an integration-free IMU workflow that maps short windows to projected speed and kinetic energy using physics-aware preprocessing, orientation-invariant Hankel embeddings, Gaussian process regression (GPR), and split conformal prediction. On event-disjoint hold-out tests, the selected GPR model (m = 10) achieves R² = 0.628, RMSE = 0.168ms⁻¹, and MAE = 0.096ms⁻¹. A four-model benchmark on identical event-grouped folds (GPR, LSTM, SVR-RBF, LSBoost) gives the lowest RMSE for LSBoost (0.158ms⁻¹); GPR is within 0.001ms⁻¹ of the strongest non-GPR comparator (LSBoost), and paired RMSE differences are non-significant (p = 0.812). Empirical conformal coverage is 87.6%/93.7%/97.9% for nominal 90%/95%/99% targets. River Calder deployments show peak kinetic energies up to 0.168 J. The framework provides uncertainty-aware kinematics and energetics for autonomous sediment-transport monitoring.