Though precise, most LiDARs are vulnerable to position and 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 limited. As a result, NASA’s 2021 Surface Topography and Vegetation Incubation Study Report lists vertical (horizontal, geolocation) accuracy as an associated parameter for all (most) identified Science and Application Knowledge Gaps, and identifies maturation of Uncertainty Quantification (UQ) methodologies on the STV Roadmap for this decade. The presented generalized Polynomial Chaos Expansion (gPCE) based method has wide ranging applicability to improve positioning, geolocation uncertainty estimates for all STV disciplines, and is extended from the bare earth to the bathymetric lidar use case, adding complexity introduced by entry angle, wave structure, and sub-surface roughness. This research addresses 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-UQ approach. Currently, the standard approach is the calculation of the Total Propagated Uncertainty, which is often plagued by simplifying approximations (e.g. strictly Gaussian uncertainty sources) and ignored covariances. gPCE intrinsically accounts for covariance between variables to determine uncertainty in a measurement, without manually constructing a covariance matrix, through a surrogate model of system response. Additionally, gPCE allows arbitrarily high order uncertainty estimates (limited only by the one-time computational cost of computing gPCE coefficients), accurate representation of non-Gaussian sources of error (e.g. wave height energy distributions), and direct integration of measurement requirements into the design of LiDAR systems, by trivializing the computation of global sensitivity analysis.

Topobathymetric scanning LiDAR deployed on unmanned aerial systems (UAS) is a powerful tool for high-resolution mapping of the dynamic interface between topography and bathymetry. However, standardized methods for empirical resolution validation have not been widely adopted across LiDAR applications. While theoretical models of idealized LiDAR sampling resolution can be used to describe topographical resolution, misrepresented or unknown behaviors in an instrument, platform, or environment can degrade expected performance or introduce georeferencing inaccuracies. Furthermore, bathymetric resolution is strongly dependent on water surface and column conditions. Thus, only empirical methods for evaluating resolution will provide reliable estimates for both topographic and bathymetric surveys. Presented is an extension of standard modulation transfer function (MTF) methods used by passive imaging systems applied to high-resolution scanning LiDAR. Compact retroreflectors characterized as point and line sources are employed to empirically assess effective LiDAR system resolution through MTF analysis in topographic and bathymetric scenes. These targets enable MTF analyses using range-height measurements without reliance on intensity data, promoting widespread applicability among LiDAR systems. Empirical MTFs calculated using these targets are compared against theory-derived counterparts as empirical measurements elucidate influences by elements that are unknown or difficult to model. Simulated point cloud data were incorporated into theoretical MTF descriptions to better represent empirically-derived topographic MTFs, revealing mirror pointing uncertainties in the across-track axis. Similarly, theoretical bathymetric MTFs augmented with simulated, subaqueous data enabled water surface slope estimation using empirical measurements of submerged retroreflector targets, where rough water surfaces strongly influenced beam steering and the corresponding point spread MTFs.

This study focuses on utilizing the increasing availability of satellite trajectory data from global navigation satellite system-enabled low-Earth orbiting satellites and their precision orbit determination (POD) solutions to expand and refine thermospheric model validation capabilities. The research introduces an updated interface for the GEODYN-II POD software, leveraging high-precision space geodetic POD to investigate satellite drag and assess density models. This work presents a case study to examine five models (NRLMSIS2.0, DTM2020, JB2008, TIEGCM, and CTIPe) using precise science orbit (PSO) solutions of the Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2). The PSO is used as tracking measurements to construct orbit fits, enabling an evaluation according to each model’s ability to redetermine the orbit. Relative in-track deviations, quantified by in-track residuals and root-mean-square errors (RMSe), are treated as proxies for model densities that differ from an unknown true density. The study investigates assumptions related to the treatment of the drag coefficient and leverages them to eliminate bias and effectively scale model density. Assessment results and interpretations are dictated by the timescale at which the scaling occurs. JB2008 requires the least scaling (~-23%) to achieve orbit fits closely matching the PSO within an in-track RMSe of 9 m when scaled over two weeks and 4 m when scaled daily. The remaining models require substantial scaling of the mean density offset (~30-75%) to construct orbit fits that meet the aforementioned RMSe criteria. All models exhibit slight over or under sensitivity to geomagnetic activity according to trends in their 24-hour scaling factors.

Upper thermosphere mass density over the declining phase of solar cycle 23 are investigated using a day-to-night ratio (DNR) of thermosphere properties as a metric to evaluate how much relative change occurs climatologically between day and night. CHAMP observations from 2002-2009, MSIS 2.0 output, and TIEGCM V2.0 simulations are analyzed to assess their relative response in DNR. The CHAMP observations demonstrate nightside densities decrease more significantly than dayside densities as solar flux decreases. This causes a steadily increasing CHAMP mass density DNR from two to four with decreasing solar flux. The MSIS 2.0 nightside densities decrease more significantly than the dayside, resulting in the same trend as CHAMP. TIEGCM V2.0 displays an opposing trend in density DNR with decreasing solar flux due to dayside densities decreasing more significantly than nightside densities. A sensitivity analysis of the two models reveals the TIEGCM V2.0 to have greater sensitivity in temperature to levels of solar flux, while MSIS 2.0 displayed a greater sensitivity in mean molecular weight. The pressure DNR from both models contributed the most to the density DNR value at 400 km. As solar flux decreases, the two models’ estimate of pressure DNR deviate appreciably and trend in opposite directions. The TIEGCM V2.0 dayside temperatures during middle-to-low solar flux are too cold relative to MSIS 2.0. Increasing the dayside temperature values by about 50 – 100 K and decreasing the nightside temperature slightly would bring the TIEGCM V2.0 into better agreement with MSIS 2.0 and CHAMP observations.

Satellite-atmosphere interactions cause large uncertainties in low-Earth orbit determination and prediction. Thus, knowledge of and the ability to predict the space environment, most notably thermospheric mass density, are essential for operating satellites in this domain. Recent progress has been made toward supplanting the existing empirical, operational methods with physics-based data-assimilative models by accounting for the complex relationship between external drivers such as solar irradiance, Joule, and particle heating, and their response in the upper atmosphere. Simultaneously, a new era of CubeSat constellations is set to provide data with which to calibrate our upper-atmosphere models at higher spatial resolution and temporal cadence. With this in mind, we provide an initial method for converting precision orbit determination (POD) solutions from global navigation satellite system (GNSS) enabled CubeSats into timeseries of thermospheric mass density. This information is then fused with a physics-based, data-assimilative technique to provide calibrated model densities.

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.