NASA’s 2021 STV Incubation Study Report lists vertical (horizontal,; geolocation) accuracy as an associated SATM product parameter for all; (most) identified Science and Application Knowledge Gaps. The presented; generalized Polynomial Chaos Expansion (gPCE) based method has wide; ranging applicability to improve positioning, geolocation uncertainty; estimates for all STV disciplines, but is presented for the bathymetric; lidar use case, due to added complexity introduced by wave structure,; roughness, and entry angle. Most LiDARs, though precise, are vulnerable; to position, pointing errors as deviations from the expected principal; axis lead to projection errors on target. While fidelity of; location/pointing solutions can be high, determination of uncertainty; remains relatively basic. Currently, the standard approach is the; calculation of the Total Propagated Uncertainty (TPU), which is often; plagued by simplifying approximations and ignored covariances.; Additionally, uncertainty sources are often exclusively modeled as; Gaussian, inaccurately capturing some variable distributions.; Prominently, wave behavior is better described by Gamma distributions; (which are supported under gPCE). This research addresses specific; knowledge gaps in bathy-LiDAR measurement uncertainty through a more; complete description of total aggregated uncertainties, from system; level to geolocation, by applying a gPCE uncertainty quantification; approach. gPCE intrinsically accounts for covariance between variables; to determine the uncertainty in a measurement, without manually; constructing a covariance matrix, through a surrogate model of system; response. Determining point-wise positioning uncertainty using gPCE is; less computationally expensive than Monte Carlo methods and more; tractable for most dimensionalities of interest (roughly from 3 to 20+).; The method also does not rely on simplifying assumptions used in typical; TPU methods. Additionally, a key attribute of this approach is that; global sensitivity analysis (GSA), after obtaining gPCE coefficients, is; trivial and nearly costless to compute. Furthermore, GSA of system; configurations/uncertainty is a powerful tool to design and develop; LiDAR systems with the measurement requirements integrated into the; design solution.
