Robust Land-Surface Parameterisation for Repeated Topographic Surveys in Dynamic Environments with Adaptive State-Space Models

The proliferation of unmanned aerial vehicles has enabled cost-effective topographic surveys to be collected at high frequencies. However, terrain analyses rarely take advantage of the information provided by repeated observations. As a result, the ability to characterize the topographic surface and surface changes resulting from dynamic surface processes is undermined by the accumulation and propagation of uncertainty. Accurate surface model parameterisation benefits all derived local characteristics, such as surface slope and curvature. To address this, several advances in adaptive Kalman filtering were evaluated with respect to surface model coefficient estimation error, and the sensitivity to initial noise statistics was tested. A simple surface with exactly known parameters was simulated for a set of common geomorphological change regimes and survey temporal distributions. The results confirmed that all Kalman filters reduced error relative to a least-squares estimator under static conditions. Only adaptive filters outperformed a least-squares estimator under dynamic conditions, where average error was often reduced by approximately 50%, and up to 80%. However, adaptive Kalman filters exhibited up to a 40% increase in maximum error relative to a least-squares estimator in response to sudden surface changes, returning to lower error within 15–25 epochs. The adaptive Kalman filters were sensitive to the overestimation of measurement noise greater than two orders of magnitude from the true noise, resulting in degraded performance. Adaptive Kalman filters consistently and substantially reduced spatio-temporal coefficient error, which includes an estimate of local vertical displacement. The results demonstrated that adaptive Kalman filters address challenges related to the sensitivity of conventional Kalman filter performance to sub-optimal parameterisation, and they are robust estimators for both terrain analysis and surface change analysis when multiple surveys are available. Therefore, adaptive Kalman filters are well-suited for analyzing the local properties of topographic surfaces in general.