Publications

The trusted inertial terrain-aided navigation (TITAN) algorithm leverages an airborne vertical synthetic aperture radar to measure the range to the closest ground points along several prescribed iso-Doppler contours. These TITAN minimum-range, prescribed-Doppler measurements are the result of a constrained nonlinear optimization problem whose optimization function and constraints both depend on the radar position and velocity. Owing to the complexity of this measurement definition, analysis of the TITAN algorithm is lacking in prior work. This publication offers such an analysis, making the following three contributions: (1) an analytical solution to the TITAN constrained optimization measurement problem, (2) a derivation of the TITAN measurement function Jacobian, and (3) a derivation of the Cramér–Rao lower bound on the estimated position and velocity error covariance. These three contributions are verified via Monte Carlo simulations over synthetic terrain, which further reveal two remarkable properties of the TITAN algorithm: (1) the along-track positioning errors tend to be smaller than the cross-track positioning errors, and (2) the cross-track positioning errors are independent of the terrain roughness.

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The use of the Global Positioning System (GPS) is a fundamental requirement for most navigation systems today, and this heavy reliance means that denial of GPS service (or extended threats) can pose a significant risk to modern navigation. There is an urgent need for enabling, high-accuracy navigation technologies that can operate without the need for GPS. Ideally, these solutions must be able to initialize in a completely GPS-free environment and continue to navigate even through challenging scenarios. The increasing risk posed to GPS means that trust in this platform is waning—and solutions are required. A future navigator should leverage GPS whenever possible and be capable of identifying and responding to risks while maintaining mission accuracy needs. In the absence of GPS, fully alternative navigation (altnav) technologies are required. This report describes an introductory view of altnav for GPS-impaired and contested environments. Various technologies are collected, presented, and evaluated as potential solutions. A wide snapshot of currently available technologies with a first-order summary of their potential is presented. While this report attempts to be as broad and complete as possible, this is a quickly evolving field.